# Publications

## Settings...

## Journal paper

### 2019

J. Milanezi Junior, J. P. C. L. Da Costa, F. Römer, R. K. Miranda, M. A. M. Marinho, and G. Del Galdo, M-estimator based Chinese Remainder Theorem with few remainders using a Kronecker product based mapping vector, in Elsevier Digital Signal Processing, Jan 2019, doi:10.1016/j.dsp.2019.01.009.

@ARTICLE{MDRMMD:19, author = {J. {Milanezi Junior} and J. P. C. L. {Da Costa} and F. Römer and R. K. Miranda and M. A. M. Marinho and G. {Del Galdo}}, title = {M-estimator based Chinese Remainder Theorem with few remainders using a Kronecker product based mapping vector}, journal = {Elsevier Digital Signal Processing}, month = Jan, year = 2019, doi = {10.1016/j.dsp.2019.01.009} }

Abstract – The Chinese Remainder Theorem (CRT) explains how to estimate an integer-valued number from the knowledge of the remainders obtained by dividing such unknown integer by co-prime integers. As an algebraic theorem, CRT is the basis for several techniques concerning data processing. For instance, considering a single-tone signal whose frequency value is above the sampling rate, the respective peak in the DFT informs the impinging frequency value modulo the sampling rate. CRT is nevertheless sensitive to errors in the remainders, and many efforts have been developed in order to improve its robustness. In this paper, we propose a technique to estimate real-valued numbers by means of CRT, employing for this goal a Kroenecker based M-Estimation (ME), specially suitable for CRT systems with low number of remainders. Since ME schemes are in general computationally expensive, we propose a mapping vector obtained via Kroenecker products which considerably reduces the computational complexity. Furthermore, our proposed technique enhances the probability of estimating an unknown number accurately even when the errors in the remainders surpass 1/4 of the greatest common divisor of all moduli. We also provide a version of the mapping vectors based on tensorial n-mode products, delivering in the end the same information of the original method. Our approach outperforms the state-of-the-art CRT methods not only in terms of percentage of successful estimations but also in terms of smaller average error.

F. Krieg, J. Kirchhof, S. Kodera, S. Lugin, A. Ihlow, T. Schwender, G. Del Galdo, F. Römer, and A. Osman, SAFT processing for manually acquired ultrasonic measurement data with 3D smartInspect, in Insight - The Journal of The British Institute of Non-Destructive Testing, vol. 61, issue 11, Nov 2019.

@ARTICLE{KKKLISDRO:19, author = {F. Krieg and J. Kirchhof and S. Kodera and S. Lugin and A. Ihlow and T. Schwender and G. {Del Galdo} and F. Römer and A. Osman}, title = {{SAFT} processing for manually acquired ultrasonic measurement data with {3D} {smartInspect}}, journal = {Insight - The Journal of The British Institute of Non-Destructive Testing}, month = Nov, year = 2019, volume = 61, issue = 11 }

Abstract – The architecture and implementation of a system for synthetic aperture focusing technique (SAFT) reconstruction on ultrasonic data acquired using a hand-held device is described. The reconstruction and the measurement process are performed simultaneously, with the goal of providing instantaneous highly focused visual feedback to the engineer. The implementation is based on the 3D smartInspect system that is currently being developed at Fraunhofer Institute for Nondestructive Testing IZFP. This system assists engineers by recording, displaying and protocolling manually acquired data. In this paper, it is shown that it is possible to enhance this system by adding simultaneous SAFT processing on top of the existing functionality. This improves the imaging quality of the system. Possible limitations on the imaging quality are investigated by real-world hardware set-ups using numerical studies.

### 2018

S. Semper, F. Römer, T. Hotz, and G. Del Galdo, Sparsity Order Estimation from a Single Compressed Observation Vector, in IEEE Transactions on Signal Processing, vol. 66, issue 15, pp. 3958 – 3971, Aug 2018, doi:10.1109/TSP.2018.2841867.

@ARTICLE{SRHD:18, author = {S. Semper and F. Römer and T. Hotz and G. {Del Galdo}}, title = {Sparsity Order Estimation from a Single Compressed Observation Vector}, journal = {IEEE Transactions on Signal Processing}, pages = {3958 -- 3971}, month = Aug, year = 2018, volume = 66, issue = 15, doi = {10.1109/TSP.2018.2841867} }

Abstract – In this work the problem of estimating the unknown degree of sparsity from compressive measurements without the need to carry out a sparse recovery step is investigated. While the sparsity order can be directly inferred from the effective rank of the observation matrix in the multiple snapshot case, this appears to be impossible in the more challenging single snapshot case. It is shown that specially designed measurement matrices allow to rearrange the measurement vector into a matrix such that its effective rank coincides with the effective sparsity order. In fact, it is proven that matrices which are composed of a Khatri-Rao product of smaller matrices generate measurements that allow to infer the sparsity order. Moreover, if some samples are used more than once, one of the matrices needs to be Vandermonde. These structural constraints reduce the degrees of freedom in choosing the measurement matrix which may incur in a degradation in the achievable coherence. Thus, this work also addresses suitable choices of the measurement matrices. In particular, Khatri-Rao and Vandermonde matrices are analyzed in terms of their coherence and a new design for Vandermonde matrices that achieves a low coherence is proposed.

### 2017

J. Steinwandt, F. Römer, M. Haardt, and G. Del Galdo, Performance Analysis of Multi-Dimensional ESPRIT-Type Algorithms for Arbitrary and Strictly Non-Circular Sources with Spatial Smoothing, in IEEE Transactions on Signal Processing, vol. 65, issue 9, pp. 2262 – 2276, May 2017, doi:10.1109/TSP.2017.2652388.

@ARTICLE{SRHD:17, author = {J. Steinwandt and F. Römer and M. Haardt and G. {Del Galdo}}, title = {Performance Analysis of {Multi-Dimensional} {ESPRIT-Type} Algorithms for Arbitrary and Strictly {Non-Circular} Sources with Spatial Smoothing}, journal = {IEEE Transactions on Signal Processing}, pages = {2262 -- 2276}, month = May, year = 2017, volume = 65, issue = 9, doi = {10.1109/TSP.2017.2652388} }

Abstract – Spatial smoothing is a widely used preprocessing scheme to improve the performance of high-resolution parameter estimation algorithms in case of coherent signals or if only a small number of snapshots is available. In this paper, we present a first-order performance analysis of the spatially smoothed versions of R-D Standard ESPRIT and R-D Unitary ESPRIT for sources with arbitrary signal constellations as well as R-D NC Standard ESPRIT and R-D NC Unitary ESPRIT for strictly second-order (SO) non-circular (NC) sources. The derived expressions are asymptotic in the effective signal-to-noise ratio (SNR), i.e., the approximations become exact for either high SNRs or a large sample size. Moreover, no assumptions on the noise statistics are required apart from a zero mean and finite SO moments. We show that both R-D NC ESPRIT-type algorithms with spatial smoothing perform asymptotically identical in the high effective SNR regime. Generally, the performance of spatial smoothing based algorithms depends on the number of subarrays, which is a design parameter that needs to be chosen beforehand. In order to gain more insights into the optimal choice of the number of subarrays, we simplify the derived analytical R-D mean square error (MSE) expressions for the special case of a single source. The obtained MSE expression explicitly depends on the number of subarrays in each dimension, which allows us to analytically find the optimal number of subarrays for spatial smoothing. Based on this result, we additionally derive the maximum asymptotic gain from spatial smoothing and compute the asymptotic efficiency for the single source case in closed-form. All the analytical results are verified by simulations.

R. M. Kehrle, J. P. C. L. Da Costa, F. Römer, L. R. A. X. Menezes, G. Del Galdo, and A. Almeida, Low Complexity Performance Assessment of a Sensor Array via Unscented Transformation, in Elsevier Digital Signal Processing, vol. 63, pp. 190 – 198, Apr 2017, doi:10.1016/j.dsp.2017.01.007.

@ARTICLE{KDRMDA:17, author = {R. M. Kehrle and J. P. C. L. {Da Costa} and F. Römer and L. R. A. X. Menezes and G. {Del Galdo} and A. Almeida}, title = {Low Complexity Performance Assessment of a Sensor Array via Unscented Transformation}, journal = {Elsevier Digital Signal Processing}, pages = {190 -- 198}, month = Apr, year = 2017, volume = 63, doi = {10.1016/j.dsp.2017.01.007} }

Abstract – Due to the advances on electronics, applications of antenna array signal processing are becoming more frequent. When employing antenna arrays for beamforming, the signal to interference and noise ratio (SINR) should be assessed. Many factors can affect the SINR such as the array element positioning error and the direction of arrival (DOA) estimation error. In these cases, the assessment is traditionally performed via the SINR average obtained using Monte Carlo (MC) simulations. However, this approach requires a great amount of realizations that demand a high computational effort and processing time due to its slow convergence. In this paper, we propose a low complexity performance assessment of the average SINR via unscented transformation. Compared to MC simulations, our proposed method requires only a few trials and has a negligible computational complexity, yet giving a comparable SINR when the DOA estimation is perturbed. When the antenna elements positioning is perturbed, a multivariate scenario arises. For multivariate scenario the proposed scheme has an exponential increase in complexity, therefore, still being advantageous for a small number of antennas.

M. Ibrahim, V. Ramireddy, A. Lavrenko, J. König, F. Römer, M. Landmann, M. Großmann, G. Del Galdo, and R. S. Thomä, Design and analysis of compressive antenna arrays for direction of arrival estimation, in Elsevier Signal Processing, vol. 138, pp. 35 – 47, Sep 2017, doi:10.1016/j.sigpro.2017.03.013.

@ARTICLE{IRLKRLGDT:17, author = {M. Ibrahim and V. Ramireddy and A. Lavrenko and J. König and F. Römer and M. Landmann and M. Großmann and G. {Del Galdo} and R. S. Thomä}, title = {Design and analysis of compressive antenna arrays for direction of arrival estimation}, journal = {Elsevier Signal Processing}, pages = {35 -- 47}, month = Sep, year = 2017, volume = 138, doi = {10.1016/j.sigpro.2017.03.013} }

Abstract – In this paper we investigate the design of compressive antenna arrays for narrow-band direction of arrival (DOA) estimation that aim to provide a larger aperture with a reduced hardware complexity and allowing reconfigurability, by a linear combination of the antenna outputs to a lower number of receiver channels. We present a basic receiver architecture of such a compressive array and introduce a generic system model that includes different options for the hardware implementation. We then discuss the design of the analog combining network that performs the receiver channel reduction, and propose two design approaches. The first approach is based on the spatial correlation function which is a low-complexity scheme that in certain cases admits a closed-form solution. The second approach is based on minimizing the Cramér-Rao Bound (CRB) with the constraint to limit the probability of false detection of paths to a pre-specified level. Our numerical simulations demonstrate the superiority of the proposed optimized compressive arrays compared to the sparse arrays of the same complexity and to compressive arrays with randomly chosen combining kernels.

A. Lavrenko, F. Römer, G. Del Galdo, and R. S. Thomä, On the SNR Variability in Noisy Compressed Sensing, in IEEE Signal Processing Letters, vol. 24, issue 8, Aug 2017, doi:10.1109/LSP.2017.2689243.

@ARTICLE{LRDT:17, author = {A. Lavrenko and F. Römer and G. {Del Galdo} and R. S. Thomä}, title = {On the {SNR} Variability in Noisy Compressed Sensing}, journal = {IEEE Signal Processing Letters}, month = Aug, year = 2017, volume = 24, issue = 8, doi = {10.1109/LSP.2017.2689243} }

Abstract – Compressed sensing (CS) is a sampling paradigm that allows to simultaneously measure and compress signals that are sparse or compressible in some domain. The choice of a sensing matrix that carries out the measurement has a defining impact on the system performance and it is often advocated to draw its elements randomly. It has been noted that in the presence of input (signal) noise, the application of the sensing matrix causes SNR degradation due to the noise folding effect. In fact, it might also result in the variations of the output SNR in compressive measurements over the support of the input signal, potentially resulting in unexpected non-uniform system performance. In this work, we study the impact of a distribution from which the elements of a sensing matrix are drawn on the spread of the output SNR. We derive analytic expressions for several common types of sensing matrices and show that the SNR spread grows with the decrease of the number of measurements. This makes its negative effect especially pronounced for high compression rates that are often of interest in CS.

J. Steinwandt, F. Römer, and M. Haardt, Generalized Least Squares for ESPRIT-type Direction of Arrival Estimation, in IEEE Signal Processing Letters, vol. 24, issue 11, pp. 1681 – 1685, Nov 2017, doi:10.1109/LSP.2017.2751303.

@ARTICLE{SRH:17, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {Generalized Least Squares for {ESPRIT-type} Direction of Arrival Estimation}, journal = {IEEE Signal Processing Letters}, pages = {1681 -- 1685}, month = Nov, year = 2017, volume = 24, issue = 11, doi = {10.1109/LSP.2017.2751303} }

Abstract – The key task in ESPRIT-based parameter estimation is finding the solution to the shift invariance equation (SIE), which is often an overdetermined, linear system of equations. Additional structure is imposed if the two selection matrices, applied to an estimate of the signal subspace, overlap such that the subspace estimation errors on both sides of the SIE are highly correlated. In this paper, we propose a novel SIE solution for Standard ESPRIT and Unitary ESPRIT based on generalized least squares (GLS), assuming a uniform linear array (ULA) and maximum subarray overlap. GLS directly incorporates the statistics of the subspace estimation error via its covariance matrix, which is found analytically by a first-order perturbation expansion. As the subspace error covariance matrix is not invertible, we introduce a regularization with a clever choice of the regularization parameter. The resulting GLS-based Standard ESPRIT and Unitary ESPRIT algorithms achieve a superior performance over existing ESPRIT-type methods and almost attain the Cramér-Rao bound (CRB).

### 2016

J. Steinwandt, F. Römer, M. Haardt, and G. Del Galdo, Deterministic Cramer-Rao Bound for Strictly Non-Circular Sources and Analytical Analysis of the Achievable Gains, in IEEE Transactions on Signal Processing, vol. 64, issue 17, pp. 4417 – 4431, Sep 2016, doi:10.1109/TSP.2016.2566603.

@ARTICLE{SRHD:16, author = {J. Steinwandt and F. Römer and M. Haardt and G. {Del Galdo}}, title = {Deterministic {Cramer-Rao} Bound for Strictly {Non-Circular} Sources and Analytical Analysis of the Achievable Gains}, journal = {IEEE Transactions on Signal Processing}, pages = {4417 -- 4431}, month = Sep, year = 2016, volume = 64, issue = 17, doi = {10.1109/TSP.2016.2566603} }

Abstract – Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as many signal sources compared to the traditional methods for arbitrary signals. In this paper, as a benchmark for these NC methods, we derive the closed-form deterministic RD NC Cramér-Rao bound (NC CRB) for the multidimensional parameter estimation of strictly non-circular (rectilinear) signal sources. Assuming a separable centro-symmetric R-D array, we show that in some special cases, the deterministic R-D NC CRB reduces to the existing deterministic R-D CRB for arbitrary signals. This suggests that no gain from strictly non-circular sources (NC gain) can be achieved under the deterministic data assumption in these cases. For more general scenarios, finding an analytical expression of the NC gain for an arbitrary number of sources is very challenging. Thus, in this paper, we simplify the derived NC CRB and the existing CRB for the special case of two closely-spaced strictly non-circular sources captured by a uniform linear array (ULA). Subsequently, we use these simplified CRB expressions to analytically compute the maximum achievable asymptotic NC gain for the considered two source case. The resulting expression only depends on the various physical parameters and we find the conditions that provide the largest NC gain for two sources. Our analysis is supported by extensive simulation results.

### 2014

Y. Cheng, S. Li, J. Zhang, F. Römer, B. Song, M. Haardt, Y. Zhou, and M. Dong, An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink, in IEEE Transactions on Vehicular Technology, vol. 68, issue 2, pp. 628 – 642, Feb 2014, doi:10.1109/TVT.2013.2280951.

@ARTICLE{CLZRSHZD:14, author = {Y. Cheng and S. Li and J. Zhang and F. Römer and B. Song and M. Haardt and Y. Zhou and M. Dong}, title = {An Efficient Transmission Strategy for the Multicarrier Multiuser {MIMO} Downlink}, journal = {IEEE Transactions on Vehicular Technology}, pages = {628 -- 642}, month = Feb, year = 2014, volume = 68, issue = 2, doi = {10.1109/TVT.2013.2280951} }

Abstract – A new transmission strategy that consists of a
spatial scheduling algorithm and two precoding algorithms
is developed for multi-carrier multi-user (MU) multipleinput
multiple-output (MIMO) systems. The scheduling
algorithm, called efficient multi-carrier ProSched (EMC-ProSched),
adopts a novel and effective scheduling metric
for each user and can efficiently search for a suitable
group of users to be served at the same time on the same
frequency. Two precoding techniques are then designed
to handle different antenna configurations. For the case
where the number of transmit antennas at the base station
(BS) is not smaller than the total number of receive antennas
at the user terminals (UTs), the linear precoding-based
geometric mean decomposition (LP-GMD) algorithm is
proposed. It suppresses the multi-user interference (MUI)
and enables an effective implementation of the same modulation
and coding scheme (MCS) on all spatial streams
of each user. Consequently a smaller signaling overhead
is required compared to the case where a different MCS
is applied on each spatial stream. When the total number
of receive antennas at the UTs exceeds the number of
transmit antennas at the BS, we propose the low complexity
coordinated beamforming (LoCCoBF) algorithm
to accomplish the goal of the MUI mitigation and to
achieve a high capacity. A system-level simulator with
a link-to-system interface is further developed under the
framework of the IEEE 802.11ac standard to evaluate the
performance of the proposed transmission strategy. The
simulation results indicate that a promising performance
can be achieved by employing the proposed transmission
strategy.

F. Römer, M. Haardt, and G. Del Galdo, Analytical performance assessment of multi-dimensional matrix- and tensor-based ESPRIT-type algorithms, in IEEE Transactions on Signal Processing, vol. 62, issue 10, pp. 2611 – 2625, May 2014, doi:10.1109/TSP.2014.2313530.

@ARTICLE{RHD:14, author = {F. Römer and M. Haardt and G. {Del Galdo}}, title = {Analytical performance assessment of multi-dimensional matrix- and tensor-based {ESPRIT-type} algorithms}, journal = {IEEE Transactions on Signal Processing}, pages = {2611 -- 2625}, month = May, year = 2014, volume = 62, issue = 10, doi = {10.1109/TSP.2014.2313530} }

Abstract – In this paper we present a generic framework for
the asymptotic performance analysis of subspace-based parameter
estimation schemes. It is based on earlier results on an
explicit first-order expansion of the estimation error in the signal
subspace obtained via an SVD of the noisy observation matrix.
We extend these results in a number of aspects. Firstly, we
demonstrate that an explicit first-order expansion of the Higher-Order SVD (HOSVD)-based subspace estimate can be derived.
Secondly, we show how to obtain explicit first-order expansions
of the estimation error of arbitrary ESPRIT-type algorithms and
provide the expressions for R-D Standard ESPRIT, R-D Unitary
ESPRIT, R-D Standard Tensor-ESPRIT, as well as R-D Unitary
Tensor-ESPRIT. Thirdly, we derive closed-form expressions for
the mean square error (MSE) and show that they only depend
on the second-order moments of the noise. Hence, to apply this
framework we only need the noise to be zero mean and possess
finite second order moments. Additional assumptions such as
Gaussianity or circular symmetry are not needed.

J. Steinwandt, F. Römer, M. Haardt, and G. Del Galdo, R-Dimensional ESPRIT-Type Algorithms for Strictly Second-Order Non-Circular Sources and Their Performance Analysis, in IEEE Transactions on Signal Processing, vol. 62, issue 18, pp. 4824 – 4838, Sep 2014, doi:10.1109/TSP.2014.2342673.

@ARTICLE{SRHD:14, author = {J. Steinwandt and F. Römer and M. Haardt and G. {Del Galdo}}, title = {{R-Dimensional} {ESPRIT-Type} Algorithms for Strictly {Second-Order} {Non-Circular} Sources and Their Performance Analysis}, journal = {IEEE Transactions on Signal Processing}, pages = {4824 -- 4838}, month = Sep, year = 2014, volume = 62, issue = 18, doi = {10.1109/TSP.2014.2342673} }

Abstract – High-resolution parameter estimation algorithms
designed to exploit the prior knowledge of incident signals from
strictly second-order (SO) non-circular (NC) sources allow for
a lower estimation error and can detect twice as many sources.
In this paper, we derive the R-D NC Standard ESPRIT and the
R-D NC Unitary ESPRIT algorithms that provide a significantly
better performance compared to their original versions for
arbitrary source signals. They are applicable to shift-invariant
R-D antenna arrays and do not require a centro-symmetric
array structure. Moreover, we present a first-order asymptotic
performance analysis of the proposed algorithms, which is based
on the estimation error of the signal subspace arising from the
noisy measurements. The derived expressions for the resulting
parameter estimation error are explicit in the noise realizations
and asymptotic in the effective signal-to-noise ratio (SNR), i.e.,
the results become exact for either high SNRs or a large sample
size. We also provide mean squared error (MSE) expressions,
where only the assumptions of a zero mean and finite SO
moments of the noise are required, but no assumptions about its
statistics are necessary. As a main result, we analytically prove
that the asymptotic performance of both R-D NC ESPRIT-type
algorithms is identical in the high effective SNR regime. Finally, a
case study shows that no improvement from strictly non-circular
sources can be achieved in the special case of a single source.

Y. Cheng, F. Römer, O. Khatib, and M. Haardt, Tensor subspace Tracking via Kronecker structured projections (TeTraKron) for time-varying multidimensional harmonic retrieval, in EURASIP Journal on Advances in Signal Processing, vol. 2014, issue 123, Aug 2014, doi:10.1186/1687-6180-2014-123.

@ARTICLE{CRKH:14, author = {Y. Cheng and F. Römer and O. Khatib and M. Haardt}, title = {Tensor subspace Tracking via Kronecker structured projections {(TeTraKron)} for time-varying multidimensional harmonic retrieval}, journal = {EURASIP Journal on Advances in Signal Processing}, month = Aug, year = 2014, volume = 2014, issue = 123, doi = {10.1186/1687-6180-2014-123} }

Abstract – We present a framework for Tensor-based subspace Tracking via Kronecker-structured projections (TeTraKron). TeTraKron allows to extend arbitrary matrix-based subspace tracking schemes to track the tensor-based subspace estimate. The latter can be computed via a structured projection applied to the matrix-based subspace estimate which enforces the multi-dimensional structure in a computationally efficient fashion. This projection is tracked by considering all matrix rearrangements of the signal tensor jointly, which can be efficiently realized via parallel processing. In addition, we incorporate forward-backward-averaging and find a similar link between the real-valued matrix-based and tensor-based subspace estimation. This enables the tracking of the real-valued tensor-based subspace estimate via a similar Kronecker-structured projection applied to the real-valued matrix-based subspace estimate. In time-varying multidimensional harmonic retrieval problems, the TeTraKron-based subspace tracking schemes outperform the original matrix-based subspace tracking algorithms as well as the batch solutions provided by the SVD and the HOSVD. Moreover, incorporating forward-backward-averaging leads to an improved accuracy of the subspace tracking, and only real-valued processing is involved. Furthermore, we evaluate the performances of ESPRIT-type parameter estimation schemes where the subspace estimates obtained by the proposed TeTraKron-based subspace tracking algorithms are used for the tracking of spatial frequencies in time-varying scenarios.

### 2013

F. Römer and M. Haardt, A semi-algebraic framework for approximate CP decompositions via Simultaneous Matrix Diagonalizations (SECSI), in Elsevier Signal Processing, vol. 93, issue 9, pp. 2722 – 2738, Sep 2013, doi:10.1016/j.sigpro.2013.02.016.

@ARTICLE{RH:13, author = {F. Römer and M. Haardt}, title = {A semi-algebraic framework for approximate {CP} decompositions via Simultaneous Matrix Diagonalizations {(SECSI)}}, journal = {Elsevier Signal Processing}, pages = {2722 -- 2738}, month = Sep, year = 2013, volume = 93, issue = 9, doi = {10.1016/j.sigpro.2013.02.016} }

Abstract – In this paper, we propose a framework to compute approximate CANDECOMP / PARAFAC (CP) decompositions. Such tensor decompositions are viable tools in a broad range of applications, creating the need for versatile tools to compute such decompositions with an adjustable complexity-accuracy trade-off. To this end, we propose a novel SEmi-algebraic framework that allows the computation of approximate CP decompositions via SImultaneous Matrix Diagonalizations (SECSI). In contrast to previous Simultaneous Matrix Diagonalization (SMD)-based approaches, we use the tensor structure to construct not only one but the full set of possible SMDs. Solving all SMDs, we obtain multiple estimates of the factor matrices and present strategies to choose the best estimate in a subsequent step. This SECSI framework retains the option to choose the number of SMDs to solve and to adopt various strategies for the selection of the final solution out of the multiple estimates. A best matching scheme based on an exhaustive search as well as heuristic selection schemes are devised to flexibly adapt to specific applications. Four example algorithms with different accuracy-complexity trade-off points are compared to state-of-the-art algorithms. We obtain more reliable estimates and a reduced computational complexity.

K. Liu, J. P. C. L. Da Costa, H. C. So, F. Römer, M. Haardt, and L. F. de A. Gadêlha, 3-D Unitary ESPRIT: Accurate attitude estimation for unmanned aerial vehicles with a hexagon-shaped ESPAR array, in Elsevier Digital Signal Processing, vol. 23, issue 3, pp. 701 – 711, May 2013, doi:10.1016/j.dsp.2012.12.010.

@ARTICLE{LDSRHd:13, author = {K. Liu and J. P. C. L. {Da Costa} and H. C. So and F. Römer and M. Haardt and L. F. {de A. Gadêlha}}, title = {{3-D} Unitary {ESPRIT:} Accurate attitude estimation for unmanned aerial vehicles with a hexagon-shaped {ESPAR} array}, journal = {Elsevier Digital Signal Processing}, pages = {701 -- 711}, month = May, year = 2013, volume = 23, issue = 3, doi = {10.1016/j.dsp.2012.12.010} }

Abstract – Accurate estimation of the attitude of unmanned aerial vehicles (UAVs) is crucial for their control and displacement. Errors in the attitude estimate may misuse the limited battery energy of UAVs or even cause an accident. For attitude estimation, proprioceptive sensors such as inertial measurement units (IMUs) are widely applied, but they are susceptible to inertial guidance error. With antenna arrays currently being installed in UAVs for communication with ground base stations, we can take advantage of the array structure in order to improve the estimates of IMUs via data fusion. In this paper, we therefore propose an attitude estimation system based on a hexagon-shaped 7-element electronically steerable parasitic antenna radiator (ESPAR) array. The ESPAR array is well-suited for installment in the UAVs with broad wings and short bodies. Our proposed solution returns an estimation for the pitch and roll based on the inter-element phase delay estimates of the line-of-sight path of the impinging signal over the antenna array. By exploiting the parallel and centrosymmetric structure in the hexagon-shaped ESPAR array, the 3-dimensional Unitary ESPRIT algorithm is applied for phase delay estimation to achieve high accuracy as well as computational efficiency. We devise an attitude estimation algorithm by exploiting the geometrical relationship between the UAV attitude and the estimated phase delays. An analytical closed-form expression of the attitude estimates is obtained by solving the established simultaneous nonlinear equations. Simulations results show the feasibility of our proposed solution for different signal-to-noise ratio levels as well as multipath scenarios.

B. Song, F. Römer, and M. Haardt, Flexible coordinated beamforming (FlexCoBF) for the downlink of multi-user mimo systems in single and clustered multiple cells, in Elsevier Signal Processing, vol. 93, issue 9, pp. 2462 – 2473, Sep 2013, doi:10.1016/j.sigpro.2013.03.012.

@ARTICLE{SRH:13, author = {B. Song and F. Römer and M. Haardt}, title = {Flexible coordinated beamforming {(FlexCoBF)} for the downlink of multi-user mimo systems in single and clustered multiple cells}, journal = {Elsevier Signal Processing}, pages = {2462 -- 2473}, month = Sep, year = 2013, volume = 93, issue = 9, doi = {10.1016/j.sigpro.2013.03.012} }

Abstract – For the multi-user MIMO downlink in a single and in clustered multiple cells, we consider the situation in which the total number of receive antennas of the served users is larger than the number of transmit antennas of the serving base station (BS). This situation is relevant for many scenarios. For instance, in multi-user MIMO broadcast channels, the BS simultaneously serves as many users as possible and hence a large total number of receive antennas is present. Furthermore, considering coordinated multi-point (CoMP) transmissions in clustered cellular scenarios, cluster edge users have to be jointly considered by adjacent clusters, which results in a large total number of receive antennas. We propose a flexible coordinated beamforming (FlexCoBF) algorithm which is applicable to this situation. Compared to the existing approaches, FlexCoBF has a much simpler design principle and an attractive flexibility in the choice of the transmit-receive strategies. The achievable sum rate performance of FlexCoBF is the same as the best known coordinated beamforming algorithm with significantly fewer iterations. Although FlexCoBF is first designed for a single cell, we show that it can be naturally extended to clustered multiple cells by introducing limited cooperation among adjacent clusters. Consequently, both inter-cluster and intra-cluster interferences are efficiently mitigated.

K. Liu, H. C. So, J. P. C. L. Da Costa, F. Römer, and L. Huang, Efficient source enumeration for accurate direction-of-arrival estimation in threshold region, in Elsevier Digital Signal Processing, Jun 2013, doi:10.1016/j.dsp.2013.06.009.

@ARTICLE{LSDRH:13, author = {K. Liu and H. C. So and J. P. C. L. {Da Costa} and F. Römer and L. Huang}, title = {Efficient source enumeration for accurate direction-of-arrival estimation in threshold region}, journal = {Elsevier Digital Signal Processing}, month = Jun, year = 2013, doi = {10.1016/j.dsp.2013.06.009} }

Abstract – Estimation of the number of signals impinging on an array of sensors, also known as source enumeration, is usually required prior to direction-of-arrival (DOA) estimation. In challenging scenarios such as the presence of closely-spaced sources and/or high level of noise, using the true source number for nonlinear parameter estimation leads to the threshold effect which is characterized by an abnormally large mean square error (MSE). In cases that sources have distinct powers and/or are closely spaced, the error distribution among parameter estimates of different sources is unbalanced. In other words, some estimates have small errors while others may be quite inaccurate with large errors. In practice, we will be only interested in the former and have no concern on the latter. To formulate this idea, the concept of effective source number (ESN) is proposed in the context of joint source enumeration and DOA estimation. The ESN refers to the actual number of sources that are visible at a given noise level by a parameter estimator. Given the numbers of sensors and snapshots, number of sources, source parameters and noise level, a Monte Carlo method is designed to determine the ESN, which is the maximum number of available accurate estimates. The ESN has a theoretical value in that it is useful for judging what makes a good source enumerator in the threshold region and can be employed as a performance benchmark of various source enumerators. Since the number of sources is often unknown, its estimate by a source enumerator is used for DOA estimation. In an effort to automatically remove inaccurate estimates while keeping as many accurate estimates as possible, we define the matched source number (MSN) as the one which in conjunction with a parameter estimator results in the smallest MSE of the parameter estimates. We also heuristically devise a detection scheme that attains the MSN for ESPRIT based on the combination of state-of-the-art source enumerators.

J. P. C. L. Da Costa, K. Liu, H. C. So, S. Schwarz, M. Haardt, and F. Römer, Multidimensional prewhitening for enhanced signal reconstruction and parameter estimation in colored noise with Kronecker correlation structure, in Elsevier Signal Processing, vol. 93, issue 11, pp. 3209 – 3226, Nov 2013, doi:10.1016/j.sigpro.2013.04.010.

@ARTICLE{DLSSHR:13, author = {J. P. C. L. {Da Costa} and K. Liu and H. C. So and S. Schwarz and M. Haardt and F. Römer}, title = {Multidimensional prewhitening for enhanced signal reconstruction and parameter estimation in colored noise with Kronecker correlation structure}, journal = {Elsevier Signal Processing}, pages = {3209 -- 3226}, month = Nov, year = 2013, volume = 93, issue = 11, doi = {10.1016/j.sigpro.2013.04.010} }

Abstract – Parameter estimation of multidimensional data in the presence of colored noise or interference with a Kronecker product covariance structure, which appears in electroencephalogram/magnetoencephalogram and multiple-input multiple-output applications, is addressed. In order to improve the accuracy of the multidimensional subspace-based estimation techniques designed for white noise, prewhitening algorithms are devised by exploiting the Kronecker structure of the noise covariance matrix. We first contribute to the development of the multidimensional prewhitening (MD-PWT) scheme which assumes that noise-only measurements are available. By applying prewhitening sequentially along various dimensions using the corresponding correlation factors estimated from the noise-only measurements, the MD-PWT significantly improves the performance of the closed-form parallel factor decomposition based parameter estimator (CFP-PE) with a small number of noise-only snapshots. When noise-only measurements are unavailable, an iterative joint estimation of noise and signal parameters and prewhitening algorithm is proposed by iteratively applying the MD-PWT and CFP-PE. Adaptive convergence thresholds are designed as the stopping conditions such that the optimal number of iterations is automatically determined. Simulation results show that the iterative scheme performs nearly the same as the MD-PWT with noise statistics, in all scenarios except for a special one of intermediate signal-to-noise ratios and high noise correlation levels.

### 2012

A. Yeredor, B. Song, F. Römer, and M. Haardt, A Sequentially Drilled Joint Congruence (SeDJoCo) Transformation With Applications in Blind Source Separation and Multiuser MIMO Systems, in IEEE Transactions on Signal Processing, vol. 60, issue 6, pp. 2744 – 2757, Jun 2012, doi:10.1109/TSP.2012.2190728.

@ARTICLE{YSRH:12, author = {A. Yeredor and B. Song and F. Römer and M. Haardt}, title = {A Sequentially Drilled Joint Congruence {(SeDJoCo)} Transformation With Applications in Blind Source Separation and Multiuser {MIMO} Systems}, journal = {IEEE Transactions on Signal Processing}, pages = {2744 -- 2757}, month = Jun, year = 2012, volume = 60, issue = 6, doi = {10.1109/TSP.2012.2190728} }

Abstract – In this paper, we consider a particular form of the classical approximate joint diagonalization (AJD) named Specially Structured Joint Diagonalization (SSJD). For a set of square, symmetric real-valued or Hermitian symmetric complex-valuedtarget matrices, this particular form seeks a single matrix B which enforces all offdiagonal elements in one special row and column of a transformed target matrix to be zeros. The number of target matrices is assumed to equal their dimension. We provide two different examples for the motivations of this form. One is encountered in the context of Maximum Likelihood blind (or semi-blind) source separation. Another is encourted in the context of coordinated beamforming for multiple-input multiple-output (MIMO) broadcast channels. Furthermore, we prove that this problem always has a solution for positive-definite symmetric realvalued or Hermitian symmetric complex-valed target matrices and present two solutions for finding matrix B. Compared to the existing solutions of this problem. One of our proposed solution provides fastest convergence, while another proposed solution achieves best sum rates performance in the application of multi-user MIMO systems.

J. Zhang, F. Römer, and M. Haardt, Relay Assisted Physical Resource Sharing: Projection Based Separation of Multiple Operators (ProBaSeMO) for Two-Way Relaying with MIMO Amplify and Forward Relays, in IEEE Transactions on Signal Processing, vol. 60, issue 9, pp. 4834 – 4848, Sep 2012, doi:10.1109/TSP.2012.2200888.

@ARTICLE{ZRH:12, author = {J. Zhang and F. Römer and M. Haardt}, title = {Relay Assisted Physical Resource Sharing: Projection Based Separation of Multiple Operators {(ProBaSeMO)} for {Two-Way} Relaying with {MIMO} Amplify and Forward Relays}, journal = {IEEE Transactions on Signal Processing}, pages = {4834 -- 4848}, month = Sep, year = 2012, volume = 60, issue = 9, doi = {10.1109/TSP.2012.2200888} }

Abstract – In this paper, we investigate a relay-assisted
resource sharing scenario, namely, multi-operator two-way
relaying with a MIMO amplify-and-forward (AF) relay.
Here, the spectrum and the relay (infrastructure) are
shared among multiple operators. We develop the projection
based separation of multiple operators (ProBaSeMo)
relay transmit strategy, which is inspired by the block
diagonalization (BD) and regularized block diagonalization
(RBD) schemes that are space-division multiple access
(SDMA) approaches for multi-user MIMO systems. If
the user terminals are equipped with multiple antennas,
appropriate precoding and decoding matrix designs are
also proposed. Compared to the time-shared approach
where the relay is used by different operators in a time
division multiple access (TDMA) manner, we demonstrate
that the ProBaSeMO algorithms can provide a significant
sharing gain in terms of the sum rate with many antennas
at the relay or in the high SNR regime in a two-operator
case. For a fixed number of antennas at the relay, an
even higher sharing gain can be obtained if the number
of operators increases.

A. Khabbazibasmenj, F. Römer, S. A. Vorobyov, and M. Haardt, Sum-rate maximization in twoway AF MIMO relaying: Polynomial time solutions to a class of DC programming problems, in IEEE Transactions on Signal Processing, vol. 60, issue 10, pp. 5478 – 5493, Oct 2012, doi:10.1109/TSP.2012.2208635.

@ARTICLE{KRVH:12, author = {A. Khabbazibasmenj and F. Römer and S. A. Vorobyov and M. Haardt}, title = {Sum-rate maximization in twoway {AF} {MIMO} relaying: Polynomial time solutions to a class of {DC} programming problems}, journal = {IEEE Transactions on Signal Processing}, pages = {5478 -- 5493}, month = Oct, year = 2012, volume = 60, issue = 10, doi = {10.1109/TSP.2012.2208635} }

Abstract – Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming
problems. DC programming problems occur also in other signal processing applications and are typically solved using different modifications of the branch-and-bound method which, however, does not have any polynomial time complexity
guarantees. In this paper, we develop two efficient polynomial time algorithms for the sum-rate maximization in two-way AF MIMO relaying. The first algorithm guarantees to find at least a Karush-Kuhn-Tucker (KKT) solution. There is a strong evidence, however, that such a solution is actually globally optimal. The second algorithm that is based on the generalized eigenvectors shows the same performance as first one with reduced computational complexity.
The objective function of the problem is represented as a product of quadratic ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative Newton-type
search over a single parameter. The other algorithm is called RAte-maximization via Generalized EigenvectorS (RAGES) and
is based on the generalized eigenvectors method and an iterative search over two (or one, in its approximate version) optimization variables. We derive an upper-bound for the optimal value of the
corresponding optimization problem and show by simulations that this upper-bound is achieved by both algorithms. It provides an evidence that the algorithms find a global optimum. The proposed
methods are also superior to other state-of-the-art algorithms.

### 2011

J. P. C. L. Da Costa, F. Römer, M. Haardt, and R. T. de Sousa Jr., Multi-Dimensional Model Order Selection, in EURASIP Journal on Advances in Signal Processing, Jul 2011, doi:10.1186/1687-6180-2011-26.

@ARTICLE{DRHd:11, author = {J. P. C. L. {Da Costa} and F. Römer and M. Haardt and R. T. {de Sousa Jr.}}, title = {{Multi-Dimensional} Model Order Selection}, journal = {EURASIP Journal on Advances in Signal Processing}, month = Jul, year = 2011, doi = {10.1186/1687-6180-2011-26} }

Abstract – Multi-dimensional model order selection (MOS) techniques achieve an improved accuracy, reliability and robustness, since they consider all dimensions jointly during the estimation of parameters. Additionally, from fundamental identifiability results of multi-dimensional decompositions, it is known that the number of main components can be larger compared to matrix-based decompositions. In this paper, we show how to use tensor calculus in order to extend matrix based MOS schemes and we also present our proposed multi-dimensional model order selection scheme based on the closed-form PARAFAC algorithm, which is only applicable to multi-dimensional data. In general, as shown bymeans of simulations, the Probability of correct Detection (PoD) of our proposed multi-dimensional MOS schemes is much better than the PoD of matrix based schemes.

### 2010

F. Römer and M. Haardt, Tensor-Based Channel Estimation (TENCE) and Iterative Refinements for Two-Way Relaying with Multiple Antennas and Spatial Reuse, in IEEE Transactions on Signal Processing, vol. 58, issue 11, pp. 5720 – 5735, Nov 2010, doi:10.1109/TSP.2010.2062179.

@ARTICLE{RH:10, author = {F. Römer and M. Haardt}, title = {{Tensor-Based} Channel Estimation {(TENCE)} and Iterative Refinements for {Two-Way} Relaying with Multiple Antennas and Spatial Reuse}, journal = {IEEE Transactions on Signal Processing}, pages = {5720 -- 5735}, month = Nov, year = 2010, volume = 58, issue = 11, doi = {10.1109/TSP.2010.2062179} }

Abstract – Relaying is one of the key technologies to satisfy the demands of future mobile communication systems. In particular,
two-way relaying is known to exploit the radio resources in a very efficient manner.
In this contribution we consider two-way relaying with amplify-and-forward (AF) MIMO relays. Since AF relays do not decode the signals, the separation of the data streams has to be performed by the terminals themselves. For this task both nodes require reliable channel knowledge of all relevant channel parameters. Therefore, we examine channel estimation schemes
for two-way relaying with AF MIMO relays. We investigate a simple Least Squares (LS) based scheme for the estimation of the compound channels as well as a tensor-based channel
estimation (TENCE) scheme which takes advantage of the special structure in the compound channel matrices to further improve the estimation accuracy. Note that TENCE is purely algebraic (i.e., it does not require any iterative procedures) and applicable to arbitrary antenna configurations. Then we demonstrate that the solution obtained by TENCE can be improved by an iterative refinement which is based on the Structured Least Squares (SLS) technique. In this application, between one and four iterations are sufficient and consequently the increase in computational complexity is moderate. The iterative refinement is optional and targeted for cases where the channel estimation accuracy is critical.
Moreover, we propose design rules for the training symbols as well as the relay amplification matrices during the training phase to facilitate the estimation procedures. Finally, we evaluate the achievable channel estimation accuracy of the LS-based compound channel estimation scheme as well as the tensor-based approach and its iterative refinement via numerical computer simulations.

A. Thakre, M. Haardt, F. Römer, and K. Giridhar, Tensor-Based Spatial Smoothing (TB-SS) Using Multiple Snapshots, in IEEE Transactions on Signal Processing, vol. 58, issue 5, pp. 2715 – 2728, May 2010, doi:10.1109/TSP.2010.2043141.

@ARTICLE{THRG:10, author = {A. Thakre and M. Haardt and F. Römer and K. Giridhar}, title = {{Tensor-Based} Spatial Smoothing {(TB-SS)} Using Multiple Snapshots}, journal = {IEEE Transactions on Signal Processing}, pages = {2715 -- 2728}, month = May, year = 2010, volume = 58, issue = 5, doi = {10.1109/TSP.2010.2043141} }

Abstract – Tensor-Based Spatial Smoothing (TB-SS) is a preprocessing technique for subspace-based parameter estimation of damped and undamped harmonics. In TB-SS multi-channel data is packed into a measurement tensor. We propose a tensor-based signal subspace estimation scheme that exploits the multi-dimensional invariance property exhibited by the highly structured measurement tensor. In the presence of noise, a tensor-based subspace estimate obtained via TB-SS is a better estimate of the desired signal subspace than the subspace estimate obtained by, for example, the singular value decomposition of a spatially smoothed matrix or a multilinear algebra approach reported in the literature. Thus TB-SS in conjunction with subspace-based parameter estimation schemes performs significantly better than subspace-based parameter estimation algorithms applied to the existing matrix-based subspace estimate. Another advantage of TB-SS over the conventional SS is that TB-SS is insensitive to changes in the number of samples per subarray provided that the number of subarrays is greater than the number of harmonics. In this paper we present, as an example, TB-SS in conjunction with ESPRIT-type algorithms for the parameter estimation of one-dimensional (1-D) damped and undamped harmonics. A closed form expression of the stochastic Cramer-Rao bound for the 1-D damped harmonic retrieval problem is also derived.

### 2009

F. Römer and M. Haardt, Algebraic Norm-Maximizing (ANOMAX) Transmit Strategy for Two-Way Relaying with MIMO Amplify and Forward Relays, in IEEE Signal Processing Letters, vol. 16, issue 10, Oct 2009, doi:10.1109/LSP.2009.2026453.

@ARTICLE{RH:09, author = {F. Römer and M. Haardt}, title = {Algebraic {Norm-Maximizing} {(ANOMAX)} Transmit Strategy for {Two-Way} Relaying with {MIMO} Amplify and Forward Relays}, journal = {IEEE Signal Processing Letters}, month = Oct, year = 2009, volume = 16, issue = 10, doi = {10.1109/LSP.2009.2026453} }

Abstract – Two-way relaying is a promising scheme to achieve the ubiquitous mobile access to a reliable high data rate service, which is targeted for future mobile communication systems.
In this contribution, we investigate two-way relaying with an amplify and forward relay, where the relay as well as the terminals are equipped with multiple antennas. Assuming that the terminals possess channel knowledge, the bidirectional two-way relaying channel is decoupled into two parallel effective single-user MIMO channels by subtracting the self-interference at the terminals. Thereby, any single-user MIMO technique can be applied to transmit the data.
We derive an algebraic norm-maximizing (ANOMAX) transmit strategy by finding the relay amplification matrix which maximizes the weighted sum of the Frobenius norms of the effective channels and discuss the implications of this solution on the resulting signal to noise ratios.
Finally, we compare ANOMAX to other existing transmission strategies via numerical computer simulations.

### 2008

M. Haardt, F. Römer, and G. Del Galdo, Higher-order SVD based subspace estimation to improve the parameter estimation accuracy in multidimensional harmonic retrieval problems, in IEEE Transactions on Signal Processing, vol. 56, issue 7, pp. 3198 – 3213, Jul 2008, doi:10.1109/TSP.2008.917929.

@ARTICLE{HRD:08, author = {M. Haardt and F. Römer and G. {Del Galdo}}, title = {Higher-order {SVD} based subspace estimation to improve the parameter estimation accuracy in multidimensional harmonic retrieval problems}, journal = {IEEE Transactions on Signal Processing}, pages = {3198 -- 3213}, month = Jul, year = 2008, volume = 56, issue = 7, doi = {10.1109/TSP.2008.917929} }

Abstract – MIMO channel modeling from channel sounder measurements requires the use of high-resolution parameter estimation algorithms. Multi-dimensional subspace-based methods, such as R-D Unitary ESPRIT, are frequently used for this task. Since the measurement data is multi-dimensional, current approaches require stacking the dimensions into one highly structured matrix. In the conventional subspace estimation step, e.g., via an SVD of this highly structured matrix, this structure is not exploited. In this paper, we define a measurement tensor and estimate the signal subspace through a higher order SVD. This allows us to exploit the structure inherent in the measurement data already in the first step of the algorithm which leads to better estimates of the signal subspace. We show how the concepts of forward-backward averaging and mapping onto the real-valued domain can be extended to tensors. As an example, we discuss the impact on the accuracy of the R-D Unitary ESPRIT algorithm. However, these new concepts can be applied to any multi-dimensional subspace-based parameter estimation scheme.

## Conference paper

### 2019

S. Semper and F. Römer, ADMM for ND Line Spectral Estimation using Grid-Free Compressive Sensing from Multiple Measurements with Applications to DOA Estimation, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2019), Brighton, UK, May 2019, doi:10.1109/ICASSP.2019.8683697.

@INPROCEEDINGS{SR:19, author = {S. Semper and F. Römer}, title = {{ADMM} for {ND} Line Spectral Estimation using {Grid-Free} Compressive Sensing from Multiple Measurements with Applications to {DOA} Estimation}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2019)}, month = May, year = 2019, address = {Brighton, UK}, doi = {10.1109/ICASSP.2019.8683697} }

Abstract – This paper is concerned with estimating unknown multidimensional frequencies from linear compressive measurements. This is accomplished by employing the recently proposed atomic norm minimization framework to recover these frequencies under a sparsity prior without imposing any grid restriction on these frequencies. To this end, we give a rigorous derivation of an iterative scheme called alternating direction of multipliers method, which is able to incorporate multiple compressive snapshots from a multi-dimensional superposition of complex harmonics. The key result here is how to formulate the objective function minimized by this scheme and its partial derivatives, which become hard to manage if the dimensionality of the frequencies is larger than 1. Moreover we demonstrate the performance of this approach in case of 3D line spectral estimation and 2D DOA estimation with a synthetic antenna array.

S. Semper, S. Pawar, and F. Römer, Combining Matrix Design for 2D DoA Estimation with Compressive Antenna Arrays using Stochastic Gradient Descent, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2019), Brighton, UK, May 2019, doi:10.1109/ICASSP.2019.8683173.

@INPROCEEDINGS{SPR:19, author = {S. Semper and S. Pawar and F. Römer}, title = {Combining Matrix Design for {2D} {DoA} Estimation with Compressive Antenna Arrays using Stochastic Gradient Descent}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2019)}, month = May, year = 2019, address = {Brighton, UK}, doi = {10.1109/ICASSP.2019.8683173} }

Abstract – Recently, compressive antenna arrays have been considered for direction of arrival (DoA) estimation with reduced hardware complexity. By utilizing compressive sensing, such arrays employ a linear combining network to combine signals from a larger set of antenna elements in the analog RF domain. In this paper, we develop a design approach based on the minimization of error between spatial correlation function (SCF) of the compressive and the uncompressed array resulting in the estimation performance of the two arrays to be as close as possible. The proposed design is based on grid-free stochastic gradient descent (SGD) optimization. In addition to a low computational cost for the proposed method, we show numerically that the resulting combining matrices perform better than the ones generated by a previous approach and combining matrices generated from a Gaussian ensemble.

S. Semper, J. Kirchhof, C. Wagner, F. Krieg, F. Römer, and G. Del Galdo, Defect Detection from Compressed 3-D Ultrasonic Frequency Measurements, in Proceedings of the 27th European Signal Processing Conference (EUSIPCO-2019), A Coruna, Spain, Sep 2019.

@INPROCEEDINGS{SKWKRD:19, author = {S. Semper and J. Kirchhof and C. Wagner and F. Krieg and F. Römer and G. {Del Galdo}}, title = {Defect Detection from Compressed {3-D} Ultrasonic Frequency Measurements}, booktitle = {Proceedings of the 27th European Signal Processing Conference (EUSIPCO-2019)}, month = Sep, year = 2019, address = {A Coruna, Spain} }

Abstract – In this paper, we propose a compressed sensing scheme for volumetric synthetic aperture measurements in ultrasonic nondestructive testing. The compression is achieved by limiting the measurement to a subset of the Fourier coefficients of the full measurement data, where we also address the issue of a suitable hardware architecture for the task. We present a theoretic analysis for one of the proposed schemes in terms of the Restricted Isometry Property and derive a scaling law for the lower bound of the number of necessary measurements for stable and efficient recovery. We verify our approach with reconstructions from measurement data of a steel specimen that was compressed synthetically in software. As a side result, our approach yields a variant of the 3-D Synthetic Aperture Focusing Technique which can deal with compressed data.

F. Krieg, S. Kodera, J. Kirchhof, F. Römer, A. Ihlow, S. Lugin, A. Osman, and G. Del Galdo, 3D reconstruction of handheld data by SAFT and its impediment by measurement inaccuracies, in Proceedings of the 2019 IEEE International Ultrasonics Symposium, Glasgow, UK, Oct 2019.

@INPROCEEDINGS{KKKRILOD:19, author = {F. Krieg and S. Kodera and J. Kirchhof and F. Römer and A. Ihlow and S. Lugin and A. Osman and G. {Del Galdo}}, title = {{3D} reconstruction of handheld data by {SAFT} and its impediment by measurement inaccuracies}, booktitle = {Proceedings of the 2019 IEEE International Ultrasonics Symposium}, month = Oct, year = 2019, address = {Glasgow, UK} }

E. Perez, J. Kirchhof, S. Semper, F. Krieg, and F. Römer, Total Focusing Method with subsampling in space and frequency domain for ultrasound NDT, in Proceedings of the 2019 IEEE International Ultrasonics Symposium, Glasgow, UK, Oct 2019.

@INPROCEEDINGS{PKSKR:19, author = {E. Perez and J. Kirchhof and S. Semper and F. Krieg and F. Römer}, title = {Total Focusing Method with subsampling in space and frequency domain for ultrasound {NDT}}, booktitle = {Proceedings of the 2019 IEEE International Ultrasonics Symposium}, month = Oct, year = 2019, address = {Glasgow, UK} }

### 2018

M. Ibrahim, W. Al-Aqqad, F. Römer, M. Käske, S. Semper, R. S. Thomä, and G. Del Galdo, Compressive Spatial Channel Sounding, in Proceedings of the 12th European Conference on Antennas and Propagation (EuCAP 2018), London, UK, Apr 2018, doi:10.1049/cp.2018.0472.

@INPROCEEDINGS{IARKSTD:18, author = {M. Ibrahim and W. Al-Aqqad and F. Römer and M. Käske and S. Semper and R. S. Thomä and G. {Del Galdo}}, title = {Compressive Spatial Channel Sounding}, booktitle = {Proceedings of the 12th European Conference on Antennas and Propagation (EuCAP 2018)}, month = Apr, year = 2018, address = {London, UK}, doi = {10.1049/cp.2018.0472} }

Abstract – In this paper we investigate the application of Compressed Sensing (CS) to MIMO channel sounding in the spatial domain. A compressive spatial channel sounder is proposed and evaluated based on real scenarios showing advantages in terms of time, hardware complexity and resolution. In particular, in the case where we use time division duplex for measuring the MIMO channel (in the form of antenna switching at the transmitter and/or the receiver), the proposed approach reduces the total number of switching periods, which implies a reduced channel acquisition time and thus an improved Doppler bandwidth. Alternatively, if we use multiple receive RF chains for the measurement, the compression allows to reduce the number of RF chains, which is a relevant advantage in terms of the overall receiver complexity, the amount of data to be processed in the digital domain (e.g., FPGA), power consumption, as well as RF hardware calibration. On the other hand, for the same measurement time and/or hardware complexity, one can increase the number of array elements to cover a larger aperture and so achieving better performance in terms of resolution.

S. Pawar, A. Lavrenko, F. Römer, M. Ibrahim, R. S. Thomä, and G. Del Galdo, Combining Matrix Design for 2D DoA Estimation with Compressive Antenna Arrays, in Proceedings of the 22nd International ITG Workshop on Smart Antennas (WSA'18), Bochum, Germany, Mar 2018.

@INPROCEEDINGS{PLRITD:18, author = {S. Pawar and A. Lavrenko and F. Römer and M. Ibrahim and R. S. Thomä and G. {Del Galdo}}, title = {Combining Matrix Design for {2D} {DoA} Estimation with Compressive Antenna Arrays}, booktitle = {Proceedings of the 22nd International ITG Workshop on Smart Antennas (WSA'18)}, month = Mar, year = 2018, address = {Bochum, Germany} }

Abstract – In compressive arrays, a (large) number of antenna outputs is linearly combined to a lower number of receiver channels with the aim to reduce hardware complexity without significantly compromising the estimation performance. In this paper, we develop a method for the combining matrix design for 2D DoA estimation with compressive arrays. We base our design on the antenna's spatial correlation function (SCF) in an attempt to produce an effective compressive array with estimation capabilities close to those of the original array before the combining. Due to the need to consider the SCF both in azimuth and elevation, the size of the resulting optimization problem becomes prohibitive.To reduce the optimization complexity, we propose an iterative design approach that allows a trade-off between complexity and the performance.

S. Semper, F. Römer, T. Hotz, and G. Del Galdo, Grid-Free Direction-of-Arrival Estimation with Compressed Sensing and Arbitrary Antenna Arrays, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2018), Calgary, Canada, Apr 2018, doi:10.1109/ICASSP.2018.8462501.

@INPROCEEDINGS{SRHD:18, author = {S. Semper and F. Römer and T. Hotz and G. {Del Galdo}}, title = {{Grid-Free} {Direction-of-Arrival} Estimation with Compressed Sensing and Arbitrary Antenna Arrays}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2018)}, month = Apr, year = 2018, address = {Calgary, Canada}, doi = {10.1109/ICASSP.2018.8462501} }

Abstract – We study the problem of direction of arrival estimation for arbitrary antenna arrays. We formulate it as a continuous line spectral estimation problem and solve it under a sparsity prior without any gridding assumptions. Moreover, we incorporate the array's beampattern in form of the Effective Aperture Distribution Function (EADF), which allows to use arbitrary (synthetic as well as measured) antenna arrays. This generalizes known atomic norm based grid-free DOA estimation methods (that have so far been limited to uniformly spaced arrays) to arbitrary antenna arrays. In addition, our formulation allows to incorporate compressed sensing in form of special linear combinations of the antennas' output ports. We provide conditions for the successful reconstruction of a certain number of targets depending on the amount of compression and the EADF of the antenna array. Our results are applicable to measurement matrices from any sub-Gaussian distribution.

F. Krieg, J. Kirchhof, F. Römer, A. Ihlow, G. Del Galdo, and A. Osman, Vergleich und Anpassung von 3D-SAFT-Implementierungen im Zeit- und Frequenzbereich für die schnelle Grobblechprüfung, in Jahrestagung der Deutschen Gesellschaft für Zerstörungefreie Prüfung (DGZfP) 2018, Leipzig, May 2018.

@INPROCEEDINGS{KKRIDO:18, author = {F. Krieg and J. Kirchhof and F. Römer and A. Ihlow and G. {Del Galdo} and A. Osman}, title = {Vergleich und Anpassung von {3D-SAFT-Implementierungen} im Zeit- und Frequenzbereich für die schnelle Grobblechprüfung}, booktitle = {Jahrestagung der Deutschen Gesellschaft für Zerstörungefreie Prüfung (DGZfP) 2018}, month = May, year = 2018, address = {Leipzig} }

S. Semper, J. Kirchhof, C. Wagner, F. Krieg, F. Römer, A. Osman, and G. Del Galdo, Defect Detection from 3D Ultrasonic Measurements Using Matrix-free Sparse Recovery Algorithms, in Proceedings of the 26th European Signal Processing Conference (EUSIPCO-2018), Rome, Italy, Sep 2018, doi:10.23919/EUSIPCO.2018.8553074.

@INPROCEEDINGS{SKWKROD:18, author = {S. Semper and J. Kirchhof and C. Wagner and F. Krieg and F. Römer and A. Osman and G. {Del Galdo}}, title = {Defect Detection from {3D} Ultrasonic Measurements Using Matrix-free Sparse Recovery Algorithms}, booktitle = {Proceedings of the 26th European Signal Processing Conference (EUSIPCO-2018)}, month = Sep, year = 2018, address = {Rome, Italy}, doi = {10.23919/EUSIPCO.2018.8553074} }

Abstract – In this paper, we propose an efficient matrix-free algorithm to reconstruct locations and size of flaws in a specimen from volumetric ultrasound data by means of a native 3D Sparse Signal Recovery scheme using Orthogonal Matching Pursuit (OMP). The efficiency of the proposed approach is achieved in two ways. First, we formulate the dictionary matrix as a block multilevel Toeplitz matrix to minimize redundancy and thus memory consumption. Second, we exploit this specific structure in the dictionary to speed up the correlation step in OMP, which is implemented matrix-free. We compare our method to state-of-the-art, namely 3D Synthetic Aperture Focusing Technique, and show that it delivers a visually comparable performance, while it gains the additional freedom to use further methods such as Compressed Sensing.

A. Lavrenko, F. Römer, G. Del Galdo, and R. S. Thomä, Sensing Matrix Sensitivity to Random Gaussian Perturbations in Compressed Sensing, in Proceedings of the 26th European Signal Processing Conference (EUSIPCO-2018), Rome, Italy, Sep 2018, doi:10.23919/EUSIPCO.2018.8553575.

@INPROCEEDINGS{LRDT:18, author = {A. Lavrenko and F. Römer and G. {Del Galdo} and R. S. Thomä}, title = {Sensing Matrix Sensitivity to Random Gaussian Perturbations in Compressed Sensing}, booktitle = {Proceedings of the 26th European Signal Processing Conference (EUSIPCO-2018)}, month = Sep, year = 2018, address = {Rome, Italy}, doi = {10.23919/EUSIPCO.2018.8553575} }

Abstract – In compressed sensing, the choice of the sensing matrix plays a crucial role: it defines the required hardware effort and determines the achievable recovery performance. Recent studies indicate that by optimizing a sensing matrix, one can potentially improve system performance compared to random ensembles. In this work, we analyze the sensitivity of a sensing matrix design to random perturbations, e.g., caused by hardware imperfections, with respect to the total (average) matrix coherence. We derive an exact expression for the average deterioration of the total coherence in the presence of Gaussian perturbations as a function of the perturbations' variance and the sensing matrix itself. We then numerically evaluate the impact it has on the recovery performance.

F. Krieg, S. Lugin, J. Kirchhof, A. Ihlow, T. Schwender, G. Del Galdo, F. Römer, and A. Osman, SAFT Processing for manually acquired ultrasonic measurement data with 3D smartInspect, in Proceedings of the International Symposium on Structural Health Monitoring and Nondestructive Testing, Saarbruecken, Germany, Oct 2018.

@INPROCEEDINGS{KLKISDRO:18, author = {F. Krieg and S. Lugin and J. Kirchhof and A. Ihlow and T. Schwender and G. {Del Galdo} and F. Römer and A. Osman}, title = {{SAFT} Processing for manually acquired ultrasonic measurement data with {3D} {smartInspect}}, booktitle = {Proceedings of the International Symposium on Structural Health Monitoring and Nondestructive Testing}, month = Oct, year = 2018, address = {Saarbruecken, Germany} }

P. Groß, A. Ihlow, R. Böttcher, S. Bessert, F. Krieg, J. Kirchhof, F. Römer, A. Osman, and G. Del Galdo, Design and prototyping of a 3-D positioner for ultrasound quality control measurements, in Proceedings of the International Symposium on Structural Health Monitoring and Nondestructive Testing, Saarbruecken, Germany, Oct 2018.

@INPROCEEDINGS{GIBBKKROD:18, author = {P. Groß and A. Ihlow and R. Böttcher and S. Bessert and F. Krieg and J. Kirchhof and F. Römer and A. Osman and G. {Del Galdo}}, title = {Design and prototyping of a {3-D} positioner for ultrasound quality control measurements}, booktitle = {Proceedings of the International Symposium on Structural Health Monitoring and Nondestructive Testing}, month = Oct, year = 2018, address = {Saarbruecken, Germany} }

Abstract – We describe the development and build-up of a 3-D positioner for ultrasonic testing with single- and multi-element transducers, supporting a scan area of up to 300 x 300 mm. The machine is realized with a delta kinematic using many components from the consumer/maker area. It can be easily mounted onto a water basin, containing the test object to be scanned. Software control is realized via G-code, as popular in CNC. With additional components, the positioner can be reconfigured and reused as a high-quality 3-D printer.

J. Kirchhof, S. Semper, and F. Römer, GPU-accelerated matrix-free 3D ultrasound reconstruction for nondestructive testing, in Proceedings of the 2018 IEEE International Ultrasonics Symposium, Kobe, Japan, Oct 2018, doi:10.1109/ULTSYM.2018.8579936.

@INPROCEEDINGS{KSR:18, author = {J. Kirchhof and S. Semper and F. Römer}, title = {{GPU-accelerated} matrix-free {3D} ultrasound reconstruction for nondestructive testing}, booktitle = {Proceedings of the 2018 IEEE International Ultrasonics Symposium}, month = Oct, year = 2018, address = {Kobe, Japan}, doi = {10.1109/ULTSYM.2018.8579936} }

Abstract – In this paper, we propose a matrix-free 3D ultrasonic reconstruction scheme based on the Fast Iterative Shrinkage-Thresholding algorithm (FISTA) implemented on a GPU. The matrix-free implementation allows to reconstruct images even for problem sizes that would be intractable when explicitly calculating the matrix. However, due to the matrix-free implementation, additional steps are necessary to estimate the stepsize parameter required by FISTA, since the optimal stepsize depends on the largest singular value of the operator matrix, which in the matrixfree version is unavailable and cannot be built due to its size. The estimation is performed based on a priori knowledge of the model. We compare our method to 3D SAFT and OMP images of volumetric ultrasound measurement data of a steel specimen to show how FISTA leads to sharper images facilitating sizing and locating of defects within a specimen.

F. Krieg, R. Pandey, J. Kirchhof, A. Ihlow, F. Römer, G. Del Galdo, and A. Osman, Progressive online 3-D SAFT processing by matrix structure exploitation, in Proceedings of the 2018 IEEE International Ultrasonics Symposium, Kobe, Japan, Oct 2018, doi:10.1109/ULTSYM.2018.8579696.

@INPROCEEDINGS{KPKIRDO:18, author = {F. Krieg and R. Pandey and J. Kirchhof and A. Ihlow and F. Römer and G. {Del Galdo} and A. Osman}, title = {Progressive online {3-D} {SAFT} processing by matrix structure exploitation}, booktitle = {Proceedings of the 2018 IEEE International Ultrasonics Symposium}, month = Oct, year = 2018, address = {Kobe, Japan}, doi = {10.1109/ULTSYM.2018.8579696} }

Abstract – In this paper, we formulate an efficient progressive version of 3-D SAFT by exploiting the block Toeplitz structure of the matrix unfolding of the underlying tensor. This reduces the calculation to a simple striding operation followed by a matrix-vector product of the corresponding submatrix per measured A-scan. Our approach enables to feedback 3-D SAFT images to the engineer during the measurement, e.g., by using augmented reality techniques. The usefulness of the progressive updates is illustrated by presenting snapshots of the iterative SAFT reconstruction of ultrasound measurement data of a steel specimen.

### 2017

J. Kirchhof, F. Krieg, F. Römer, A. Ihlow, A. Osman, and G. Del Galdo, Sparse Signal Recovery for Ultrasonic Detection and Reconstruction of Shadowed Flaws, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2017), New Orleans, USA, pp. 816 – 820, Mar 2017, doi:10.1109/ICASSP.2017.7952269.

@INPROCEEDINGS{KKRIOD:17, author = {J. Kirchhof and F. Krieg and F. Römer and A. Ihlow and A. Osman and G. {Del Galdo}}, title = {Sparse Signal Recovery for Ultrasonic Detection and Reconstruction of Shadowed Flaws}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2017)}, pages = {816 -- 820}, month = Mar, year = 2017, address = {New Orleans, USA}, doi = {10.1109/ICASSP.2017.7952269} }

Abstract – In this paper we propose a method to improve the detection of shadowed flaws in ultrasonic non-destructive testing (NDT). The B-scans are expressed in the context of Sparse Signal Recovery (SSR), where the shadowing effect is incorporated during the reconstruction: Whenever a new defect is found, its shadow on all other dictionary atoms is determined and the dictionary is updated accordingly. We develop models for determining the affected dictionary entries as well as for the intensity of the attenuation due to the shadow. Using Orthogonal Matching Pursuit (OMP), we demonstrate that the proposed method significantly improves the reconstruction amplitudes, i.e., the detection reliability, compared to conventional detection without incorporation of shadowing.

J. Steinwandt, F. Römer, and M. Haardt, Second-Order Performance Analysis of Standard ESPRIT, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2017), New Orleans, USA, pp. 3051 – 3055, Mar 2017, doi:10.1109/ICASSP.2017.7952717.

@INPROCEEDINGS{SRH:17, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {{Second-Order} Performance Analysis of Standard {ESPRIT}}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2017)}, pages = {3051 -- 3055}, month = Mar, year = 2017, address = {New Orleans, USA}, doi = {10.1109/ICASSP.2017.7952717} }

Abstract – This paper provides a second-order (SO) analytical performance analysis of the 1-D Standard ESPRIT algorithm. Existing performance analysis frameworks are based on first-order (FO) approximations of the parameter estimation error, which are asymptotic in the effective signal-to-noise ratio (SNR), i.e., they become exact for either high SNRs or a large sample size. However, these FO expressions do not capture the algorithmic behavior in the threshold region at low SNRs or for a small sample size. Yet, such conditions are often encountered in practice. Therefore, we present a closed-form expression for the parameter estimation error of 1-D Standard ESPRIT up to the SO that is valid in a wider effective SNR range. Moreover, we derive an analytical mean square error (MSE) expression, where we assume a zero-mean circularly symmetric complex Gaussian noise distribution. Finally, we use the existing FO MSE expression and the derived SO MSE expression to analytically compute the SNR breakdown threshold of the MSE threshold region. Empirical simulations verify the analytical expressions.

J. Kirchhof, F. Krieg, F. Römer, A. Ihlow, A. Osman, and G. Del Galdo, 3D-SAFT auf vorverarbeiteten Ultraschallsignalen - schneller messen bei verbesserter Auflösung, in Jahrestagung der Deutschen Gesellschaft für Zerstörungefreie Prüfung (DGZfP) 2017, Koblenz, May 2017.

@INPROCEEDINGS{KKRIOD:17, author = {J. Kirchhof and F. Krieg and F. Römer and A. Ihlow and A. Osman and G. {Del Galdo}}, title = {{3D-SAFT} auf vorverarbeiteten Ultraschallsignalen - schneller messen bei verbesserter Auflösung}, booktitle = {Jahrestagung der Deutschen Gesellschaft für Zerstörungefreie Prüfung (DGZfP) 2017}, month = May, year = 2017, address = {Koblenz} }

F. Krieg, J. Kirchhof, F. Römer, A. Ihlow, G. Del Galdo, and A. Osman, Implementation Issues of 3D SAFT in Time and Frequency Domain for the Fast Inspection of Heavy Plates, in Proceedings of the 2017 IEEE International Ultrasonics Symposium, Washington, D.C., USA, Sep 2017, doi:10.1109/ULTSYM.2017.8092833.

@INPROCEEDINGS{KKRIDO:17, author = {F. Krieg and J. Kirchhof and F. Römer and A. Ihlow and G. {Del Galdo} and A. Osman}, title = {Implementation Issues of {3D} {SAFT} in Time and Frequency Domain for the Fast Inspection of Heavy Plates}, booktitle = {Proceedings of the 2017 IEEE International Ultrasonics Symposium}, month = Sep, year = 2017, address = {Washington, D.C., USA}, doi = {10.1109/ULTSYM.2017.8092833} }

Abstract – When testing components in production facilities via ultrasound a good focusing of the measurements for the precise identification of inclusions is required. Often, this is obtained in post-processing by the Synthetic Aperture Focusing Technique (SAFT). This approach usually suffers from high computation times. In this paper, we compare approaches for the implementation of SAFT on the example of the inspection of heavy plates, where the fastest possible processing is required in order to allow full inspection in the production line. We tune time- and frequency domain algorithms for the inspection of planar objects and compare them regarding computation cost under the constraint of obtaining a sufficient reconstruction quality. In frequency-domain, we compare two approaches, namely the Phase-shift migration and tuned-versions of Stolt's migration with different interpolation strategies. In time-domain, we propose and compare heuristics for the delay-and-sum SAFT. We show that algorithm tuning can dramatically reduce computation times without significant degradation of the reconstruction results. Theoretic bounds for computation times and memory requirements related to the parameters of the reconstruction scenario are given and verified by measurements.

C. Grandinetti, J. Kirchhof, F. Krieg, F. Römer, A. Ihlow, G. Del Galdo, H. Theado, and A. Osman, Implementation of sparse signal recovery on FPGA for ultrasonic NDT, in Proceedings of the 2017 IEEE International Ultrasonics Symposium, Washington, D.C., USA, Sep 2017, doi:10.1109/ULTSYM.2017.8092308.

@INPROCEEDINGS{GKKRIDTO:17, author = {C. Grandinetti and J. Kirchhof and F. Krieg and F. Römer and A. Ihlow and G. {Del Galdo} and H. Theado and A. Osman}, title = {Implementation of sparse signal recovery on {FPGA} for ultrasonic {NDT}}, booktitle = {Proceedings of the 2017 IEEE International Ultrasonics Symposium}, month = Sep, year = 2017, address = {Washington, D.C., USA}, doi = {10.1109/ULTSYM.2017.8092308} }

Abstract – For several use cases of complex processing algorithms on ultrasound NDT data, it is mandatory to ensure real-time signal processing speed. This can be achieved by using e.g. a field programmable gate array (FPGA). Sparse signal recovery (SSR) and compressed sensing (CS) methods are used for superior reconstruction of flaws from compressed measurement data. SSR and CS are currently a hot research topic in various fields of application. However, they are not yet implemented for ultrasound NDT in a real-time manner.

A. Lavrenko, F. Römer, G. Del Galdo, and R. S. Thomä, Multiband TDOA estimation from sub-Nyquist samples with distributed wideband sensing nodes, in Proceedings of the 5th IEEE Global Conference on Signal and Information Processing (GlobalSIP), Montral, Canada, Nov 2017, doi:10.1109/GlobalSIP.2017.8308611.

@INPROCEEDINGS{LRDT:17, author = {A. Lavrenko and F. Römer and G. {Del Galdo} and R. S. Thomä}, title = {Multiband {TDOA} estimation from {sub-Nyquist} samples with distributed wideband sensing nodes}, booktitle = {Proceedings of the 5th IEEE Global Conference on Signal and Information Processing (GlobalSIP)}, month = Nov, year = 2017, address = {Montral, Canada}, doi = {10.1109/GlobalSIP.2017.8308611} }

Abstract – n this work, we estimate relative autocorrelation functions of multiple unknown transmissions that occupy distinct narrowband frequency bands from their sub-Nyquist samples. To be able to do so, we employ a network of distributed sensing nodes that are equipped with a sub-Nyquist receiver system and have access to a common clock. Utilizing low-rate out-puts of different nodes, we recover the central frequencies and the relative autocorrelation functions of individual transmissions within the wideband input, where the latter can then be used to determine corresponding time differences of arrival (TDoAs). We propose two recovery approaches; we either recover the central frequencies and the relative autocorrelations jointly or adopt a two-step procedure where the two are estimated independently. Our numerical results confirm the applicability of the proposed methods for relative multiband autocorrelation estimation from sub-Nyquist samples.

F. Römer, M. Großmann, T. Schön, R. Gruber, A. Jung, S. Oeckl, and G. Del Galdo, Differential SART for sub-Nyquist Tomographic Reconstruction in Presence of Misalignments, in Proceedings of the 25th European Signal Processing Conference (EUSIPCO-2017), Kos, Greece, Aug 2017, doi:10.23919/EUSIPCO.2017.8081631.

@INPROCEEDINGS{RGSGJOD:17, author = {F. Römer and M. Großmann and T. Schön and R. Gruber and A. Jung and S. Oeckl and G. {Del Galdo}}, title = {Differential {SART} for {sub-Nyquist} Tomographic Reconstruction in Presence of Misalignments}, booktitle = {Proceedings of the 25th European Signal Processing Conference (EUSIPCO-2017)}, month = Aug, year = 2017, address = {Kos, Greece}, doi = {10.23919/EUSIPCO.2017.8081631} }

Abstract – In this paper we study tomographic reconstruction methods in the case that prior knowledge about the object is available. In particular, we consider the case that a reference object that is similar in shape and orientation is available, which is very common in non-destructive testing applications. We demonstrate that a differential version of existing reconstruction methods can easily be derived which reconstructs only the deviation between test and reference object. Since this difference volume is significantly more sparse, the differential reconstruction can be implemented very efficiently. We also discuss the case where knowledge about the misalignment between test and reference object is available, in which case the efficiency of the differential reconstruction can be improved even further. The resulting algorithm is faster, more accurate, and less sensitive to the choice of the step size parameters and regularization than state of the art reconstruction methods.

K. Liu, F. Römer, J. P. C. L. Da Costa, J. Xiong, Y. Yan, W. Wang, and G. Del Galdo, Tensor-Based Sparsity Order Estimation for Big Data Applications, in Proceedings of the 25th European Signal Processing Conference (EUSIPCO-2017), Kos, Greece, Aug 2017, doi:10.23919/EUSIPCO.2017.8081287.

@INPROCEEDINGS{LRDXYWD:17, author = {K. Liu and F. Römer and J. P. C. L. {Da Costa} and J. Xiong and Y. Yan and W. Wang and G. {Del Galdo}}, title = {{Tensor-Based} Sparsity Order Estimation for Big Data Applications}, booktitle = {Proceedings of the 25th European Signal Processing Conference (EUSIPCO-2017)}, month = Aug, year = 2017, address = {Kos, Greece}, doi = {10.23919/EUSIPCO.2017.8081287} }

Abstract – In Big Data Processing we typically face very large data sets that are highly structured. To save the computation and storage cost, it is desirable to extract the essence of the data from a reduced number of observations. One example of such a structural constraint is sparsity. If the data possesses a sparse representation in a suitable domain, it can be recovered from a small number of linear projections into a low-dimensional space. In this case, the degree of sparsity, referred to as sparsity order, is of high interest. It has recently been shown that if the measurement matrix obey certain structural constraints, one can estimate the sparsity order directly from the compressed data. The rich structure of the measurement matrix allows to rearrange the multiple-snapshot measurement vectors into a fourth-order tensor with rank equal to the desired sparsity order. In this paper, we exploit the multilinear structure of the data for accurate sparsity order estimation with improved identifiability. We discuss the choice of the parameters, i.e., the block size, block offset, and number of blocks, to maximize the sparsity order that can be inferred from a certain number of observations, and compare state-of-the-art order selection algorithms for sparsity order estimation under the chosen parameter settings. By performing an extensive campaign of simulations, we show that the discriminant function based method and the random matrix theory algorithm outperform other approaches in small and large snapshot-number scenarios, respectively.

R. K. Miranda, J. P. C. L. Da Costa, G. Del Galdo, and F. Römer, Broadband Beamforming via Frequency Invariance Transformation and PARAFAC Decomposition, in Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2017), Curacao, Dutch Antilles, Dec 2017.

@INPROCEEDINGS{MDDR:17, author = {R. K. Miranda and J. P. C. L. {Da Costa} and G. {Del Galdo} and F. Römer}, title = {Broadband Beamforming via Frequency Invariance Transformation and {PARAFAC} Decomposition}, booktitle = {Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2017)}, month = Dec, year = 2017, address = {Curacao, Dutch Antilles} }

J. Steinwandt, F. Römer, and M. Haardt, Performance Analysis of ESPRIT-Type Algorithms for Co-Array Structures, in Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2017), Curacao, Dutch Antilles, Dec 2017.

@INPROCEEDINGS{SRH:17, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {Performance Analysis of {ESPRIT-Type} Algorithms for {Co-Array} Structures}, booktitle = {Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2017)}, month = Dec, year = 2017, address = {Curacao, Dutch Antilles} }

Abstract – In the recent field of co-array signal processing, sparse linear arrays are processed to form a virtual uniform linear array (ULA), termed co-array, that allows to resolve more sources than physical sensors. The extra degrees of freedom (DOFs) are leveraged by the assumption that the signals are uncorrelated, which requires a large sample size. In this paper, we first review the Standard ESPRIT and Unitary ESPRIT algorithms for co-array processing. Secondly, we propose a performance analysis for both methods, which is asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. Based on the derived analytical expressions, we study the effects of a small sample size such as the residual sample signal correlation and the sample noise contribution on the estimation accuracy of the proposed algorithms. Simulation results verify the derived analytical expressions.

### 2016

M. Ibrahim, F. Römer, N. Hadaschik, H. M. Tröger, B. Sackenreuter, N. Franke, J. Robert, and G. Del Galdo, Temporal wireless synchronization with compressed opportunistic signals, in Proceedings of the IEEE Radio Wireless Week, Wireless Sensors and Sensor Networks Symposium, Austin, TX, Jan 2016, doi:10.1109/WISNET.2016.7444331.

@INPROCEEDINGS{IRHTSFRD:16, author = {M. Ibrahim and F. Römer and N. Hadaschik and H. M. Tröger and B. Sackenreuter and N. Franke and J. Robert and G. {Del Galdo}}, title = {Temporal wireless synchronization with compressed opportunistic signals}, booktitle = {Proceedings of the IEEE Radio Wireless Week, Wireless Sensors and Sensor Networks Symposium}, month = Jan, year = 2016, address = {Austin, TX}, doi = {10.1109/WISNET.2016.7444331} }

Abstract – In this paper we introduce a wireless temporal synchronization scheme based on wideband signals of opportunity (SOO) such as DVB-T or LTE signals. Since these signals may not be decodable we show that it is necessary that one (reference) node broadcasts an excerpt of the SOO to all other nodes to provide a reference. However, the transmission of this reference signals requires a high bandwidth. Therefore, we propose to replace this transmission with a lower-bandwidth "compressed" version of this reference signal, using ideas from the field of compressed sensing (CS). We show that the high time resolution of the original wideband SOO can be maintained so that accurate temporal synchronization is possible. On the other hand, the compression leads to higher sidelobes in the correlation function which reduces the effective SNR. Therefore, the compression rate allows to control the trade-off between the required bandwidth and the SNR.

J. Steinwandt, F. Römer, and M. Haardt, Analytical Performance Assessment of ESPRIT-type Algorithms for Coexisting Circular and Strictly Non-circular Signals, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2016), Shanghai, China, Mar 2016, doi:10.1109/ICASSP.2016.7472214.

@INPROCEEDINGS{SRH:16, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {Analytical Performance Assessment of {ESPRIT-type} Algorithms for Coexisting Circular and Strictly Non-circular Signals}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2016)}, month = Mar, year = 2016, address = {Shanghai, China}, doi = {10.1109/ICASSP.2016.7472214} }

J. Steinwandt, F. Römer, and M. Haardt, Sparsity-based Direction-of-Arrival Estimation for Non-circular Sources, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2016), Shanghai, China, Mar 2016, doi:10.1109/ICASSP.2016.7472277.

@INPROCEEDINGS{SRH:16, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {Sparsity-based {Direction-of-Arrival} Estimation for Non-circular Sources}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2016)}, month = Mar, year = 2016, address = {Shanghai, China}, doi = {10.1109/ICASSP.2016.7472277} }

M. Großmann, V. Ramireddy, J. König, M. Landmann, F. Römer, G. Del Galdo, and R. Perthold, Antenna Array Optimization Strategies for Robust Direction Finding, in Proceedings of the 10th European Conference on Antennas and Propagation (EuCAP 2016), Davos, Switzerland, Apr 2016, doi:10.1109/EuCAP.2016.7481144.

@INPROCEEDINGS{GRKLRDP:16, author = {M. Großmann and V. Ramireddy and J. König and M. Landmann and F. Römer and G. {Del Galdo} and R. Perthold}, title = {Antenna Array Optimization Strategies for Robust Direction Finding}, booktitle = {Proceedings of the 10th European Conference on Antennas and Propagation (EuCAP 2016)}, month = Apr, year = 2016, address = {Davos, Switzerland}, doi = {10.1109/EuCAP.2016.7481144} }

Abstract – This paper focuses on the optimization of uniform circular antenna array (UCA) structures equipped with analog combining networks for direction finding applications. For such type of arrays, the specific choice of the combining matrix has a crucial impact on the effective radiation pattern and the sensitivity of direction-of-arrival (DOA) estimation. A design framework for constructing the combining network is proposed that improves the DOA estimation performance of the array while limiting the probability of false detection of the DOA estimator to a desired value. In detail, we first derive an analytical expression for the false detection probability of the DOA estimator. This function together with the Cramer-Rao bound (CRB) are then used to find the optimal combining matrix and array aperture size for a given number of sensor elements and combiner output (baseband) channels. We provide design examples to demonstrate the effectiveness of our approach.

A. Lavrenko, F. Römer, S. Stein, D. Cohen, G. Del Galdo, R. S. Thomä, and Y. C. Eldar, Spatially Resolved sub-Nyquist Sensing of Multiband Signals with Arbitrary Antenna Arrays, in Proceedings of the 17th IEEE International Workshop on Signal Processing Advances in Wireless Communication (SPAWC 2016), Edinburgh, UK, Jul 2016, doi:10.1109/SPAWC.2016.7536776.

@INPROCEEDINGS{LRSCDTE:16, author = {A. Lavrenko and F. Römer and S. Stein and D. Cohen and G. {Del Galdo} and R. S. Thomä and Y. C. Eldar}, title = {Spatially Resolved {sub-Nyquist} Sensing of Multiband Signals with Arbitrary Antenna Arrays}, booktitle = {Proceedings of the 17th IEEE International Workshop on Signal Processing Advances in Wireless Communication (SPAWC 2016)}, month = Jul, year = 2016, address = {Edinburgh, UK}, doi = {10.1109/SPAWC.2016.7536776} }

Abstract – In recent years it has been shown that wideband analog signals can be sampled significantly below the Nyquist rate without loss of information, provided that the unknown frequency support occupies only a small fraction of the overall bandwidth. The modulated wideband converter (MWC) is a particular architecture that implements this idea. In this paper we discuss how the use of antenna arrays allows to extend this concept towards spatially resolved wideband spectrum sensing by leveraging the sparsity in the angular-frequency domain. In our system each antenna element of the array is sampled at a sub-Nyquist rate by an individual MWC block. This results in a trade-off between the number of antennas and MWC channels per antenna. We derive bounds on the minimal total number of channels and minimal sampling rate required for perfect recovery of the 2D angular-frequency spectrum of the incoming signal and present a concrete reconstruction approach. The proposed system is applicable to arbitrary antenna arrays, provided that the array manifold is ambiguity-free.

J. Steinwandt, F. Römer, and M. Haardt, Analytical Performance Evaluation of Multi-Dimensional Tensor-ESPRIT-Based Algorithms for Strictly Non-Circular Sources, in Proceedings of the 9-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2016), Rio de Janeiro, Brazil, Jul 2016, doi:10.1109/SAM.2016.7569659.

@INPROCEEDINGS{SRH:16, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {Analytical Performance Evaluation of {Multi-Dimensional} {Tensor-ESPRIT-Based} Algorithms for Strictly {Non-Circular} Sources}, booktitle = {Proceedings of the 9-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2016)}, month = Jul, year = 2016, address = {Rio de Janeiro, Brazil}, doi = {10.1109/SAM.2016.7569659} }

Abstract – Exploiting inherent signal structure is a common approach towards improving the performance of conventional parameter estimation algorithms. It has recently been shown that the multi-dimensional (R-D) nature of the signals and their statistical properties, i.e., their second-order (SO) strictly non-circular (NC) structure, can be exploited simultaneously by R-D NC Tensor-ESPRIT-type algorithms. In this contribution, we develop an analytical first-order performance evaluation of R-D NC Standard Tensor-ESPRIT and R-D NC Unitary Tensor-ESPRIT. The derived expressions are asymptotic in the effective signal-to-noise ratio (SNR), i.e., they become exact for high SNRs or a large sample size. Moreover, apart from a zero mean and finite SO statistics, no assumptions on the noise statistics are required. We show that as in the corresponding NC matrix case, the performance of R-D NC Standard Tensor-ESPRIT and R-D NC Unitary Tensor-ESPRIT is asymptotically identical. Simulations verify the derived expressions.

S. Varatharaajan, F. Römer, G. Kostka, F. Keil, F. Uhrmann, and G. Del Galdo, On Poisson Compressed Sensing and Parameter Estimation in Sheet-of-Light Surface Scanning, in Proceedings of the 24th European Signal Processing Conference (EUSIPCO-2016), Budapest, Hungary, Aug 2016, doi:10.1109/EUSIPCO.2016.7760289.

@INPROCEEDINGS{VRKKUD:16, author = {S. Varatharaajan and F. Römer and G. Kostka and F. Keil and F. Uhrmann and G. {Del Galdo}}, title = {On Poisson Compressed Sensing and Parameter Estimation in {Sheet-of-Light} Surface Scanning}, booktitle = {Proceedings of the 24th European Signal Processing Conference (EUSIPCO-2016)}, month = Aug, year = 2016, address = {Budapest, Hungary}, doi = {10.1109/EUSIPCO.2016.7760289} }

Abstract – Compressed Sensing (CS) has been successfully applied in a number of imaging systems to increase the speed of the measurement and/or enhance scan resolution. In this paper, we apply CS to 3-D surface acquisition using Sheet of Light (SOL) scanning. We formulate the estimation of the height profile of a target object as a compressive parameter estimation problem and investigate the achievable estimation accuracy of a CS-SOL system in the presence of noise with the help of the Cramer-Rao Lower Bound (CRLB). In the context of CS, Gaussian noise models are typically analyzed. However, in imaging applications there are noise sources that can be modeled as Poisson noise, which dominate the distortions particularly in low light settings. Therefore, we focus on compressive parameter estimation in presence of Poisson noise. This analysis allows us to compare different measurement strategies and quantify the estimation accuracy as a function of the system parameters.

F. Römer, M. Ibrahim, N. Franke, N. Hadaschik, A. Eidloth, B. Sackenreuter, and G. Del Galdo, Measurement Matrix Design for Compressed Sensing Based Time Delay Estimation, in Proceedings of the 24th European Signal Processing Conference (EUSIPCO-2016), Budapest, Hungary, Aug 2016, doi:10.1109/EUSIPCO.2016.7760290.

@INPROCEEDINGS{RIFHESD:16, author = {F. Römer and M. Ibrahim and N. Franke and N. Hadaschik and A. Eidloth and B. Sackenreuter and G. {Del Galdo}}, title = {Measurement Matrix Design for Compressed Sensing Based Time Delay Estimation}, booktitle = {Proceedings of the 24th European Signal Processing Conference (EUSIPCO-2016)}, month = Aug, year = 2016, address = {Budapest, Hungary}, doi = {10.1109/EUSIPCO.2016.7760290} }

Abstract – In this paper we study the problem of estimating the unknown delay(s) in a system where we receive a linear combination of several delayed copies of a known transmitted waveform. This problem arises in many applications such as timing-based localization or wireless synchronization. Since accurate delay estimation requires wideband signals, traditional systems need high-speed AD converters which poses a significant burden on the hardware implementation. Compressive sensing (CS) based system architectures that take measurements at rates significantly below the Nyquist rate and yet achieve accurate delay estimation have been proposed with the goal to alleviate the hardware complexity. In this paper, we particularly discuss the design of the measurement kernels based on a frequency-domain representation and show numerically that an optimized choice can outperform randomly chosen functionals in terms of the delay estimation accuracy.

J. Kirchhof, F. Krieg, F. Römer, A. Ihlow, A. Osman, and G. Del Galdo, Speeding up 3D SAFT for ultrasonic NDT by Sparse Deconvolution, in Proceedings of the 2016 IEEE International Ultrasonics Symposium, Tours, France, Sep 2016, doi:10.1109/ULTSYM.2016.7728434.

@INPROCEEDINGS{KKRIOD:16, author = {J. Kirchhof and F. Krieg and F. Römer and A. Ihlow and A. Osman and G. {Del Galdo}}, title = {Speeding up {3D} {SAFT} for ultrasonic {NDT} by Sparse Deconvolution}, booktitle = {Proceedings of the 2016 IEEE International Ultrasonics Symposium}, month = Sep, year = 2016, address = {Tours, France}, doi = {10.1109/ULTSYM.2016.7728434} }

Abstract – Abstract—In this paper we propose to pre-process ultrasonic measurements (A-scans) in Non-Destructive Testing (NDT) by sparse deconvolution before post-processing the data with the Synthetic Aperture Focusing Technique (SAFT). Compared to state-of-the-art SAFT post-processing of raw A-scan measurements, pre-processing by sparse deconvolution can improve NDT in the following ways: First, the temporal resolution of signal reflections is increased. Second, because the A-scans appear as a sparse signal of spikes, it is possible to formulate the time-domain SAFT algorithm in a new fashion that is both faster compared to conventional SAFT and the deconvolved input data can be focussed better leading to a higher resolution. Since sparse deconvolution could be implemented directly into the ultrasonic probe hardware/software measurement setup, this approach can dramatically speed up measurements in time-critical environments. We test the proposed scheme on CIVA simulation data as well as measurements and show B- and C-images of raw SAFT vs. Orthogonal Matching Pursuit (OMP) + SAFT and Basis Pursuit Denoising (BPDN) + SAFT.

A. Lavrenko, F. Römer, G. Del Galdo, and R. S. Thomä, On The Earth Mover's Distance as a Performance Metric For Sparse Support Recovery, in Proceedings of the 4th IEEE Global Conference on Signal and Information Processing (GlobalSIP), Greater Washington, D.C., USA, Dec 2016, doi:10.1109/GlobalSIP.2016.7906065.

@INPROCEEDINGS{LRDT:16, author = {A. Lavrenko and F. Römer and G. {Del Galdo} and R. S. Thomä}, title = {On The Earth Mover's Distance as a Performance Metric For Sparse Support Recovery}, booktitle = {Proceedings of the 4th IEEE Global Conference on Signal and Information Processing (GlobalSIP)}, month = Dec, year = 2016, address = {Greater Washington, D.C., USA}, doi = {10.1109/GlobalSIP.2016.7906065} }

Abstract – Compressed sensing (CS) is a recently emerged framework for simultaneous sampling and compression of signals that are sparse or compressible in some representation. Besides signal reconstruction, the CS framework is often adopted for compressive parameter estimation, e.g., in such applications as compressive direction of arrival (DoA) estimation, spectrum sensing, delay estimation, etc. In CS, the recovery performance is usually expressed in terms of Euclidean or Hamming distances between the original and recovered signals. Such metrics are well suited for performance evaluation in terms of recovery rates but provide little insight into the accuracy of the estimates. In this work we study an alternative performance metric based on the Earth Mover's Distance (EMD). We derive the EMD in the context of support recovery for supports with equal as well as arbitrary cardinalities. Simulation results suggest that the EMD provides a better alternative to commonly used in CS metrics in that it reflects the estimation accuracy in case of the imperfect support recovery.

R. K. Miranda, J. P. C. L. Da Costa, F. Römer, F. Raschke, T. Eishima, Y. Nakamura, and G. Del Galdo, Implementation of Improved Software Defined Radio Modulation Scheme and Command and Telemetry Software Interface for Small Satellites in 5G Systems, in Proceedings of the 19th International Conference on OFDM and Frequency Domain Techniques (ICOF 2016), Essen, Germany, Aug 2016.

@INPROCEEDINGS{MDRREND:16, author = {R. K. Miranda and J. P. C. L. {Da Costa} and F. Römer and F. Raschke and T. Eishima and Y. Nakamura and G. {Del Galdo}}, title = {Implementation of Improved Software Defined Radio Modulation Scheme and Command and Telemetry Software Interface for Small Satellites in {5G} Systems}, booktitle = {Proceedings of the 19th International Conference on OFDM and Frequency Domain Techniques (ICOF 2016)}, month = Aug, year = 2016, address = {Essen, Germany} }

R. K. Miranda, J. P. C. L. Da Costa, T. Eishima, Y. Nakamura, G. Del Galdo, and F. Römer, Procedures for Integrating, Testing and Operating Advanced Microsatellites, in Proceecings of the 4th IFAC Symposium on Telematics Applications 2016, Porto Alegre, Brazil, Nov 2016.

@INPROCEEDINGS{MDENDR:16, author = {R. K. Miranda and J. P. C. L. {Da Costa} and T. Eishima and Y. Nakamura and G. {Del Galdo} and F. Römer}, title = {Procedures for Integrating, Testing and Operating Advanced Microsatellites}, booktitle = {Proceecings of the 4th IFAC Symposium on Telematics Applications 2016}, month = Nov, year = 2016, address = {Porto Alegre, Brazil} }

J. Steinwandt, F. Römer, C. Steffens, M. Haardt, and M. Pesavento, Gridless Super-Resolution Direction Finding for Strictly Non-Circular Sources Based on Atomic Norm Minimization, in Proceedings of the 50-th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov 2016, doi:10.1109/ACSSC.2016.7869631.

@INPROCEEDINGS{SRSHP:16, author = {J. Steinwandt and F. Römer and C. Steffens and M. Haardt and M. Pesavento}, title = {Gridless {Super-Resolution} Direction Finding for Strictly {Non-Circular} Sources Based on Atomic Norm Minimization}, booktitle = {Proceedings of the 50-th Asilomar Conference on Signals, Systems, and Computers}, month = Nov, year = 2016, address = {Pacific Grove, CA}, doi = {10.1109/ACSSC.2016.7869631} }

Abstract – The recently developed super-resolution framework by Candés enables the direction-of-arrival (DOA) estimation from a sparse spatial power spectrum in the continuous domain with infinite precision. By means of atomic norm minimization (ANM), the discretization of the spatial domain is no longer required, which overcomes the basis mismatch problem in conventional compressed sensing (CS)-based DOA estimation. In this paper, we incorporate additional signal structure, i.e., the strict second-order non-circularity (NC) of the signals, into the ANM framework for the multiple measurement vector (MMV) model. Due to the NC preprocessing step, the NC ANM problem provides a two-level Hermitian Toeplitz structured solution matrix, which possesses a two-dimensional Vandermonde decomposition such that desired spatial frequencies can be uniquely extracted via NC Standard/Unitary ESPRIT. The presented NC ANM procedure efficiently exploits the NC signal structure, resulting in a reduced estimation error compared to the conventional ANM approach. Simulation results demonstrate the superior performance of the proposed method.

### 2015

A. Lavrenko, F. Römer, G. Del Galdo, and R. S. Thomä, Sparsity Order Estimation for Sub-Nyquist Sampling and Recovery of Sparse Multiband Signals, in Proceedings of the IEEE International Conference on Communications - Signal Processing for Communication Symposium, London, UK, Jun 2015, doi:10.1109/ICC.2015.7249100.

@INPROCEEDINGS{LRDT:15, author = {A. Lavrenko and F. Römer and G. {Del Galdo} and R. S. Thomä}, title = {Sparsity Order Estimation for {Sub-Nyquist} Sampling and Recovery of Sparse Multiband Signals}, booktitle = {Proceedings of the IEEE International Conference on Communications - Signal Processing for Communication Symposium}, month = Jun, year = 2015, address = {London, UK}, doi = {10.1109/ICC.2015.7249100} }

Abstract – The application of the Compressed Sensing (CS) paradigm to the sampling of sparse wireless signals allows a significant reduction of the sampling rate compared to the one dictated by the Nyquist sampling theorem. The majority of the theoretical results derived within CS are expressed in terms of the known sparsity order of the signal. In this work we address the problem of sparsity order estimation of multiband signals with unknown sparse spectral supports. We show that it can be estimated directly in the compressed domain as the dimension of the signal subspace of the observations' covariance matrix. We analyze how the results of the sparsity estimation can be utilized during the reconstruction step and which requirements it imposes on the performance of the subspace estimation algorithms. The results of the numerical study demonstrate that the reconstruction step is particularly sensitive to type II errors. This in turn indicates that the classical non-parametric model order selection algorithms might be unfavorable for this application since they tend to underestimate model order in the low SNR regime. As a remedy we propose to apply parametric approaches that allow to compromise resulting probabilities of over- and underestimation.

J. Steinwandt, F. Römer, and M. Haardt, ESPRIT-Type Algorithms for a Received Mixture of Circular and Strictly Non-Circular Signals, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2015), Brisbane, Australia, Apr 2015, doi:10.1109/ICASSP.2015.7178483.

@INPROCEEDINGS{SRH:15, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {{ESPRIT-Type} Algorithms for a Received Mixture of Circular and Strictly {Non-Circular} Signals}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2015)}, month = Apr, year = 2015, address = {Brisbane, Australia}, doi = {10.1109/ICASSP.2015.7178483} }

M. Ibrahim, F. Römer, and G. Del Galdo, On the design of the measurement matrix for compressed sensing based DOA estimation, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2015), Brisbane, Australia, Apr 2015, doi:10.1109/ICASSP.2015.7178648.

@INPROCEEDINGS{IRD:15, author = {M. Ibrahim and F. Römer and G. {Del Galdo}}, title = {On the design of the measurement matrix for compressed sensing based {DOA} estimation}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2015)}, month = Apr, year = 2015, address = {Brisbane, Australia}, doi = {10.1109/ICASSP.2015.7178648} }

T. Schön, F. Römer, S. Oeckl, M. Großmann, R. Gruber, A. Jung, and G. Del Galdo, Cycle Time Reduction in Process Integrated Computed Tomography using Compressed Sensing, in Proceedings of the 13th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (Fully 3D), Newport, RI, May 2015.

@INPROCEEDINGS{SROGGJD:15, author = {T. Schön and F. Römer and S. Oeckl and M. Großmann and R. Gruber and A. Jung and G. {Del Galdo}}, title = {Cycle Time Reduction in Process Integrated Computed Tomography using Compressed Sensing}, booktitle = {Proceedings of the 13th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (Fully 3D)}, month = May, year = 2015, address = {Newport, RI} }

Abstract – In this contribution we investigate whether reconstruction algorithms for X-ray computed tomography (CT) based on the compressed sensing approach are applicable to reduce the cycle time for process integrated CT inspection. In particular we study how the image quality degrades when obtained from fewer projections and a low-complexity reconstruction algorithm (i.e., using only a few iterations). For this purpose, we analyze the convergence behavior using different parameter choices for the reconstruction algorithm and demonstrate the benefits of applying prior knowledge of the specimen. The performance of the studied approaches is evaluated on real measurement data obtained from a large number of combustion motor pistons.

S. Skoblikov, F. Römer, M. Ibrahim, R. S. Thomä, and G. Del Galdo, DoA Estimation with Reflectarray According to Single Pixel Camera Principle, in 3rd International Workshop on Compressed Sensing applied to Radar, Pisa, Italy, Jun 2015, doi:10.1109/CoSeRa.2015.7330306.

@INPROCEEDINGS{SRITD:15, author = {S. Skoblikov and F. Römer and M. Ibrahim and R. S. Thomä and G. {Del Galdo}}, title = {{DoA} Estimation with Reflectarray According to Single Pixel Camera Principle}, booktitle = {3rd International Workshop on Compressed Sensing applied to Radar}, month = Jun, year = 2015, address = {Pisa, Italy}, doi = {10.1109/CoSeRa.2015.7330306} }

Abstract – This paper suggests using a tunable reflectarray as a hardware source of Sensing Functions (SFs) for Direction of Arrival (DoA) estimation based on Compressed Sensing (CS). Reflectarray is much more scalable than a conventional antenna array. This higher scalability can be exploited to build a measurement hardware with large aperture and high number of degrees of freedom. We introduce the simplified reflectarray propagation model, based on which we propose a number of possible measurement architectures, for each of them we show how the Sensing Matrix (SM) will be defined. Finally, a typical non-sparse beampattern is obtained using numeric simulation.

S. Skoblikov, M. Ibrahim, F. Römer, and R. S. Thomä, Numerical Assessment of Reflectarray Applicability to CS-based DoA Estimation, in Proceedings of the International Radar Symposium 2015, Dresden, Germany, Jun 2015, doi:10.1109/IRS.2015.7226353.

@INPROCEEDINGS{SIRT:15, author = {S. Skoblikov and M. Ibrahim and F. Römer and R. S. Thomä}, title = {Numerical Assessment of Reflectarray Applicability to {CS-based} {DoA} Estimation}, booktitle = {Proceedings of the International Radar Symposium 2015}, month = Jun, year = 2015, address = {Dresden, Germany}, doi = {10.1109/IRS.2015.7226353} }

Abstract – This paper examines the performance of tunable reflectarray for Direction of Arrival (DoA) estimation based on Compressed Sensing (CS). Using a reflectarray lifts the limitation on array size compared to classical antenna arrays and provides significantly increased number and complexity of the Sensing Functions (SFs), which boosts the performance of the CS. The paper presents the data model of the reflectarray and analyzes its performance in terms of manifold
spatial correlation.

A. Lavrenko, F. Römer, G. Del Galdo, R. S. Thomä, and O. Arikan, Detection of time-varying support via rank evolution approach for effective joint sparse recovery, in Proceedings of the 23rd European Signal Processing Conference (EUSIPCO-2015), Nice, France, Aug 2015, doi:10.1109/EUSIPCO.2015.7362677.

@INPROCEEDINGS{LRDTA:15, author = {A. Lavrenko and F. Römer and G. {Del Galdo} and R. S. Thomä and O. Arikan}, title = {Detection of time-varying support via rank evolution approach for effective joint sparse recovery}, booktitle = {Proceedings of the 23rd European Signal Processing Conference (EUSIPCO-2015)}, month = Aug, year = 2015, address = {Nice, France}, doi = {10.1109/EUSIPCO.2015.7362677} }

Abstract – Efficient recovery of sparse signals from few linear projections is a primary goal in a number of applications, most notably in a recently-emerged area of compressed sensing. The multiple measurement vector (MMV) joint sparse recovery is an extension of the single vector sparse recovery problem to the case when a set of consequent measurements share the same support. In this contribution we consider a modification of the MMV problem where the signal support can change from one block of data to another and the moment of change is not known in advance. We propose an approach for the support change detection based on the sequential rank estimation of a windowed block of the measurement data. We show that under certain conditions it allows for an unambiguous determination of the moment of change, provided that the consequent data vectors are incoherent to each other.

M. Ibrahim, F. Römer, and G. Del Galdo, An Adaptively Focusing Measurement Design for Compressed Sensing Based DOA Estimation, in Proceedings of the 23rd European Signal Processing Conference (EUSIPCO-2015), Nice, France, Aug 2015, doi:10.1109/EUSIPCO.2015.7362505.

@INPROCEEDINGS{IRD:15, author = {M. Ibrahim and F. Römer and G. {Del Galdo}}, title = {An Adaptively Focusing Measurement Design for Compressed Sensing Based {DOA} Estimation}, booktitle = {Proceedings of the 23rd European Signal Processing Conference (EUSIPCO-2015)}, month = Aug, year = 2015, address = {Nice, France}, doi = {10.1109/EUSIPCO.2015.7362505} }

Abstract – In this paper we investigate the design of the measurement matrix for applying Compressed Sensing (CS) to the problem of Direction Of Arrival (DOA) estimation with antenna arrays. Instead of choosing the coefficients of the compression matrix randomly, we propose a systematic design methodology for constructing a measurement matrix that focuses the array towards a specific area of interest and thereby achieves a superior DOA estimation performance. The focusing is performed in a sequential manner, i.e., we start with a uniform measurement design from which regions of interest can be extracted that the subsequent measurements then focus on. By continuously updating these target regions, gradual movement of the sources can also be tracked over time. Numerical results demonstrate that the focused measurements possess a superior SNR leading to significantly enhanced DOA estimates.

J. Steinwandt, F. Römer, and M. Haardt, Deterministic Cramer-Rao Bound for a Mixture of Circular and Strictly Non-Circular Signals, in Proceedings of the Twelfth International Symposium on Wireless Communication Systems (ISWCS 2015), Brussels, Belgium, Aug 2015, doi:10.1109/ISWCS.2015.7454431.

@INPROCEEDINGS{SRH:15, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {Deterministic {Cramer-Rao} Bound for a Mixture of Circular and Strictly {Non-Circular} Signals}, booktitle = {Proceedings of the Twelfth International Symposium on Wireless Communication Systems (ISWCS 2015)}, month = Aug, year = 2015, address = {Brussels, Belgium}, doi = {10.1109/ISWCS.2015.7454431} }

Abstract – The problem of estimating the signal parameters under a received mixture of circular and strictly second-order (SO) non-circular (NC) signals has recently attracted considerable attention. Several high-resolution algorithms have been proposed for this scenario that improve the estimation accuracy of the traditional schemes and simultaneously increase the number of resolvable signals. In this paper, as a benchmark for this new class of algorithms, we derive a closed-form expression of the deterministic Cramer-Rao bound (CRB), termed deterministic C-NC CRB, for the corresponding data model. The obtained result allows to assess the maximum achievable performance gain in this scenario. The derivation is based on the Slepian-Bangs formula, which is still applicable in the deterministic data assumption. Simulation results show that the C-NC CRB decreases when the number of strictly non-circular signals within a fixed number of sources increases. In this case, also the individual bounds of the circular signals decrease, which suggests that the presence of strictly non-circular sources reduces the estimation error of the circular signals.

M. Ibrahim, F. Römer, N. Hadaschik, H. M. Tröger, B. Sackenreuter, N. Franke, J. Robert, and G. Del Galdo, Compressed Temporal Synchronization With Opportunistic Signals, in Proceedings of the 49-th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov 2015, doi:10.1109/ACSSC.2015.7421114.

@INPROCEEDINGS{IRHTSFRD:15, author = {M. Ibrahim and F. Römer and N. Hadaschik and H. M. Tröger and B. Sackenreuter and N. Franke and J. Robert and G. {Del Galdo}}, title = {Compressed Temporal Synchronization With Opportunistic Signals}, booktitle = {Proceedings of the 49-th Asilomar Conference on Signals, Systems, and Computers}, month = Nov, year = 2015, address = {Pacific Grove, CA}, doi = {10.1109/ACSSC.2015.7421114} }

Abstract – In this paper we propose a temporal synchronization method using opportunistic signals for wireless networks. Instead of broadcasting a dedicated broadband signal throughout the network for synchronization, high-bandwidth opportunistic signals already existing in the environment can be used. To avoid the necessity that all the nodes in the network are able to decode the opportunistic reference signal, a central node should receive the reference signal and then sends it again to all other nodes. Using ideas from the compressed sensing (CS) area, the high-bandwidth reference signal to be transmitted can be compressed efficiently before being sent to the other nodes, while still achieving an accurate correlation function compared to the low bandwidth reference signal scenario. In this way, only a low-bandwidth signal needs to be transmitted. Numerical results demonstrate that the proposed compressed technique achieves a similar performance at a much lower cost compared to using the high-bandwidth opportunistic signal directly.

B. Oezer, A. Lavrenko, S. Gezici, F. Römer, G. Del Galdo, and O. Arikan, Adaptive Measurement Matrix Design for Compressed DoA Estimation with Sensor Arrays, in Proceedings of the 49-th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov 2015, doi:10.1109/ACSSC.2015.7421455.

@INPROCEEDINGS{OLGRDA:15, author = {B. Oezer and A. Lavrenko and S. Gezici and F. Römer and G. {Del Galdo} and O. Arikan}, title = {Adaptive Measurement Matrix Design for Compressed {DoA} Estimation with Sensor Arrays}, booktitle = {Proceedings of the 49-th Asilomar Conference on Signals, Systems, and Computers}, month = Nov, year = 2015, address = {Pacific Grove, CA}, doi = {10.1109/ACSSC.2015.7421455} }

Abstract – We propose a novel adaptive design technique for compressive 3-D Direction of Arrival (DoA) estimation with sensor arrays. Common CS measurement matrix designs do not necessarily yield the best performance in terms of a specific processing task. Therefore we apply a design technique based on the minimization of the Cramer-Rao Lower Bound (CRLB) and develop specific approaches for two distinct DoA applications: detection of the newly appearing targets (surveillance mode) and tracking of the previously detected targets (tracking mode). Numerical results suggest that the developed designs allow to provide the near optimal performance in terms of the CRLB.

R. K. Miranda, J. P. C. L. Da Costa, F. Römer, A. Almeida, and G. Del Galdo, Generalized Sidelobe Cancellers for Multidimensional Separable Arrays, in Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2015), Cancun, Mexico, Dec 2015, doi:10.1109/CAMSAP.2015.7383769.

@INPROCEEDINGS{MDRAD:15, author = {R. K. Miranda and J. P. C. L. {Da Costa} and F. Römer and A. Almeida and G. {Del Galdo}}, title = {Generalized Sidelobe Cancellers for Multidimensional Separable Arrays}, booktitle = {Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2015)}, month = Dec, year = 2015, address = {Cancun, Mexico}, doi = {10.1109/CAMSAP.2015.7383769} }

Abstract – The usage of antenna arrays brought innumerable benefits to radio systems in the last decades. Arrays can have multidimensional structures that can be exploited to achieve superior performance and lower complexity. However, the literature has not explored yet all the advantages arising from these features. This paper uses tensors to provide a method to design efficient beamformers for multidimensional antenna arrays. In this work, the generalized sidelobe canceller (GSC) is extended to a multidimensional array to create the proposed $R$-Dimensional GSC (R-D GSC). The proposed scheme has a lower computational complexity and, under certain conditions, exhibits an improved signal to interference and noise ratio (SINR).

### 2014

F. Römer, M. Ibrahim, R. Alieiev, M. Landmann, R. S. Thomä, and G. Del Galdo, Polarimetric Compressive Sensing Based DOA Estimation, in Proceedings of the 18th International ITG Workshop on Smart Antennas (WSA'14), Erlangen, Germany, Mar 2014.

@INPROCEEDINGS{RIALTD:14, author = {F. Römer and M. Ibrahim and R. Alieiev and M. Landmann and R. S. Thomä and G. {Del Galdo}}, title = {Polarimetric Compressive Sensing Based {DOA} Estimation}, booktitle = {Proceedings of the 18th International ITG Workshop on Smart Antennas (WSA'14)}, month = Mar, year = 2014, address = {Erlangen, Germany} }

Abstract – In this paper, we discuss direction of arrival (DOA) estimation
based on the full polarimetric array manifold using a
Compressive Sensing (CS)-based formulation. We first show
that the existing non-polarimetric CS-based description of the
DOA estimation problem can be extended to the polarimetric
setting, giving rise to an amplitude vector that possesses a
structured sparsity. We explain how DOAs can be estimated
from this vector for incoming waves of arbitrary polarization.
We then discuss the "gridding" problem, i.e., the effect of
DOAs that are not on the sampling grid which was chosen
for the discretization of the array manifold. We propose an
estimator of these grid offsets which extends earlier work to
the polarimetric setting. Numerical results demonstrate that
the proposed scheme can achieve a DOA estimation accuracy
close to the Cramér-Rao Bound for arbitrarily polarized
waves.

F. Römer, G. Del Galdo, and M. Haardt, Tensor-based algorithms for learning multidimensional separable dictionaries, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014), Florence, Italy, May 2014.

@INPROCEEDINGS{RDH:14, author = {F. Römer and G. {Del Galdo} and M. Haardt}, title = {Tensor-based algorithms for learning multidimensional separable dictionaries}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014)}, month = May, year = 2014, address = {Florence, Italy} }

Abstract – Compressive Sensing (CS) allows to acquire signals at sampling rates significantly lower than the Nyquist rate, provided that the signals possess a sparse representation in an appropriate basis. However, in some applications of CS, the dictionary providing the sparse description is partially or entirely unknown. It has been shown that dictionary learning algorithms are able to estimate the basis vectors from a set of training samples. In some applications the dictionary is multidimensional, e.g., when estimating jointly azimuth and elevation in a 2-D direction of arrival (DOA) estimation context. In this paper we show that existing dictionary learning algorithms can be extended to exploit this structure, thereby providing a more accurate estimate of the dictionary. As examples we choose two prominent dictionary learning algorithms, the method of optimal directions (MOD) and the KSVD algorithm. We propose tensor-based multidimensional extensions for both algorithms and show their improved performances numerically.

M. Ibrahim, F. Römer, R. Alieiev, G. Del Galdo, and R. S. Thomä, On the estimation of grid offsets in CS-based direction-of-arrival estimation, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014), Florence, Italy, May 2014.

@INPROCEEDINGS{IRADT:14, author = {M. Ibrahim and F. Römer and R. Alieiev and G. {Del Galdo} and R. S. Thomä}, title = {On the estimation of grid offsets in {CS-based} direction-of-arrival estimation}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014)}, month = May, year = 2014, address = {Florence, Italy} }

Abstract – Compressed Sensing (CS) has been recently applied to direction of arrival (DOA) estimation, leveraging the fact that a superposition of planar wavefronts corresponds to a sparse angular power spectrum. However, to apply the CS framework we need to construct a finite dictionary by sampling the angular domain with a predefined sampling grid. Therefore, the target locations are almost surely not located exactly on a subset of these grid points. This leads to a model mismatch which deteriorates the performance of the estimators. In this paper we take an analytical approach to investigate the effect of such grid offsets on the recovered spectra. We show that each off-grid source can be well approximated by the closest two neighboring points on the grid. We propose a simple and efficient scheme to estimate the grid offset for a single source or multiple well-separated sources. We also discuss a numerical procedure for the joint estimation of the grid offsets of closer sources. Simulation results demonstrate the effectiveness of the proposed methods.

J. Steinwandt, F. Römer, and M. Haardt, Asymptotic Performance Analysis of ESPRIT-Type Algorithms for Circular and Strictly Non-circular Sources With Spatial Smoothing, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014), Florence, Italy, May 2014.

@INPROCEEDINGS{SRH:14, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {Asymptotic Performance Analysis of {ESPRIT-Type} Algorithms for Circular and Strictly Non-circular Sources With Spatial Smoothing}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014)}, month = May, year = 2014, address = {Florence, Italy} }

J. Steinwandt, F. Römer, and M. Haardt, Analytical ESPRIT-Based Performance Study: What Can We Gain From Non-Circular Sources?, in Proceedings of the 8-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2014), A Coruna, Spain, Jun 2014.

@INPROCEEDINGS{SRH:14, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {Analytical {ESPRIT-Based} Performance Study: What Can We Gain From {Non-Circular} Sources?}, booktitle = {Proceedings of the 8-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2014)}, month = Jun, year = 2014, address = {A Coruna, Spain} }

Abstract – It is well known that parameter estimation algorithms designed to exploit the prior knowledge of the strict second-order (SO) non-circularity (NC) of incident signals can estimate the parameters of twice as many sources and achieve significant gains in reducing the estimation error. So far, the magnitude of the NC gain could only be quantified through simulations. In this paper, we adopt a first-order performance analysis framework to analytically compute the asymptotic NC gain of NC Standard ESPRIT. As finding a generic expression for arbitrary scenarios is an intricate task, we consider the case of two uncorrelated strictly non-circular sources captured by a uniform linear array (ULA). We assume a maximum phase separation of the sources, which yields the largest NC gain. For this scenario, we derive simplified asymptotic mean squared error (MSE) expressions of NC Standard ESPRIT and Standard ESPRIT, which are used to compute the NC gain. While the simplified MSE expression of Standard ESPRIT depends on the source separation, we show that if NC Standard ESPRIT is applied in this case, the two non-circular sources entirely decouple. Thus, the NC gain can theoretically approach infinity if the separation of the two sources tends to zero. Our derived expressions are verified by simulation results.

F. Römer, A. Lavrenko, G. Del Galdo, T. Hotz, O. Arikan, and R. S. Thomä, Sparsity Order Estimation for Single Snapshot Compressed Sensing, in Proceedings of the 48-th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov 2014.

@INPROCEEDINGS{RLDHAT:14, author = {F. Römer and A. Lavrenko and G. {Del Galdo} and T. Hotz and O. Arikan and R. S. Thomä}, title = {Sparsity Order Estimation for Single Snapshot Compressed Sensing}, booktitle = {Proceedings of the 48-th Asilomar Conference on Signals, Systems, and Computers}, month = Nov, year = 2014, address = {Pacific Grove, CA} }

Abstract – In this paper we discuss the estimation of the sparsity order for a Compressed Sensing scenario where only a single snapshot is available. We demonstrate that a specific design of the sensing matrix enables us to transform this problem into the estimation of a matrix rank in the presence of additive noise. Thereby, we can apply existing model order selection algorithms to determine the sparsity order. We also argue that the proposed sensing matrix design may have benefits that go beyond the estimation of the sparsity both for the measurement as well as for the reconstruction strategy.

A. Lavrenko, F. Römer, G. Del Galdo, R. S. Thomä, and O. Arikan, An empirical eigenvalue threshold test for sparsity level estimation from compressed measurements, in Proceedings of the 22-nd European Signal Processing Conference (EUSIPCO-2014), Lisbon, Portugal, Sep 2014.

@INPROCEEDINGS{LRDTA:14, author = {A. Lavrenko and F. Römer and G. {Del Galdo} and R. S. Thomä and O. Arikan}, title = {An empirical eigenvalue threshold test for sparsity level estimation from compressed measurements}, booktitle = {Proceedings of the 22-nd European Signal Processing Conference (EUSIPCO-2014)}, month = Sep, year = 2014, address = {Lisbon, Portugal} }

Abstract – Compressed sensing allows for a significant reduction of the number of measurements when the signal of interest is of a sparse nature. Most computationally efficient algorithms for signal recovery rely on some knowledge of the sparsity level, i.e., the number of non-zero elements. However, the sparsity level is often not known a priori and can even vary with time. In this contribution we show that it is possible to estimate the sparsity level directly in the compressed domain, provided that multiple independent observations are available. In fact, one can use classical model order selection algorithms for this purpose. Nevertheless, due to the influence of the measurement process they may not perform satisfactorily in the compressed sensing setup. To overcome this drawback, we propose an approach which exploits the empirical distributions of the noise eigenvalues. We demonstrate its superior performance compared to state-of-the-art model order estimation algorithms numerically.

A. Lavrenko, F. Römer, G. Del Galdo, and R. S. Thomä, On the Sensing Matrix Performance for Support Recovery of Noisy Sparse Signals, in Proceedings of the 2nd IEEE Global Conference on Signal and Information Processing (GlobalSIP), Atlanta, GA, Dec 2014.

@INPROCEEDINGS{LRDT:14, author = {A. Lavrenko and F. Römer and G. {Del Galdo} and R. S. Thomä}, title = {On the Sensing Matrix Performance for Support Recovery of Noisy Sparse Signals}, booktitle = {Proceedings of the 2nd IEEE Global Conference on Signal and Information Processing (GlobalSIP)}, month = Dec, year = 2014, address = {Atlanta, GA} }

Abstract – The compressed sensing paradigm allows a significant reduction of the sampling rate compared to the one dictated by the Nyquist sampling theorem, given that the signal of interest can be represented by small number of non-zero coefficients in a certain basis. In this contribution we analyze the explicit dependence between a deterministic sensing matrix and the support recovery performance. We do so by deriving the probability of wrong support recovery and output SNR in the presence of additive input noise. Due to tractability, a closed-form analytical expression can only be found for the 1-sparse case. However, we present numerical evidence that the expressions obtained for 1-sparse case qualitatively capture the trend for the more general N-sparse case as well. Additionally, the investigations reveal that when designing a measurement, along with the low coherence one has to ensure a stable output SNR. We provide an example of a sensing matrix that, despite having slightly higher coherence, is superior compared to the conventional random matrix with i.i.d. Gaussian entries in terms of the support recovery performance due to providing a constant output SNR.

### 2013

J. Steinwandt, F. Römer, and M. Haardt, Performance Analysis of ESPRIT-Type Algorithms for Non-Circular Source, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013), Vancouver, Canada, May 2013.

@INPROCEEDINGS{SRH:13, author = {J. Steinwandt and F. Römer and M. Haardt}, title = {Performance Analysis of {ESPRIT-Type} Algorithms for {Non-Circular} Source}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013)}, month = May, year = 2013, address = {Vancouver, Canada} }

Abstract – High-resolution parameter estimation algorithms designed to benefit from the presence of non-circular (NC) source signals allow for an increased identifiability and a lower estimation error. In this paper, we present a 1-D first-order performance analysis of the NC standard ESPRIT and NC Unitary ESPRIT estimation schemes for strictly second-order (SO) non-circular sources, where NC Unitary ESPRIT has a lower complexity and a better performance in the low signal-to-noise ratio (SNR) regime. Our derived expressions are asymptotic in the effective SNR and explicit in the noise realizations, i.e., no assumptions about the noise statistics are necessary. As a main result, we show that the asymptotic performance of both NC ESPRIT-type algorithms is identical in the effective SNR and that NC Unitary ESPRIT is even applicable to array geometries without a centro-symmetric structure as required for Unitary ESPRIT.

J. Zhang, M. Haardt, and F. Römer, Robust Design of Block Diagonalization Using Perturbation Analysis, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013), Vancouver, Canada, May 2013.

@INPROCEEDINGS{ZHR:13, author = {J. Zhang and M. Haardt and F. Römer}, title = {Robust Design of Block Diagonalization Using Perturbation Analysis}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013)}, month = May, year = 2013, address = {Vancouver, Canada} }

Abstract – Block diagonalization (BD) is a low-complexity linear precoding technique for multi-user MIMO (MU-MIMO) downlink systems, which can provide a performance that is close to the MU-MIMO capacity. However, imperfect channel state information (CSI) will result in a degraded performance of the BD scheme. Thus, studying the performance of BD under imperfect CSI is crucial for a practical system design since the robustness of BD to real-world imperfections should be verified. In this paper we apply a first-order perturbation analysis of the SVD to derive analytic expressions of the signal to interference plus noise ratio (SINR) for each subchannel of each UT using BD in presence of imperfect CSI. To demonstrate the usefulness of these expressions, a robust BD technique via worst SINR maximization is developed. Numerical simulations show the accuracy and the usefulness of the derived
analytical results.

F. Römer and G. Del Galdo, Tensor-Based Dictionary Learning for Multidimensional Sparse Recovery: the K-HOSVD, in 2nd International Workshop on Compressed Sensing applied to Radar, Bonn, Germany, Sep 2013.

@INPROCEEDINGS{RD:13, author = {F. Römer and G. {Del Galdo}}, title = {{Tensor-Based} Dictionary Learning for Multidimensional Sparse Recovery: the {K-HOSVD}}, booktitle = {2nd International Workshop on Compressed Sensing applied to Radar}, month = Sep, year = 2013, address = {Bonn, Germany} }

F. Römer, R. Alieiev, M. Ibrahim, G. Del Galdo, and R. S. Thomä, An Analytical Study of Sparse Recovery Algorithms in Presence of an Off-Grid Source, in 2nd International Workshop on Compressed Sensing applied to Radar, Bonn, Germany, Sep 2013.

@INPROCEEDINGS{RAIDT:13, author = {F. Römer and R. Alieiev and M. Ibrahim and G. {Del Galdo} and R. S. Thomä}, title = { { An} Analytical Study of Sparse Recovery Algorithms in Presence of an {Off-Grid} Source}, booktitle = {2nd International Workshop on Compressed Sensing applied to Radar}, month = Sep, year = 2013, address = {Bonn, Germany} }

A. Lavrenko, F. Römer, R. S. Thomä, and G. Del Galdo, On the Choice of Mixing Sequences for SNR Improvement in Modulated Wideband Convertor, in 2nd International Workshop on Compressed Sensing applied to Radar, Bonn, Germany, Sep 2013.

@INPROCEEDINGS{LRTD:13, author = {A. Lavrenko and F. Römer and R. S. Thomä and G. {Del Galdo}}, title = { { On} the Choice of Mixing Sequences for {SNR} Improvement in Modulated Wideband Convertor}, booktitle = {2nd International Workshop on Compressed Sensing applied to Radar}, month = Sep, year = 2013, address = {Bonn, Germany} }

K. Liu, H. C. So, J. P. C. L. Da Costa, F. Römer, L. Huang, and R. T. de Sousa Jr., On the Use of Order Selection Rules for Accurate Parameter Estimation in Threshold Region, in Proceedings of the 21-th European Signal Processing Conference (EUSIPCO-2013), Marrakech, Morocco, Sep 2013.

@INPROCEEDINGS{LSDRHd:13, author = {K. Liu and H. C. So and J. P. C. L. {Da Costa} and F. Römer and L. Huang and R. T. {de Sousa Jr.}}, title = {On the Use of Order Selection Rules for Accurate Parameter Estimation in Threshold Region}, booktitle = {Proceedings of the 21-th European Signal Processing Conference (EUSIPCO-2013)}, month = Sep, year = 2013, address = {Marrakech, Morocco} }

Abstract – Finding the number of signals is crucial to parametric direction-of-arrival (DOA) estimation methods such as MUSIC and ESPRIT. In challenging scenarios such as low signal-to-noise ratio (SNR) and/or presence of closely-spaced sources, only part of the parameters can be accurately estimated while others cannot. The number of former estimates is termed as the effective model order (EMO). We first propose a procedure to determine the EMO via Monte Carlo simulation. Ideally an order selection rule should return a source number estimate equal to EMO, since using an overestimated signal number larger than the EMO in a parameter estimator introduces inaccurate parameter estimates, which is a waste of resources in some applications, while using an underestimate renders some strong signals being treated as noise, which causes an accuracy loss in their parameter estimates. We propose to combine an under-enumerator with an over-enumerator for accurate parameter estimation in the threshold region. Simulations results using the combination of the Baysian information criterion with Akaike information criterion in ESPRIT show that our proposal retains the benefit of the under-enumerators with only accurate estimates while remarkably improves the estimation accuracy.

B. Song, F. Römer, and M. Haardt, A tensor-based subspace method for blind estimation of MIMO channels, in Proceedings of the Tenth International Symposium on Wireless Communication Systems (ISWCS 2013), Ilmenau, Germany, Aug 2013.

@INPROCEEDINGS{SRH:13, author = {B. Song and F. Römer and M. Haardt}, title = {A tensor-based subspace method for blind estimation of {MIMO} channels}, booktitle = {Proceedings of the Tenth International Symposium on Wireless Communication Systems (ISWCS 2013)}, month = Aug, year = 2013, address = {Ilmenau, Germany} }

J. Steinwandt, F. Römer, and M. Haardt, Performance Analysis of ESPRIT-Type Algorithms for Strictly Non-Circular Sources Using Structured Least Squares, in Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2013), Saint Martin, French Antilles, Dec 2013.

@INPROCEEDINGS{SRH:13, author = {J. Steinwandt and F. Römer and M. Haardt}, title = { Performance Analysis of {ESPRIT-Type} Algorithms for Strictly {Non-Circular} Sources Using Structured Least Squares}, booktitle = {Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2013)}, month = Dec, year = 2013, address = {Saint Martin, French Antilles} }

F. Römer, E. Kasnakli, Y. Cheng, and M. Haardt, Tensor subspace tracking via Kronecker structured projections (TeTraKron), in Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2013), Saint Martin, French Antilles, Dec 2013.

@INPROCEEDINGS{RKCH:13, author = {F. Römer and E. Kasnakli and Y. Cheng and M. Haardt}, title = {Tensor subspace tracking via Kronecker structured projections {(TeTraKron)}}, booktitle = {Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2013)}, month = Dec, year = 2013, address = {Saint Martin, French Antilles} }

Abstract – We present a framework for Tensor-based subspace
Tracking via Kronecker-structured projections (TeTraKron).
TeTraKron allows to extend arbitrary matrix-based subspace
tracking schemes to track the tensor-based subspace estimate.
The latter can be computed via a structured projection applied
to the matrix-based subspace estimate which enforces the multidimensional
structure in a computationally efficient fashion. This
projection is tracked by considering all matrix rearrangements
of the signal tensor jointly, which can be efficiently realized via
parallel processing. In time-varying scenarios, the TeTraKron-based
tracking schemes outperform the original algorithms as
well as the batch solutions provided by the SVD and the HOSVD.

### 2012

J. Zhang, F. Römer, M. Haardt, A. Khabbazibasmenj, and S. A. Vorobyov, Sum rate maximization for multi-pair two-way relaying with single-antenna amplify and forward relays, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2012), Kyoto, Japan, Mar 2012.

@INPROCEEDINGS{ZRHKV:12, author = {J. Zhang and F. Römer and M. Haardt and A. Khabbazibasmenj and S. A. Vorobyov}, title = {Sum rate maximization for multi-pair two-way relaying with single-antenna amplify and forward relays}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2012)}, month = Mar, year = 2012, address = {Kyoto, Japan} }

A. Khabbazibasmenj, S. A. Vorobyov, F. Römer, and M. Haardt, Polynomial-time DC (POTDC) for sum-rate maximization in two-way AF MIMO relaying, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2012), Kyoto, Japan, Mar 2012.

@INPROCEEDINGS{KVRH:12, author = {A. Khabbazibasmenj and S. A. Vorobyov and F. Römer and M. Haardt}, title = {Polynomial-time {DC} {(POTDC)} for sum-rate maximization in two-way {AF} {MIMO} relaying}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2012)}, month = Mar, year = 2012, address = {Kyoto, Japan} }

M. Muma, Y. Cheng, F. Römer, M. Haardt, and A. M. Zoubir, Robust source number enumeration for R-dimensional arrays in case of brief sensor failures, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2012), Kyoto, Japan, Mar 2012.

@INPROCEEDINGS{MCRHZ:12, author = {M. Muma and Y. Cheng and F. Römer and M. Haardt and A. M. Zoubir}, title = {Robust source number enumeration for R-dimensional arrays in case of brief sensor failures}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2012)}, month = Mar, year = 2012, address = {Kyoto, Japan} }

J. Zhang, N. Bornhorst, F. Römer, M. Haardt, and M. Pesavento, Optimal and Suboptimal Beamforming for Multi-Operator Two-Way Relaying with a MIMO Amplify-and-Forward Relay, in Proceedings of the 16th International ITG Workshop on Smart Antennas (WSA'12), Dresden, Germany, Mar 2012.

@INPROCEEDINGS{ZBRHP:12, author = {J. Zhang and N. Bornhorst and F. Römer and M. Haardt and M. Pesavento}, title = {Optimal and Suboptimal Beamforming for {Multi-Operator} {Two-Way} Relaying with a {MIMO} {Amplify-and-Forward} Relay}, booktitle = {Proceedings of the 16th International ITG Workshop on Smart Antennas (WSA'12)}, month = Mar, year = 2012, address = {Dresden, Germany} }

Abstract – In this work, we consider optimal and suboptimal
beamforming designs in a multi-operator two-way relaying network
with a multiple-input-multiple-output (MIMO) amplifyand-
forward (AF) relay. Such a network is interference limited
and thus, an interference nulling strategy is reasonable. We first
derive the necessary condition for interference nulling and introduce
a closed-form algebraic solution, i.e., the projection based
separation of multiple operators (ProBaSeMO). This solution can
be adjusted to satisfy various system design criteria. However,
it is only suboptimal. For the design of optimal relay transmit
strategies, we study two QoS design criteria for the network. The
first is to minimize the relay transmit power subject to a signalto-
interference-plus-noise ratio (SINR) constraints at each user.
The second is the SINR balancing technique with a relay transmit
power constraint. These two problems are non-convex. However,
we show that both problems can be efficiently solved using convex
approximation techniques. The simulation results verify the suboptimality
of the ProBaSeMO method when compared to the
optimal designs. However, the ProBaSeMO technique approaches
optimality as the number of relay antennas increases and enjoys
a significantly reduced computational complexity.

M. Weis, F. Römer, M. Haardt, and P. Husar, Dual-Symmetric Parallel Factor Analysis Using Procrustes Estimation and Khatri-Rao Factorization, in Proceedings of the 20-th European Signal Processing Conference (EUSIPCO-2012), Bucharest, Romania, Aug 2012.

@INPROCEEDINGS{WRHH:12, author = {M. Weis and F. Römer and M. Haardt and P. Husar}, title = {{Dual-Symmetric} Parallel Factor Analysis Using Procrustes Estimation and {Khatri-Rao} Factorization}, booktitle = {Proceedings of the 20-th European Signal Processing Conference (EUSIPCO-2012)}, month = Aug, year = 2012, address = {Bucharest, Romania} }

Abstract – The higher-order tensor analysis of multi-channel signals and systems has developed to one of the key signal processing areas over the past few years. In this contribution we present a new algorithm for the Parallel Factor (PARAFAC) analysis of tensors obeying a special kind of symmetry, which we refer to as dual-symmetry. This iterative algorithm is based on alternating Procrustes estimation and Khatri-Rao factorization (ProKRaft). The PARAFAC analysis of dual-symmetric tensors is of high interest for every correlation-based multi-channel algorithm, such as analytical channel models. It can also be used for the computation of the Independent Component Analysis (ICA), which is one of the most frequently applied methods in signal processing. Based on Monte-Carlo simulations we show that the new algorithm outperforms other state-of-the-art approaches while being very robust with respect to outliers. Furthermore, we evaluate its performance for the computation of the ICA also in comparison to other ICA algorithms.

Y. Cheng, S. Li, J. Zhang, F. Römer, M. Haardt, Y. Zhou, and M. Dong, Linear Precoding-based Geometric Mean Decomposition (LP-GMD) for Multi-User MIMO Systems, in Proceedings of the Ninth International Symposium on Wireless Communication Systems (ISWCS 2012), Paris, France, Aug 2012.

@INPROCEEDINGS{CLZRHZD:12, author = {Y. Cheng and S. Li and J. Zhang and F. Römer and M. Haardt and Y. Zhou and M. Dong}, title = {Linear Precoding-based Geometric Mean Decomposition {(LP-GMD)} for {Multi-User} {MIMO} Systems}, booktitle = {Proceedings of the Ninth International Symposium on Wireless Communication Systems (ISWCS 2012)}, month = Aug, year = 2012, address = {Paris, France} }

S. Li, Y. Cheng, J. Zhang, F. Römer, B. Song, M. Haardt, Y. Zhou, and M. Dong, Efficient Spatial Scheduling and Precoding Algorithms for MC MU MIMO System, in Proceedings of the Ninth International Symposium on Wireless Communication Systems (ISWCS 2012), Paris, France, Aug 2012.

@INPROCEEDINGS{LCZRSHZD:12, author = {S. Li and Y. Cheng and J. Zhang and F. Römer and B. Song and M. Haardt and Y. Zhou and M. Dong}, title = {Efficient Spatial Scheduling and Precoding Algorithms for {MC} {MU} {MIMO} System}, booktitle = {Proceedings of the Ninth International Symposium on Wireless Communication Systems (ISWCS 2012)}, month = Aug, year = 2012, address = {Paris, France} }

Y. Cheng, N. Song, F. Römer, M. Haardt, H. Henniger, R. Metzig, and E. Diedrich, Satellite ground stations with electronic beam steering, in Proceedings of the 1st IEEE-AESS Conference in Europa about Space and Satellite Telecommunications, Rome, Italy, Oct 2012.

@INPROCEEDINGS{CSRHHMD:12, author = {Y. Cheng and N. Song and F. Römer and M. Haardt and H. Henniger and R. Metzig and E. Diedrich}, title = {Satellite ground stations with electronic beam steering}, booktitle = {Proceedings of the 1st IEEE-AESS Conference in Europa about Space and Satellite Telecommunications}, month = Oct, year = 2012, address = {Rome, Italy} }

Abstract – In this work, we propose the electronic beam steering
via antenna arrays as a substitute for large parabolic antennas
at ground stations. We concentrate on two array geometries,
faceted arrays and hemispherical arrays. A thorough analysis
is carried out of the radiation characteristics, the array size, as
well as the antenna element distribution and spacing. Moreover,
in order to fulfill the requirement of the array design, that is, to
achieve a higher gain at low elevation angles where the longer
spacecraft to ground station distance leads to a larger range
loss, we propose to adjust the number of active elements, i.e.,
some antenna elements are turned on while others are turned
off according to the required level of antenna gain. This also
contributes to a concept of an optimized array design for this
specific application. In the simulations, the array optimization
for both array geometries is further investigated and realized
with a realistic ephemeris incorporated. The numerical results
support the proposal of replacing large reflector antennas by the
electronic beam steering via antenna arrays at ground stations.

S. Gherekhloo, B. Zafar, F. Römer, and M. Haardt, Impact of Synchronization Errors on Alamouti-STBC-based Cooperative MIMO Schemes, in Proceedings of the 7-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2012), Hoboken, NJ, Jul 2012.

@INPROCEEDINGS{GZRH:12, author = {S. Gherekhloo and B. Zafar and F. Römer and M. Haardt}, title = {Impact of Synchronization Errors on {Alamouti-STBC-based} Cooperative {MIMO} Schemes}, booktitle = {Proceedings of the 7-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2012)}, month = Jul, year = 2012, address = {Hoboken, NJ} }

Abstract – The effect of synchronization errors on the performance
of a cooperative MIMO scheme that uses the Alamouti
space-time code is studied in this paper. The focus is on finding
a lower bound of the received Signal to Interference and
Noise Ratio (SINR). The synchronization error, caused by the
distributed nature of the scheme, is considered as inaccurate
channel state information, which is modeled as an additive
deterministic norm-bounded inaccuracy matrix. A closed-form
expression is derived for the SINR. Using this, a closed-form
expression of the Bit Error Rate (BER) in the high SNR regime
for the worst case error vector is also derived. This worst case
performance is of interest to system designers as it helps them
to design the system with specific guarantees about the outage
behavior. One interesting observation from the presented results
is that the larger the synchronization error gets, the quicker we
reach the interference limited high SNR region, in which the
'MIMO benefits' are absent.

J. Zhang, F. Römer, and M. Haardt, Distributed Beamforming for Two-Way Relaying Networks with Individual Power Constraints, in Proceedings of the 46-th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov 2012.

@INPROCEEDINGS{ZRH:12, author = {J. Zhang and F. Römer and M. Haardt}, title = {Distributed Beamforming for {Two-Way} Relaying Networks with Individual Power Constraints}, booktitle = {Proceedings of the 46-th Asilomar Conference on Signals, Systems, and Computers}, month = Nov, year = 2012, address = {Pacific Grove, CA} }

Abstract – In this paper we study the sum rate maximization problem in a multi-pair two-way relaying network with multiple single antenna amplify-and-forward relays where each relay has its own transmit power constraint. The optimization problem is non-convex and in general NP-hard. First, we propose a monotonic optimization based algorithm.
Due to its high computational complexity, this algorithm can only be used as a benchmark. Afterwards, inspired by the polynomial time
difference of convex functions (POTDC) method, we develop a suboptimal solution which has lower complexity but comparable performance.
To further reduce the computational complexity, we propose two other algorithms, i.e., the total SINR eigen-beamformer and an interference neutralization based design which are the low SNR and high SNR approximations of the original optimization problem, respectively.
Simulation results show that all the proposed suboptimal methods only suffer small losses compared to the global optimal solution
especially when there is a sufficient number of relays in the network.

F. Römer, C. Schröter, and M. Haardt, A Semi-algebraic Framework for Approximate CP Decompositions via Joint Matrix Diagonalization and Generalized Unfoldings, in Proceedings of the 46-th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov 2012, doi:10.1109/ACSSC.2012.6489396.

@INPROCEEDINGS{RSH:12, author = {F. Römer and C. Schröter and M. Haardt}, title = {A Semi-algebraic Framework for Approximate {CP} Decompositions via Joint Matrix Diagonalization and Generalized Unfoldings}, booktitle = {Proceedings of the 46-th Asilomar Conference on Signals, Systems, and Computers}, month = Nov, year = 2012, address = {Pacific Grove, CA}, doi = {10.1109/ACSSC.2012.6489396} }

Abstract – The Canonical Polyadic (CP) decomposition of R-way arrays is a powerful tool in multilinear algebra. Algorithms to compute an approximate CP decomposition from noisy observations are often based on Alternating Least Squares (ALS) which may require a large number of iterations to converge. To avoid this drawback we investigate semi-algebraic approaches that algebraically reformulate the CP decomposition into a set of simultaneous matrix diagonalization (SMD) problems. In particular, we propose a SEmi-algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalization (SMD) and generalized unfoldings (SECSI-GU). SECSI-GU combines the benefits of two existing semi-algebraic approaches based on SMDs: the SECSI framework which selects the model estimate from multiple candidates obtained by solving multiple SMDs and the "Semi-Algebraic Tensor Decomposition" (SALT) algorithm which considers a "generalized" unfolding of the tensor in order to enhance the identifiability for tensors with R > 3 dimensions. The resulting SECSI-GU framework offers a large number of degrees of freedom to flexibly adapt the performance-complexity trade-off. As we show in numerical simulations, it outperforms SECSI and SALT for tensors with R > 3 dimensions.

### 2011

F. Römer and M. Haardt, Analytical Performance Assessment of 1-D Structured Least Squares, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2011), Prague, Czech Republic, May 2011.

@INPROCEEDINGS{RH:11, author = {F. Römer and M. Haardt}, title = {Analytical Performance Assessment of {1-D} Structured Least Squares}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2011)}, month = May, year = 2011, address = {Prague, Czech Republic} }

Abstract – In this paper, we derive the analytical performance of 1-D standard ESPRIT and 1-D Unitary ESPRIT using one iteration of Structured Least Squares to solve the shift invariance equations. First, we provide the estimation error of the k-th spatial frequency as an explicit expression of the noise realization, which requires no assumptions about the statistics of the noise. Then, we compute the statistical expectation over zero mean circularly symmetric white noise and provide explicit formulas for the resulting mean square errors. All expressions are asymptotic in the effective SNR, i.e., they become exact as either the number of snapshots or the SNR tends to infinity.

J. Zhang, F. Römer, and M. Haardt, Beamforming design for multi-user two-way relaying with MIMO amplify and forward relays, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2011), Prague, Czech Republic, May 2011.

@INPROCEEDINGS{ZRH:11, author = {J. Zhang and F. Römer and M. Haardt}, title = {Beamforming design for multi-user two-way relaying with {MIMO} amplify and forward relays}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2011)}, month = May, year = 2011, address = {Prague, Czech Republic} }

J. Li, J. Zhang, F. Römer, M. Haardt, C. Scheunert, E. Jorswieck, M. Hekrdla, and J. Sykora, Relay-assisted spectrum and infrastructure sharing between multiple operators, in Proceedings of the Future Network and Mobile Summit 2011, Warsaw, Poland, Jun 2011.

@INPROCEEDINGS{LZRHSJHS:11, author = {J. Li and J. Zhang and F. Römer and M. Haardt and C. Scheunert and E. Jorswieck and M. Hekrdla and J. Sykora}, title = {Relay-assisted spectrum and infrastructure sharing between multiple operators}, booktitle = {Proceedings of the Future Network and Mobile Summit 2011}, month = Jun, year = 2011, address = {Warsaw, Poland} }

Abstract – Relay-assisted physical resource sharing has the potential to improve the spectral efficiency, enhance the coverage, and decrease the expenditures for operators. By sharing the infrastructure (relay) and the spectrum, a new type of interference is created on the physical layer. Handling the interference demands novel physical layer techniques that are investigated in SAPHYRE project. In this paper, we describe
three relay sharing examples where the spectrum and the infrastructure (relay) are shared between multiple operators and introduce initial physical layer solutions. The first example considers a DS/CDMA system and studies the resource allocation
problem using a game theory approach. The results show that the proposed approach can achieve a significant gain in a heavily loaded system. The second one deals with a MIMO system and introduces a sub-optimal transmit strategy inspired by the interference channel. Numerical results demonstrate that the proposed approach results in significant gains in terms of sum rate compared to an exclusive assignment of the
resources. The last case is inspired by wireless network coding and shows the hierarchical exclusive code (HXC) design of a 2-source relay network.

Z. Lu, A. M. Zoubir, F. Römer, and M. Haardt, Source Enumeration Using the Bootstrap for Very Few Samples, in Proceedings of the 19-th European Signal Processing Conference (EUSIPCO-2011), Barcelona, Spain, Aug 2011.

@INPROCEEDINGS{LZRH:11, author = {Z. Lu and A. M. Zoubir and F. Römer and M. Haardt}, title = {Source Enumeration Using the Bootstrap for Very Few Samples}, booktitle = {Proceedings of the 19-th European Signal Processing Conference (EUSIPCO-2011)}, month = Aug, year = 2011, address = {Barcelona, Spain} }

Abstract – We consider the problem of source enumeration in array processing when only few samples are available. In this case, the noise eigenvalues spread, so that most existing methods, which assume equality of the noise eigenvalues implicitly, suffer large performance loss or even break down. We present a method based on hypothesis testing with the bootstrap. The test statistic is derived by using the exponential profile property of the noise eigenvalues. Simulations show the significant performance gain offered by the proposed method in terms of correctly detecting the number of sources for a very small sample size.

J. Li, F. Römer, and M. Haardt, Spectrum and Infrastructure Sharing in the MIMO Interference Relay Channels, in Proceedings of the 19-th European Signal Processing Conference (EUSIPCO-2011), Barcelona, Spain, Aug 2011.

@INPROCEEDINGS{LRH:11, author = {J. Li and F. Römer and M. Haardt}, title = {Spectrum and Infrastructure Sharing in the {MIMO} Interference Relay Channels}, booktitle = {Proceedings of the 19-th European Signal Processing Conference (EUSIPCO-2011)}, month = Aug, year = 2011, address = {Barcelona, Spain} }

Abstract – In this paper, single-stream transmission in the MIMO interference relay channel is studied. Two independent transceiver pairs with multiple antennas belonging to different operators communicate with the assistance of one relay, which operates in half-duplex mode and employs an amplify and forward strategy. The relay that is shared between the two operators also has multiple antennas. First, the interference
relay channel is converted to the conventional interference channel via a preliminarily determined relay amplification matrix. Various relay amplification matrices are investigated
for this conversion. Then, the flexible coordinated beamforming for the interference relay channel (IRC FlexCoBF) is proposed for the transceivers. The IRC FlexCoBF algorithm is compared to the alternative schemes proposed in the literature. Simulations show that IRC FlexCoBF achieves a better sum rate performance. Furthermore, a higher robustness to the interferences is demonstrated for IRC FlexCoBF compared to the state of the art. Simulation results show that by sharing a relay between two operators a significant gain in sum rate can be achieved compared to the relay channel.

F. Römer, N. Sarmadi, B. Song, M. Haardt, M. Pesavento, and A. B. Gershman, Tensor-Based Semi-Blind Channel Estimation for MIMO OSTBC-Coded Systems, in Proceedings of the 45-th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov 2011.

@INPROCEEDINGS{RSSHPG:11, author = {F. Römer and N. Sarmadi and B. Song and M. Haardt and M. Pesavento and A. B. Gershman}, title = {{Tensor-Based} {Semi-Blind} Channel Estimation for {MIMO} {OSTBC-Coded} Systems}, booktitle = {Proceedings of the 45-th Asilomar Conference on Signals, Systems, and Computers}, month = Nov, year = 2011, address = {Pacific Grove, CA} }

Abstract – We propose a novel semi-blind tensor-based MIMO
channel estimation scheme that employs orthogonal space-time block codes and per-antenna power loading at the transmitter. Our scheme eliminates the unknown transmit codewords and constructs a tensor model that contains the channel coefficients by performing post-processing at the receiver. Then, the channel matrix has been found through appropriate tensor decompositions of the post-processed data. Since the inherent structure of the data model has been exploited, we obtain a more accurate channel estimate compared to previously devised matrix-based approaches. Further, introduced ambiguities have been resolved via additional pilot symbols in a semi-blind manner. Simulation results demonstrate performance improvements of our proposed tensor-based approach with respect to some current state-of-the art semi-blind channel estimation schemes.

J. Li, F. Römer, and M. Haardt, Efficient Relay Sharing (EReSh) between multiple operators in amplify-and-forward relaying systems, in Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2011), San Juan, Puerto Rico, pp. 249 – 252, Dec 2011.

@INPROCEEDINGS{LRH:11, author = {J. Li and F. Römer and M. Haardt}, title = {Efficient Relay Sharing {(EReSh)} between multiple operators in amplify-and-forward relaying systems}, booktitle = {Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2011)}, pages = {249 -- 252}, month = Dec, year = 2011, address = {San Juan, Puerto Rico} }

J. P. C. L. Da Costa, F. Römer, D. Schulz, and R. T. de Sousa Jr., Subspace based Multi-Dimensional Model Order Selection in Colored Noise Scenarios, in Proceedings of the IEEE Information Theory Workshop (ITW 2011), Paraty, Brazil, Oct 2011.

@INPROCEEDINGS{DRSd:11, author = {J. P. C. L. {Da Costa} and F. Römer and D. Schulz and R. T. {de Sousa Jr.}}, title = {Subspace based {Multi-Dimensional} Model Order Selection in Colored Noise Scenarios}, booktitle = {Proceedings of the IEEE Information Theory Workshop (ITW 2011)}, month = Oct, year = 2011, address = {Paraty, Brazil} }

### 2010

B. Song, F. Römer, and M. Haardt, Using a new Structured Joint Congruence (STJOCO) Transformation of Hermitian matrices for precoding in multi-user MIMO systems, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2010), Dallas, TX, Mar 2010.

@INPROCEEDINGS{SRH:10, author = {B. Song and F. Römer and M. Haardt}, title = {Using a new Structured Joint Congruence {(STJOCO)} Transformation of Hermitian matrices for precoding in multi-user {MIMO} systems}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2010)}, month = Mar, year = 2010, address = {Dallas, TX} }

F. Römer, H. Becker, and M. Haardt, Analytical performance assessment for multi-dimensional Tensor-ESPRIT-type parameter estimation algorithms, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2010), Dallas, TX, Mar 2010.

@INPROCEEDINGS{RBH:10, author = {F. Römer and H. Becker and M. Haardt}, title = {Analytical performance assessment for multi-dimensional {Tensor-ESPRIT-type} parameter estimation algorithms}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2010)}, month = Mar, year = 2010, address = {Dallas, TX} }

Abstract – Subspace-based high-resolution parameter algorithms such as ESPRIT, MUSIC, or RARE are known as efficient and versatile tools in various signal processing applications including radar, sonar, medical imaging, or the analysis of MIMO channel sounder measurements. Since these techniques are based on the singular value decomposition (SVD), their performance can be analyzed with the help of SVD-based perturbation theory. Recently we have demonstrated that in the R-dimensional case (R-D), the estimation accuracy of these schemes can be improved by replacing the measurement matrix by a measurement tensor and the SVD by the Higher-Order SVD (HOSVD). In case of ESPRIT, this gives rise to the family of Tensor-ESPRIT algorithms, e.g., standard Tensor-ESPRIT and Unitary Tensor-ESPRIT. In this paper we derive the analytical performance for Tensor-ESPRIT-type algorithms via a recently introduced perturbation theory for the HOSVD-based signal subspace estimate. All expressions are asymptotic in the SNR, but not in the sample size. We first present the explicit equations as a function of the current noise realization, where no assumptions on the statistics of symbols or noise are required. Next, we show the result of performing statistical expectation over white Gaussian noise. To demonstrate the usefulness of the results we also present a compact expression for the asymptotic efficiency in the case of a single source, which is only a function of the array size.

F. Römer and M. Haardt, A low-complexity relay transmit strategy for two-way relaying with MIMO amplify and forward relays, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2010), Dallas, TX, Mar 2010.

@INPROCEEDINGS{RH:10, author = {F. Römer and M. Haardt}, title = {A low-complexity relay transmit strategy for two-way relaying with {MIMO} amplify and forward relays}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2010)}, month = Mar, year = 2010, address = {Dallas, TX} }

Abstract – In this paper we consider two-way relaying with a MIMO amplify and forward (AF) relay. In the literature, the relay amplification matrix which maximizes the sum rate in two-way relaying is not known for the general MIMO case. However, the maximization of the channels' Frobenius norms is easily achieved via the Algebraic Norm-Maximizing (ANOMAX) transmit strategy. While this scheme provides a significant improvement in the received signals' strengths, it does not reach the full multiplexing gain for high SNRs due to its low rank nature. Therefore, we propose a simple strategy to restore the rank while preserving the same subspaces via an optimization over the profile of the singular values. The resulting scheme is called rank-restored ANOMAX (RR-ANOMAX). The main benefit of this approach is that the computational complexity is very low. Moreover, its performance is very close to the one-way upper-bound which is obtained by considering the two transmission directions as independent one-way relaying channels.

J. P. C. L. Da Costa, F. Römer, M. Weis, and M. Haardt, Robust R-D parameter estimation via closed-form PARAFAC, in Proceedings of the International ITG Workshop on Smart Antennas (WSA'10), Bremen, Germany, Feb 2010.

@INPROCEEDINGS{DRWH:10, author = {J. P. C. L. {Da Costa} and F. Römer and M. Weis and M. Haardt}, title = {Robust {R-D} parameter estimation via closed-form {PARAFAC}}, booktitle = {Proceedings of the International ITG Workshop on Smart Antennas (WSA'10)}, month = Feb, year = 2010, address = {Bremen, Germany} }

Abstract – R-dimensional parameter estimation problems are common in a variety of signal processing applications. In order to solve such problems, we propose a robust multidimensional model order selection scheme and a robust multidimensional parameter estimation scheme using the closed-form PARAFAC algorithm, which is a recently proposed way to compute the PARAFAC decomposition based on several simultaneous diagonalizations. In general, R-dimensional (R-D) model order selection (MOS) techniques, e.g., the R-D Exponential Fitting Test (R-D EFT), are designed for multidimensional data by taking into account its multidimensional structure. However, the R-D MOS techniques assume that the data is contaminated by white Gaussian noise. To deal with colored noise, we propose the closed-form PARAFAC based model order selection (CFP-MOS) technique based on multiple estimates of the factor matrices provided as an intermediate step by the closed-form PARAFAC algorithm. Additionally, we propose the closed-form PARAFAC based parameter estimator (CFP-PE), which can be applied to extract spatial frequencies in case of arbitrary array geometries.

J. P. C. L. Da Costa, F. Römer, and M. Haardt, Iterative sequential GSVD (I-S-GSVD) based prewhitening for multidimensional HOSVD based subspace estimation without knowledge of the noise covariance information, in Proceedings of the International ITG Workshop on Smart Antennas (WSA'10), Bremen, Germany, Feb 2010.

@INPROCEEDINGS{DRH:10, author = {J. P. C. L. {Da Costa} and F. Römer and M. Haardt}, title = {Iterative sequential {GSVD} {(I-S-GSVD)} based prewhitening for multidimensional {HOSVD} based subspace estimation without knowledge of the noise covariance information}, booktitle = {Proceedings of the International ITG Workshop on Smart Antennas (WSA'10)}, month = Feb, year = 2010, address = {Bremen, Germany} }

Abstract – Recently, the Sequential GSVD (S-GSVD) based prewhitening scheme has been proposed to improve R-dimensional subspace-based parameter estimation schemes in the presence of colored noise or interference with Kronecker structure. To apply the S-GSVD, second order statistics of the noise should be estimated, e.g., via samples captured in the absence of the desired signal components. In this contribution, we propose the Iterative Sequential Generalized Singular Value Decomposition (I-S-GSVD) based prewhitening scheme for multidimensional HOSVD based subspace estimation when information about the noise statistics is not available. Even without the availability of samples in the absence of the desired signals components, it is possible to obtain the prewhitening correlation factors and the signal parameters in an iterative way using a deterministic algorithm in combination with the S-GSVD. This combination constitutes our proposed I-S-GSVD. Finally, the I-S-GSVD inherits the computational efficiency from the S-GSVD compared to matrix based prewhitening schemes.

B. Song, F. Römer, and M. Haardt, Flexible Coordinated Beamforming (FlexCoBF) Algorithm for the Downlink of Multi-User MIMO Systems, in Proceedings of the International ITG Workshop on Smart Antennas (WSA'10), Bremen, Germany, Feb 2010.

@INPROCEEDINGS{SRH:10, author = {B. Song and F. Römer and M. Haardt}, title = {Flexible Coordinated Beamforming {(FlexCoBF)} Algorithm for the Downlink of {Multi-User} {MIMO} Systems}, booktitle = {Proceedings of the International ITG Workshop on Smart Antennas (WSA'10)}, month = Feb, year = 2010, address = {Bremen, Germany} }

Abstract – We propose a Flexible Coordinated Beamforming (FlexCoBF) algorithm for the Multi-User MIMO downlink in the case where the total number of receive antennas exceeds the number of transmit antennas at the base station. This case is relevant for many scenarios that have been discussed recently. For instance, for coordinated multipoint (CoMP) transmissions, which play a significant role in LTE to achieve the IMT-Advanced requirements [1], we have to consider users across cell borders jointly and hence a large total number of receive antennas is present. FlexCoBF is significantly more flexible compared to previous approaches, since the linear transmit as well as receive strategies can be chosen arbitrarily. Moreover, we achieve the same sum rate as the best known coordinated beamforming (CBF) algorithm with significantly fewer iterations.

F. Römer, J. Zhang, M. Haardt, and E. Jorswieck, Spectrum and Infrastructure Sharing in Wireless Networks: A Case Study with Relay-Assisted Communications, in Proceedings of the Future Network and Mobile Summit 2010, Florence, Italy, Jun 2010.

@INPROCEEDINGS{RZHJ:10, author = {F. Römer and J. Zhang and M. Haardt and E. Jorswieck}, title = {Spectrum and Infrastructure Sharing in Wireless Networks: A Case Study with {Relay-Assisted} Communications}, booktitle = {Proceedings of the Future Network and Mobile Summit 2010}, month = Jun, year = 2010, address = {Florence, Italy} }

Abstract – Physical resource sharing between wireless operators and service providers can be used to support efficient, competitive, and innovative wireless communication markets. By sharing resources, which are usually exclusively allocated such as spectrum or infrastructure, interference is created on the physical layer. Handling this new type of interference poses a significant and novel challenge to the design of suitable transmission techniques. In this paper, we investigate the example of two-way relaying with amplify and forward relays as a case study. Here, two operators physically share their spectrum and the relay (infrastructure). We demonstrate that both operators can serve their users by using multiple antennas at the relay via a naive scheme inspired by the block diagonalization method. Numerical results verify that already this simple approach results in significant gains in terms of the sum data rates as compared to an exclusive (orthogonal) assignment of the resources. This shows that cooperation leads to a more efficient use of the shared resources.

P. Komulainen, A. Tölli, B. Song, F. Römer, E. Björnson, and M. Bengtsson, CSI Acquisition Concepts for Advanced Antenna Schemes in the WINNER+ Project, in Proceedings of the Future Network and Mobile Summit 2010, Florence, Italy, Jun 2010.

@INPROCEEDINGS{KTSRBB:10, author = {P. Komulainen and A. Tölli and B. Song and F. Römer and E. Björnson and M. Bengtsson}, title = {{CSI} Acquisition Concepts for Advanced Antenna Schemes in the {WINNER+} Project}, booktitle = {Proceedings of the Future Network and Mobile Summit 2010}, month = Jun, year = 2010, address = {Florence, Italy} }

Abstract – This paper summarizes four novel advanced antenna concepts explored in the framework of the WINNER+ project. The concepts are related to multiuser MIMO communication in cellular networks, focusing on the acquisition and application of channel state information (CSI) at the transmitter in time-division-duplex (TDD) mode. The concepts include new ideas for CSI modeling and sounding for the purposes of multiuser precoding, and methods for pilot signal design with the aim to support the estimation of different CSI quantities. Furthermore, a new relaying strategy for terminal-to-terminal communication is described. All the ideas are feasible for adoption into practical upcoming communication systems such as LTE-Advanced, and most of the proposed concepts have only a minor impact on standards. Our study indicates that the CSI at its best is not only about estimating the channel responses between different antenna pairs. What counts is the nature of the intended communication link as well as the form in which CSI is applied.

E. Jorswieck, L. Badia, T. Fahldieck, D. Gesbert, S. Gustafsson, M. Haardt, K. Ho, E. Karipidis, A. Kortke, E. Larsson, H. Mark, M. Nawrocki, R. Piesiewicz, F. Römer, M. Schubert, J. Sykora, P. Trommelen, B. van den Ende, and M. Zorzi, Resource Sharing in Wireless Networks: The SAPHYRE Approach, in Proceedings of the Future Network and Mobile Summit 2010, Florence, Italy, Jun 2010.

@INPROCEEDINGS{JBFGGHHKKLMNPRSSTvZ:10, author = {E. Jorswieck and L. Badia and T. Fahldieck and D. Gesbert and S. Gustafsson and M. Haardt and K. Ho and E. Karipidis and A. Kortke and E. Larsson and H. Mark and M. Nawrocki and R. Piesiewicz and F. Römer and M. Schubert and J. Sykora and P. Trommelen and B. {van den Ende} and M. Zorzi}, title = {Resource Sharing in Wireless Networks: The {SAPHYRE} Approach}, booktitle = {Proceedings of the Future Network and Mobile Summit 2010}, month = Jun, year = 2010, address = {Florence, Italy} }

Abstract – Physical resource sharing between wireless operators and service providers is necessary in order to support efficient, competitive, and innovative wireless communication markets. By sharing resources, such as spectrum or infrastructure, which are usually exclusively allocated interference is created on the physical layer. Therefore, the economic gains, regulatory overhead, and engineering efforts need to be addressed by a consolidated cross-layer approach. This paper describes briefly the
approach taken by the EU FP7 project SAPHYRE.

F. Römer and M. Haardt, Sum-rate maximization in two-way relaying systems with MIMO amplify and forward relays via generalized eigenvectors, in Proceedings of the 18-th European Signal Processing Conference (EUSIPCO-2010), Aalborg, Denmark, Aug 2010.

@INPROCEEDINGS{RH:10, author = {F. Römer and M. Haardt}, title = {Sum-rate maximization in two-way relaying systems with {MIMO} amplify and forward relays via generalized eigenvectors}, booktitle = {Proceedings of the 18-th European Signal Processing Conference (EUSIPCO-2010)}, month = Aug, year = 2010, address = {Aalborg, Denmark} }

Abstract – In this paper we consider two-way relaying with a MIMO amplify and forward (AF) relay. Assuming that the terminals have perfect channel knowledge, the bidirectional two-way relaying channel is decoupled into two parallel effective single-user channels by subtracting the self-interference at the terminals. We derive the relay amplification matrix which maximizes the (weighted) sum rate in the case where the terminals have a single antenna. By algebraic manipulation of the rate expressions we can rewrite the optimization problem as a generalized eigenvalue expression which depends on two real-valued parameters. The optimum is then found by a 2-D exhaustive search, which can be efficiently implemented via the bisection method. The resulting method is called RAGES (RAte-Maximization via Generalized Eigenvectors for Single-antenna terminals). Moreover, both parameters have a physical interpretation which allows to find sub-optimal heuristics to reduce the complexity of the search even further. As shown in simulations, a corresponding suboptimal 1-D search is very close to the optimum sum rate.

M. Weis, D. Jannek, T. Günther, P. Husar, F. Römer, and M. Haardt, Temporally resolved multi-way component analysis of dynamic sources in event-related EEG data using PARAFAC2, in Proceedings of the 18-th European Signal Processing Conference (EUSIPCO-2010), Aalborg, Denmark, Aug 2010.

@INPROCEEDINGS{WJGHRH:10, author = {M. Weis and D. Jannek and T. Günther and P. Husar and F. Römer and M. Haardt}, title = {Temporally resolved multi-way component analysis of dynamic sources in event-related {EEG} data using {PARAFAC2}}, booktitle = {Proceedings of the 18-th European Signal Processing Conference (EUSIPCO-2010)}, month = Aug, year = 2010, address = {Aalborg, Denmark} }

Abstract – The identification of signal components in electroencephalographic (EEG) data is a major task in neuroscience. The interest to this area has regained new interest due to the possibilities of multidimensional signal processing. In this contribution we analyze event-related multi-channel EEG recordings on the basis of the time-varying spectrum for each channel. To identify the signal components it is a common approach to use parallel factor (PARAFAC) analysis. However, the PARAFAC model cannot cope with components appearing time-shifted over the different channels. Furthermore, it is not possible to track PARAFAC components over time. We show how to overcome these problems by using the PARAFAC2 decomposition, which renders it an attractive approach for processing EEG data with highly dynamic (moving) sources. Additionally, we introduce the concept of PARAFAC2 component amplitudes, which resolve the scaling ambiguity in the PARAFAC2 model and can be used to judge the relevance of the components.

M. Weis, D. Jannek, F. Römer, T. Günther, M. Haardt, and P. Husar, Multi-Dimensional PARAFAC2 Component Analysis of Multi-Channel EEG Data Including Temporal Tracking, in Proceedings of the 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology (EMBC 2010), Buenos Aires, Argentina, Sep 2010.

@INPROCEEDINGS{WJRGHH:10, author = {M. Weis and D. Jannek and F. Römer and T. Günther and M. Haardt and P. Husar}, title = {{Multi-Dimensional} {PARAFAC2} Component Analysis of {Multi-Channel} {EEG} Data Including Temporal Tracking}, booktitle = {Proceedings of the 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology (EMBC 2010)}, month = Sep, year = 2010, address = {Buenos Aires, Argentina} }

Abstract – The identification of signal components in the electroencephalographic (EEG) data originating from neural activities is a long standing problem in neuroscience. This area has regained new attention due to the possibilities of multidimensional signal processing. In this Work we analyze measured visual-evoked potentials on the basis of the time-varying spectrum for each channel. To identify the signal components the parallel factor (PARAFAC) analysis is commonly used in literature. However, the PARAFAC decomposition is not able to cope with components appearing time-shifted over the different channels. Furthermore, it is not possible to track PARAFAC components over time. In this contribution we derive how to overcome these problems by using the PARAFAC2 model, which renders it an attractive approach for processing EEG data with highly dynamic (moving) sources.

J. P. C. L. Da Costa, D. Schulz, F. Römer, M. Haardt, and J. A. Apolinário, Robust R-D Parameter Estimation via Closed-Form PARAFAC in Kronecker Colored Environment, in Proceedings of the Seventh International Symposium on Wireless Communication Systems (ISWCS 2010), York, UK, Sep 2010.

@INPROCEEDINGS{DSRHA:10, author = {J. P. C. L. {Da Costa} and D. Schulz and F. Römer and M. Haardt and J. A. Apolinário}, title = {Robust {R-D} Parameter Estimation via {Closed-Form} {PARAFAC} in Kronecker Colored Environment}, booktitle = {Proceedings of the Seventh International Symposium on Wireless Communication Systems (ISWCS 2010)}, month = Sep, year = 2010, address = {York, UK} }

Abstract – To estimate parameters from measurements sampled on a multidimensional grid, Parallel Factor Analysis (PARAFAC) based schemes are very appealing, since they are applicable to mixed array geometries, which are a mixture of arbitrary arrays and outer product based arrays. Moreover, for PARAFAC based schemes, errors in some dimensions do not affect the estimation of parameters in the other dimensions. Particularly, the closed-form PARAFAC based parameter estimator has the additional advantage of being non-iterative.
In this contribution, we propose a PARAFAC decomposition for colored noise with a Kronecker structure called Sequential Generalized Singular Value Decomposition (S-GSVD) based closed-form PARAFAC. Our proposed estimator joins the advantages of the closed-form PARAFAC - such as the applicability to mixed array geometries and the robustness to arrays with positioning errors - with the suitability of the S-GSVD for data contaminated by Kronecker colored noise or interference.

M. Weis, D. Jannek, T. Günther, P. Husar, M. Haardt, and F. Römer, Space-Time-Frequency Component Analysis of Visual Evoked Potentials based on the PARAFAC2 Model, in Proceedings of the 55th International Scientific Colloquium (IWK) Ilmenau, Ilmenau, Germany, Sep 2010.

@INPROCEEDINGS{WJGHHR:10, author = {M. Weis and D. Jannek and T. Günther and P. Husar and M. Haardt and F. Römer}, title = {{Space-Time-Frequency} Component Analysis of Visual Evoked Potentials based on the {PARAFAC2} Model}, booktitle = {Proceedings of the 55th International Scientific Colloquium (IWK) Ilmenau}, month = Sep, year = 2010, address = {Ilmenau, Germany} }

Abstract – In this contribution we focus on analyzing measured electroencephalographic (EEG) data to identify the components of neural activity. The component analysis of EEG data is widely used in neuroscience. In the functional diagnosis of evoked potentials, the EEG component analysis is of high relevance for an objective electrophysiological assessment. Moreover, these techniques can be used to detect and localize epileptic seizure onset zones on the scalp as well as projections of cognitive processing like speech or auditory handling. Different component analysis techniques have been applied over the last years, e.g., independent component analysis (ICA), and the singular value decomposition (SVD). However, these methods cannot exploit the multi-dimensional (space-time-frequency) structure of the EEG data. Moreover, to obtain matrix decompositions like the SVD or the ICA, artificial assumptions like orthogonality or independence have to be imposed. For these reasons, tensor decompositions are a more promising approach to handle EEG signals. Especially the well known parallel factor (PARAFAC) analysis is widely used in recent literature, because it is essentially unique under mild conditions without any artificial constraints. For the efficient multi-way component analysis of EEG data it is necessary to resolve the temporal evolution as well as the frequency content of the EEG recordings. In order to achieve this, a time-frequency analysis (TFA) is applied to each channel. After the TFA, the EEG signals vary over time, frequency, and space (channels). The common approaches for the space-time-frequency component analysis of EEG data to date are based on the PARAFAC model. However, this model is not able to resolve EEG components which appear time-shifted over the different channels. In this contribution we introduce the PARAFAC2 decomposition for the space-time-frequency analysis of EEG data. Thereby, we show that the PARAFAC2 model supports time-shifted component signals. The validity of the model is demonstrated on measured visual-evoked potentials (VEP). Furthermore, we show how the PARAFAC2 model can be adopted in order to track the different EEG components over time, which provides new insights into the temporal evolution of EEG components.

B. Song, F. Römer, and M. Haardt, Blind estimation of SIMO channels using a tensor-based subspace method, in Proceedings of the 44-th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov 2010.

@INPROCEEDINGS{SRH:10, author = {B. Song and F. Römer and M. Haardt}, title = {Blind estimation of {SIMO} channels using a tensor-based subspace method}, booktitle = {Proceedings of the 44-th Asilomar Conference on Signals, Systems, and Computers}, month = Nov, year = 2010, address = {Pacific Grove, CA} }

### 2009

M. Weis, F. Römer, M. Haardt, D. Jannek, and P. Husar, Multi-dimensional Space-Time-Frequency component analysis of event-related EEG data using closed-form PARAFAC, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2009), Taipei, Taiwan, Apr 2009.

@INPROCEEDINGS{WRHJH:09, author = {M. Weis and F. Römer and M. Haardt and D. Jannek and P. Husar}, title = {Multi-dimensional {Space-Time-Frequency} component analysis of event-related {EEG} data using closed-form {PARAFAC}}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2009)}, month = Apr, year = 2009, address = {Taipei, Taiwan} }

Abstract – The efficient analysis of electroencephalographic
(EEG) data is a long standing problem in neuroscience, which has regained new interest due to the possibilities of multidimensional signal processing. We analyze event related multi-channel EEG recordings on the basis of the time-varying spectrum for each channel. It is a common approach to use wavelet transformations for the time-frequency analysis (TFA) of the data. To identify the signal components we decompose the data into time-frequency-space atoms using Parallel Factor (PARAFAC) analysis. In this paper we show that a TFA based on the Wigner-Ville distribution together with the recently developed closed-form PARAFAC algorithm enhance the separability of the signal components. This renders it an attractive approach for processing EEG data. Additionally, we introduce the new concept of component amplitudes, which resolve the scaling ambiguity in the PARAFAC model and can be used to judge the relevance of the individual components.

F. Römer and M. Haardt, Tensor-Based Channel Estimation (TENCE) for Two-Way Relaying with Multiple Antennas and Spatial Reuse, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2009), Taipei, Taiwan, Apr 2009.

@INPROCEEDINGS{RH:09, author = {F. Römer and M. Haardt}, title = {{Tensor-Based} Channel Estimation {(TENCE)} for {Two-Way} Relaying with Multiple Antennas and Spatial Reuse}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2009)}, month = Apr, year = 2009, address = {Taipei, Taiwan} }

Abstract – In this paper we study two-way relaying with amplify-and-forward (AF) relays. In two-way relaying, two terminals exchange data with the help of an intermediate relay station. In order to enable mass deployment of these relays, we focus on very simple AF relays that do not have any channel state information. Hence, to separate the data streams in two-way relaying, both user terminals need reliable knowledge of all relevant channel parameters. We therefore propose the novel tensor-based channel estimation algorithm TENCE that provides both terminals with full knowledge of all channel parameters involved in the transmission. The solution is algebraic, i.e., it does not require any iterative procedures. Moreover, TENCE is applicable to arbitrary antenna configurations. We also derive criteria for the design of the pilot symbols and the corresponding relay amplification matrices. Computer simulations demonstrate the achievable channel estimation accuracy.

F. Römer and M. Haardt, Multidimensional Unitary Tensor-ESPRIT for Non-Circular Sources, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2009), Taipei, Taiwan, Apr 2009.

@INPROCEEDINGS{RH:09, author = {F. Römer and M. Haardt}, title = {Multidimensional Unitary {Tensor-ESPRIT} for {Non-Circular} Sources}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2009)}, month = Apr, year = 2009, address = {Taipei, Taiwan} }

Abstract – Recently, many authors have shown that high-resolution parameter estimation schemes can be significantly improved if the sources are non-circular. For example, enhanced versions of Root MUSIC and standard ESPRIT for non-circular sources as well as the entirely real-valued NC Unitary ESPRIT algorithm have been proposed. We can achieve further enhancements in the R-dimensional (R-D) case by using tensor algebra to express and manipulate multidimensional signals in their natural R-D structure.
This has led to tensor-based parameter estimation algorithms with enhanced estimation accuracy such as R-D Unitary Tensor-ESPRIT. In this paper we demonstrate how to achieve both benefits at the same time. This is not straightforward since the usual method to exploit non-circular sources destroys the tensor structure and therefore a new approach had to be found. This approach allows us to derive the NC R-D Unitary Tensor-ESPRIT algorithm which exploits the non-circularity of the sources and the R-D structure of the measured signals jointly. Numerical computer simulations demonstrate the benefit in terms of a significantly improved accuracy compared to state of the art algorithms.

F. Römer and M. Haardt, Structured Least Squares (SLS) based enhancements of Tensor-Based Channel Estimation (TENCE) for Two-Way Relaying with Multiple Antennas, in Proceedings of the International ITG Workshop on Smart Antennas (WSA'09), Berlin, Germany, Feb 2009.

@INPROCEEDINGS{RH:09, author = {F. Römer and M. Haardt}, title = {Structured Least Squares {(SLS)} based enhancements of {Tensor-Based} Channel Estimation {(TENCE)} for {Two-Way} Relaying with Multiple Antennas}, booktitle = {Proceedings of the International ITG Workshop on Smart Antennas (WSA'09)}, month = Feb, year = 2009, address = {Berlin, Germany} }

Abstract – In this paper, we develop a novel tensor-based channel estimation algorithm for two-way relaying with amplify and forward (AF) relays. In two-way relaying two terminals transmit simultaneously to one relay station which then amplifies the received signal and transmits it back to the terminals. With sufficient channel knowledge the terminals can subtract the interference their own transmissions have caused to their received signal and subsequently decode the data from the other terminal. While this relaying scheme uses the radio resources in a particularly efficient way, reliable channel knowledge is crucial to obtain an acceptable link quality.
It has been shown that we can estimate all relevant channel parameters via the purely algebraic TENCE algorithm. In this paper, we introduce a novel tensor-based approach to enhance these estimates even further via an iterative procedure based on Structured Least Squares (SLS).
The improvement in channel estimation accuracy is demonstrated via computer simulations at the end of the paper. We also show that the number of required iterations is only between one and four, even in critical scenarios.

J. P. C. L. Da Costa, M. Haardt, and F. Römer, Sequential GSVD Based Prewhitening for Multidimensional HOSVD Based Subspace Estimation, in Proceedings of the International ITG Workshop on Smart Antennas (WSA'09), Berlin, Germany, Feb 2009.

@INPROCEEDINGS{DHR:09, author = {J. P. C. L. {Da Costa} and M. Haardt and F. Römer}, title = {Sequential {GSVD} Based Prewhitening for Multidimensional {HOSVD} Based Subspace Estimation}, booktitle = {Proceedings of the International ITG Workshop on Smart Antennas (WSA'09)}, month = Feb, year = 2009, address = {Berlin, Germany} }

J. P. C. L. Da Costa, A. Thakre, F. Römer, and M. Haardt, Comparison of model order selection techniques for high-resolution parameter estimation algorithms, in Proceedings of the 54th International Scientific Colloquium (IWK) Ilmenau, Ilmenau, Germany, Sep 2009.

@INPROCEEDINGS{DTRH:09, author = {J. P. C. L. {Da Costa} and A. Thakre and F. Römer and M. Haardt}, title = {Comparison of model order selection techniques for high-resolution parameter estimation algorithms}, booktitle = {Proceedings of the 54th International Scientific Colloquium (IWK) Ilmenau}, month = Sep, year = 2009, address = {Ilmenau, Germany} }

Abstract – In sensor array processing it is often required to know the number of signals received by an antenna array, since in practice only a limited number of observations is available. Robust techniques for the estimation of the model order are needed. In this paper, we propose general application rules for the most recent model order selection techniques in the literature considering different one-dimensional scenarios. Other important contributions are a more general and improved form of the modified exponential fitting test (M-EFT) and extensions of other known model order selection techniques for the case that the number of sensors is greater than the number of snapshots.

J. P. C. L. Da Costa, F. Römer, and M. Haardt, Deterministic prewhitening to improve subspace based parameter estimation techniques in severely colored noise environments, in Proceedings of the 54th International Scientific Colloquium (IWK) Ilmenau, Ilmenau, Germany, Sep 2009.

@INPROCEEDINGS{DRH:09, author = {J. P. C. L. {Da Costa} and F. Römer and M. Haardt}, title = {Deterministic prewhitening to improve subspace based parameter estimation techniques in severely colored noise environments}, booktitle = {Proceedings of the 54th International Scientific Colloquium (IWK) Ilmenau}, month = Sep, year = 2009, address = {Ilmenau, Germany} }

Abstract – Colored noise is encountered in a variety of signal processing applications. For such applications the prewhitening step becomes essential, since parameter estimation without prewhitening can be severely degraded.
Traditionally stochastic prewhitening techniques transform the colored noise into white noise keeping the SNR constant. In this paper, we propose a deterministic approach for subspace prewhitening, where we remove the correlation, which increases the SNR. Consequently, in high noise correlation scenarios, where the subspace is prewhitened by our deterministic approach, there is a significant improvement in the parameter estimation accuracy.
The proposed deterministic prewhitening requires knowledge of the noise correlation. Therefore, we also propose solutions to estimate the correlation coefficients.

F. Römer, H. Becker, M. Haardt, and M. Weis, Analytical Performance Evaluation for HOSVD-based Parameter Estimation Schemes, in Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2009), Aruba, Dutch Antilles, Dec 2009, doi:10.1109/CAMSAP.2009.5413232.

@INPROCEEDINGS{RBHW:09, author = {F. Römer and H. Becker and M. Haardt and M. Weis}, title = {Analytical Performance Evaluation for {HOSVD-based} Parameter Estimation Schemes}, booktitle = {Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2009)}, month = Dec, year = 2009, address = {Aruba, Dutch Antilles}, doi = {10.1109/CAMSAP.2009.5413232} }

Abstract – Subspace-based high-resolution parameter estimation schemes are used in a variety of signal processing applications including radar, sonar, communications, medical imaging, and the estimation of the parameters of the dominant multipath components from MIMO channel sounder measurements. It is of great theoretical and practical interest to predict the performance of these schemes analytically. Since they rely on the estimate of the signal subspace obtained via a singular value decomposition (SVD), significant contributions to the perturbation analysis of the SVD have been made in the last decades.
Recently, we have shown that in multidimensional harmonic retrieval problems, the measurement matrix can be replaced by a measurement tensor which allows to exploit the natural multidimensional structure of the data. Replacing the SVD by a multidimensional extension known as Higher-Order SVD (HOSVD) gives rise to the class of HOSVD-based parameter estimation schemes such as R-D standard Tensor-ESPRIT and R-D Unitary Tensor-ESPRIT (R>=2).
To study the performance of these tensor-based methods, an extension of the performance analysis for the matrix signal subspace (computed from the SVD) to the tensor signal subspace (computed from the HOSVD) is required. In this paper we demonstrate how an arbitrary first order perturbation analysis for the SVD can be transformed into the corresponding prediction for the HOSVD. As an example, we demonstrate the performance assessment for 2-D standard Tensor-ESPRIT and compare analytical results with simulation results. The results can be extended to the evaluation of any HOSVD-based parameter estimation scheme.

F. Römer and M. Haardt, Near-far Robustness and Optimal Power Allocation for two-way Relaying with MIMO Amplify and Forward Relays, in Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2009), Aruba, Dutch Antilles, Dec 2009.

@INPROCEEDINGS{RH:09, author = {F. Römer and M. Haardt}, title = {Near-far Robustness and Optimal Power Allocation for two-way Relaying with {MIMO} Amplify and Forward Relays}, booktitle = {Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2009)}, month = Dec, year = 2009, address = {Aruba, Dutch Antilles} }

Abstract – In this paper we consider two-way relaying with a MIMO amplify and forward (AF) relay. Assuming single stream transmission and perfect channel state information (CSI) we are able to analytically express the signal to noise ratios (SNR) at the user terminals. These SNR expressions are first used to study the near-far robustness by analyzing their asymptotic behaviour when the signal from one of the users is significantly stronger than the signal received from the other terminal.
Subsequently we demonstrate how to achieve individual SNR targets for both terminals via a combined strategy of user power control and the algebraic norm-maximizing (ANOMAX) transmit strategy at the relay. We also derive a simple necessary and sufficient condition to guarantee that the region of achievable SNR targets is convex. At the end of the paper we demonstrate via numerical computer simulations that the weighting parameter in ANOMAX can be used to reduce the required transmit power for given SNR targets.

### 2008

F. Römer and M. Haardt, A closed-form solution for parallel factor (PARAFAC) analysis, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2008), Las Vegas, NV, pp. 2365 – 2368, Apr 2008.

@INPROCEEDINGS{RH:08, author = {F. Römer and M. Haardt}, title = {A closed-form solution for parallel factor {(PARAFAC)} analysis}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2008)}, pages = {2365 -- 2368}, month = Apr, year = 2008, address = {Las Vegas, NV} }

Abstract – Parallel Factor Analysis (PARAFAC) is a branch of multi-way signal processing that has received increased attention recently. This is due to the large class of applications as well as the milestone identifiability results demonstrating the superiority to matrix (two-way) analysis approaches. A significant amount of research was dedicated to iterative methods to estimate the factors from noisy data. In many situations these require many iterations and are not guaranteed to converge to the global optimum. Therefore, suboptimal closed-form solutions were proposed as initializations.
In this contribution we derive a closed-form solution to completely replace the iterative approach by transforming PARAFAC into several joint diagonalization problems. Thereby, we obtain several estimates for each of the factors and present a new "best matching" scheme to select the best estimate for each factor.
In contrast to the techniques known from the literature, our closed-form solution can efficiently exploit symmetric as well as Hermitian symmetric models and solve the underdetermined case, if there are at least two modes that are non-degenerate and full rank. This closed-form solution achieves approximately the same performance as previously proposed iterative solutions and even outperforms them in critical scenarios.

F. Römer and M. Haardt, A closed-form solution for multilinear PARAFAC decompositions, in Proceedings of the 5-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2008), Darmstadt, Germany, pp. 487 – 491, Jul 2008.

@INPROCEEDINGS{RH:08, author = {F. Römer and M. Haardt}, title = {A closed-form solution for multilinear {PARAFAC} decompositions}, booktitle = {Proceedings of the 5-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2008)}, pages = {487 -- 491}, month = Jul, year = 2008, address = {Darmstadt, Germany} }

Abstract – In this paper we study the R-way Parallel Factor
Analysis (also referred to as R-way PARAFAC) problem. This branch of multi-way signal processing has received increased attention recently which is due to the versatility of themodel as well as the identifiability results demonstrating its superiority to matrix-only (2-way) approaches. In R-way PARAFAC analysis, the goal is to decompose an R-dimensional tensor into a minimal sum of rank-1 terms. So far, there exist sub-optimal closed-form solutions as well as iterative techniques for finding these decompositions. However, the latter often require many iterations to converge. In this contribution we demonstrate that the R-way PARAFAC decomposition can be reduced to a set of simultaneous matrix diagonalization problems. Exploiting the structure of the R-dimensional problem, we obtain several estimates for each of the factors and present a "best matching" scheme to select the best estimate for each factor. By means of computer simulations we compare our closed-form solution to an iterative technique and demonstrate the enhanced robustness in critical scenarios.

J. P. C. L. Da Costa, M. Haardt, and F. Römer, Robust methods based on the HOSVD for estimating the model order in PARAFAC models, in Proceedings of the 5-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2008), Darmstadt, Germany, pp. 510 – 514, Jul 2008.

@INPROCEEDINGS{DHR:08, author = {J. P. C. L. {Da Costa} and M. Haardt and F. Römer}, title = {Robust methods based on the {HOSVD} for estimating the model order in {PARAFAC} models}, booktitle = {Proceedings of the 5-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2008)}, pages = {510 -- 514}, month = Jul, year = 2008, address = {Darmstadt, Germany} }

Abstract – Parallel Factor (PARAFAC) analysis represents a
decomposition of a tensor into a minimum sum of rank one tensors. For this task, one crucial problem is the estimation of the number of rank one components that are required to represent the tensor. This problem is also known as model order estimation. Recently we have developed new R-dimensional techniques based on the HOSVD to estimate the number of components in multi-dimensional harmonic retrieval problems (i.e., R-D EFT, R-D AIC, and R-D MDL). In this paper, we apply these R-D methods to the PARAFAC model, which is a more general multi-way data model, and show that they outperform T-CORCONDIA, a nonsubjective form of CORCONDIA, in terms of the probability of detection as well as the required computational complexity.

D. Jannek, F. Römer, M. Weis, M. Haardt, and P. Husar, Identification of signal components in multi-channel EEG signals via closed-form PARAFAC analysis and appropriate preprocessing, in Proc. 4th European Medical and Biological Engineering Conference (EMBEC 2008), Antwerp, Belgium, Nov 2008.

@INPROCEEDINGS{JRWHH:08, author = {D. Jannek and F. Römer and M. Weis and M. Haardt and P. Husar}, title = {Identification of signal components in multi-channel {EEG} signals via closed-form {PARAFAC} analysis and appropriate preprocessing}, booktitle = {Proc. 4th European Medical and Biological Engineering Conference (EMBEC 2008)}, month = Nov, year = 2008, address = {Antwerp, Belgium} }

Abstract – It is a major task in EEG analysis to identify signal components based on time-frequency distributions. The main objective is to decompose a multichannel EEG into time-frequency-space atoms. A lot of work was done in the field of subspace estimation with two of the aforementioned three dimensions, e.g., by using an SVD, PCA or ICA as well as space-time filtering or beam-forming. A more powerful approach is the use of tensor decompositions. For example, PARAFAC (Parallel Factor) analysis decomposes a tensor into rank-one components and thereby represents a multidimensional extension of the SVD. This renders it an attractive approach for EEG signal analysis. The selection of an appropriate time-frequency preprocessing scheme improves the results of the PARAFAC analysis. In a first study, we have investigated several time-frequency preprocessing techniques to create a tensor in time, frequency, and space for multi-channel EEG signals. The common approach in PARAFAC analysis is the use of a wavelet transformation based on the MORLET wavelet as a preprocessing step. In this paper, we show that preprocessing based on the Wigner distribution leads to much better results than a wavelet analysis. First results have been obtained by the use of EEG signals of evoked potentials.

M. Olsson, A. Osseiran, F. Römer, and T. Wild, Multi-antenna processing in the WINNER air interface, in Proceedings of the XXIX General Assembly of the International Union of Radio Science (URSI 2008), Chicago, IL, Aug 2008.

@INPROCEEDINGS{OORW:08, author = {M. Olsson and A. Osseiran and F. Römer and T. Wild}, title = {Multi-antenna processing in the {WINNER} air interface}, booktitle = {Proceedings of the XXIX General Assembly of the International Union of Radio Science (URSI 2008)}, month = Aug, year = 2008, address = {Chicago, IL} }

Abstract – This paper summarizes work on multi-antenna processing that has been carried out in the European research project WINNER (Wireless World Initiative New Radio). An overview of the WINNER multi-antenna concept is given, and its preferred configurations and their performance in two different deployment and propagation scenarios are presented. The WINNER multi-antenna concept is a generic and flexible MIMO transmission framework, capable of realizing configurations suitable to a wide range of scenarios. For a wide area scenario, it is shown that SDMA (Spatial Division Multiple Access) based on a fixed beamforming scheme, a so-called Grid-of-Beams, is able to capture most of the available gain in the spatial domain. In a local area scenario on the other hand, where large amounts of high quality channel knowledge can be acquired, it is shown that the combination of SDMA and spatial multiplexing achieved by advanced multi-user MIMO precoding efficiently exploits the spatial domain and provides high performance.

F. Römer, M. Fuchs, and M. Haardt, Distributed MIMO systems with spatial reuse for high-speed-indoor mobile radio access, in Proceedings of the 20-th Meeting of the Wireless World Research Forum (WWRF), Ottawa, ON, Canada, Apr 2008.

@INPROCEEDINGS{RFH:08, author = {F. Römer and M. Fuchs and M. Haardt}, title = {Distributed {MIMO} systems with spatial reuse for high-speed-indoor mobile radio access}, booktitle = {Proceedings of the 20-th Meeting of the Wireless World Research Forum (WWRF)}, month = Apr, year = 2008, address = {Ottawa, ON, Canada} }

Abstract – This paper introduces a system concept for indoor (local area) mobile radio access. By taking advantage of a distributed deployment of multiple antennas at the transmitter and the individual characteristics of the mobile radio channel in indoor scenarios we demonstrate that multiple users may be spatially divided which spares the rare time and frequency resources. This leads to a high spectral efficiency, supporting the large data rates that are expected for this type of scenario. The main innovations of our approach are the combination of a distributed antenna deployment with sophisticated multi-user MIMO schemes, the introduction of spatial pilot reuse to significantly lower the pilot overhead, and the joint optimization of the pilot strategy for both downlink and uplink while keeping the user terminal complexity low. Realistic system level evaluations demonstrate the spectral efficiency achievable by our proposed system concept even under consideration of many real-world effects such as channel estimation errors and delays, RF impairments, and pilot and signaling overhead.

B. Song, F. Römer, and M. Haardt, Efficient channel quantization scheme for multi-user MIMO broadcast channels with RBD precoding, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2008), Las Vegas, NV, pp. 2389 – 2392, Apr 2008.

@INPROCEEDINGS{SRH:08, author = {B. Song and F. Römer and M. Haardt}, title = {Efficient channel quantization scheme for multi-user {MIMO} broadcast channels with {RBD} precoding}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2008)}, pages = {2389 -- 2392}, month = Apr, year = 2008, address = {Las Vegas, NV} }

Abstract – Regularized block diagonalization (RBD) is a new linear precoding technique for the multi-antenna broadcast channel and has a significantly improved sum rate and diversity order compared to all previously proposed linear precoding techniques. We consider a limited feedback system with RBD precoding, in which each receiver has perfect channel state information (CSI) and quantizes its channel. The transmitter receives the quantized CSI with a finite number of feedback bits from each receiver. In contrast to zeroforcing (ZF) or block diagonalization (BD) precoding, where the transmitter only requires the channel direction information which refers to the knowledge of subspaces spanned by the users' channel matrices, for RBD precoding the transmitter additionally requires the channel magnitude information which defines the strength of the eigenmodes of the users' channel matrices. The key contribution of
our work is that we propose a new scheme for the channel quantization to supply the transmitter with both channel direction and magnitude information. Based on this new scheme, firstly, we investigate a random vector quantization (RVQ). We derive a bound for the throughput loss due to imperfect CSI and find a way to achieve the bound by linearly increasing the number of feedback bits with the system SNR. Secondly, we modify the LBG vector quantization algorithm to obtain a dominant eigenvector based LBG (DELBG) vector quantization which can significantly reduce the number of feedback bits compared to RVQ. Finally, we demonstrate that the DE-LBG vector quantization can be applied to an OFDM-based multi-user MIMO system.

### 2007

F. Römer and M. Haardt, Tensor-structure structured least squares (TS-SLS) to improve the performance of multi-dimensional ESPRIT-type algorithms, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2007), Honolulu, HI, vol. II, pp. 893 – 896, Apr 2007.

@INPROCEEDINGS{RH:07, author = {F. Römer and M. Haardt}, title = {Tensor-structure structured least squares {(TS-SLS)} to improve the performance of multi-dimensional {ESPRIT-type} algorithms}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2007)}, pages = {893 -- 896}, month = Apr, year = 2007, address = {Honolulu, HI}, volume = {II} }

Abstract – Multidimensional ESPRIT-type parameter estimation
algorithms obtain their frequency estimates from the solution of sets of highly structured equations (the shift invariance equations). The Structured Least Squares (SLS) algorithm is known as an efficient method to obtain these solutions since the inherent structure is explicitly taken into account. In this contribution we show that if the underlying R-dimensional signals are represented by tensors, this structure can be exploited even further. In addition to an improved signal subspace estimate, the SLS algorithm is modified to directly exploit the tensor structure of the signal subspace obtained through the higher order SVD. The resulting algorithm which we term Tensor-Structure SLS offers a superior performance compared to existing approaches in critical cases, e.g., if there are highly correlated sources or a small number of available snapshots.

J. P. C. L. Da Costa, M. Haardt, F. Römer, and G. Del Galdo, Enhanced model order estimation using higher-order arrays, in Proceedings of the 41-st Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, pp. 412 – 416, Nov 2007.

@INPROCEEDINGS{DHRD:07, author = {J. P. C. L. {Da Costa} and M. Haardt and F. Römer and G. {Del Galdo}}, title = {Enhanced model order estimation using higher-order arrays}, booktitle = {Proceedings of the 41-st Asilomar Conference on Signals, Systems, and Computers}, pages = {412 -- 416}, month = Nov, year = 2007, address = {Pacific Grove, CA} }

Abstract – Frequently, R-dimensional subspace-based methods
are used to estimate the parameters in multi-dimensional harmonic retrieval problems in a variety of signal processing applications. Since the measured data is multi-dimensional, traditional approaches require stacking the dimensions into one highly structured matrix. Recently, we have shown how an HOSVD based low-rank approximation of the measurement tensor leads to an improved signal subspace estimate, which can be exploited in any multi-dimensional subspace-based parameter estimation scheme. To achieve this goal, it is required to estimate the model order of the multi-dimensional data. In this paper, we show how the HOSVD of the measurement tensor also enables us to improve the model order estimation step. This is due to the fact that only one set of eigenvalues is available in the matrix case. Applying the HOSVD, we obtain R+1 sets of n-mode singular values of the measurement tensor that are used jointly to improve the accuracy of the model order selection significantly.

F. Römer and M. Haardt, Deterministic Cramér-Rao Bounds for strict sense non-circular sources, in Proceedings of the International ITG/IEEE Workshop on Smart Antennas (WSA'07), Vienna, Austria, Feb 2007.

@INPROCEEDINGS{RH:07, author = {F. Römer and M. Haardt}, title = {Deterministic {Cramér-Rao} Bounds for strict sense non-circular sources}, booktitle = {Proceedings of the International ITG/IEEE Workshop on Smart Antennas (WSA'07)}, month = Feb, year = 2007, address = {Vienna, Austria} }

Abstract – In this contribution, the Cramér-Rao Bound (CRB) for direction of arrival (DOA) estimation in presence of strict sense non-circular sources is given. These types of sources are used in numerous practical systems and enhancements to parameter estimation methods exploiting non-circularity have received considerable attention recently. While closed-form expressions for the CRB for other types of non-circularity are known, the closed-form expression for the CRB for this data model is not available in the literature to date. After providing the closed-form expression, some interesting special cases are discussed. The cases where strict sense non-circularity does not provide any gain over generic source constellations are stated. Moreover, it is demonstrated that under certain conditions the joint CRB may decouple into independent groups. It is also shown that the number of sources which can be estimated jointly is increased. The analytical results are supported by computer simulations which show the Cram�r-Rao Bounds along with the corresponding versions of the Unitary ESPRIT algorithm.

### 2006

F. Römer, M. Haardt, and G. Del Galdo, Higher order SVD based subspace estimation to improve multi-dimensional parameter estimation algorithms, in Proceedings of the 40-th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, pp. 961 – 965, Nov 2006.

@INPROCEEDINGS{RHD:06, author = {F. Römer and M. Haardt and G. {Del Galdo}}, title = {Higher order {SVD} based subspace estimation to improve multi-dimensional parameter estimation algorithms}, booktitle = {Proceedings of the 40-th Asilomar Conference on Signals, Systems, and Computers}, pages = {961 -- 965}, month = Nov, year = 2006, address = {Pacific Grove, CA} }

Abstract – MIMO channel modeling from channel sounder measurements requires the use of high-resolution parameter estimation algorithms. Multi-dimensional subspace-based methods, such as R-D Unitary ESPRIT, are frequently used for this task. Since the measurement data is multi-dimensional, current approaches require stacking the dimensions into one highly structured matrix. In the conventional subspace estimation step, e.g., via an SVD of this highly structured matrix, this structure is not exploited. In this paper, we define a measurement tensor and estimate the signal subspace through a higher order SVD. This allows us to exploit the structure inherent in the measurement data already in the first step of the algorithm which leads to better estimates of the signal subspace. We show how the concepts of forward-backward averaging and mapping onto the real-valued domain can be extended to tensors. As an example, we discuss the impact on the accuracy of the R-D Unitary ESPRIT algorithm. However, these new concepts can be applied to any multi-dimensional subspace-based parameter estimation scheme.

F. Römer and M. Haardt, Efficient 1-D and 2-D DOA estimation for non-circular sources with hexagonal shaped ESPAR arrays, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006), Toulouse, France, pp. 881 – 884, May 2006.

@INPROCEEDINGS{RH:06, author = {F. Römer and M. Haardt}, title = {Efficient {1-D} and {2-D} {DOA} estimation for non-circular sources with hexagonal shaped {ESPAR} arrays}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006)}, pages = {881 -- 884}, month = May, year = 2006, address = {Toulouse, France} }

Abstract – This contribution is focused on direction of
arrival (DoA) estimation with a regular-hexagonal shaped ESPAR (electronically steerable parasitic antenna radiator) array that has received increased attention recently. It is shown how the estimation accuracy is improved by employing noncircular (NC) signal constellations that facilitate the application of the NC Unitary ESPRIT algorithm. It is demonstrated how this method allows the joint estimation of the azimuth and the elevation angles of up to eight uncorrelated sources with a 7-element ESPAR array. Moreover, the achievable benefits of using non-circular sources are assessed by studying deterministic Cramer-Rao bounds. It is shown that for special phase constellations between the impinging wavefronts the estimation accuracy is independent of the angular separation of the corresponding DoAs.

### 2005

F. Römer and M. Haardt, Using 3-D Unitary ESPRIT on a hexagonal shaped ESPAR antenna for 1-D and 2-D direction of arrival estimation, in Proceedings of the International ITG/IEEE Workshop on Smart Antennas (WSA'05), Duisburg, Germany, Apr 2005.

@INPROCEEDINGS{RH:05, author = {F. Römer and M. Haardt}, title = {Using {3-D} Unitary {ESPRIT} on a hexagonal shaped {ESPAR} antenna for {1-D} and {2-D} direction of arrival estimation}, booktitle = {Proceedings of the International ITG/IEEE Workshop on Smart Antennas (WSA'05)}, month = Apr, year = 2005, address = {Duisburg, Germany} }

Abstract – In this work we discuss the problem of direction of arrival estimation with a regular-hexagonal shaped 7-element ESPAR (electronically steerable parasitic antenna radiator) array which has been studied in recent publications. In order to exploit symmetries and invariances of the hexagonal shape we define three spatial frequencies instead of one. Estimates for these spatial frequencies can be found using a 3-dimensional version of the Unitary ESPRIT algorithm, which has not been applied to an antenna array on a hexagonal grid before. This algorithm enables us to find estimates for 1-D directions of arrival (i.e., the azimuth angles) or 2-D directions of arrival (i.e., the azimuth and the elevation angles). Automatic pairing of these angles will be ensured by means of the Simultaneous Schur decomposition as a final step in the estimation procedure. After giving
details on how to obtain estimates for the spatial frequencies from the observed array output, we discuss various ways how these estimates can be combined efficiently to obtain the direction of arrival angles. Where applicable, results are supported by computer simulations.

### 2004

M. Haardt and F. Römer, Enhancements of Unitary ESPRIT for non-circular sources, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2004), Montreal, Canada, vol. II, pp. 101 – 104, May 2004, doi:10.1109/ICASSP.2004.1326204.

@INPROCEEDINGS{HR:04, author = {M. Haardt and F. Römer}, title = {Enhancements of Unitary {ESPRIT} for non-circular sources}, booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2004)}, pages = {101 -- 104}, month = May, year = 2004, address = {Montreal, Canada}, volume = {II}, doi = {10.1109/ICASSP.2004.1326204} }

Abstract – Subspace based high-resolution parameter estimation algorithms often use forward-backward averaging to enhance their resolution, especially in case of correlated sources. Further enhancements can be achieved if the source signals are non-circular. In this paper, we derive an efficient subspace estimation scheme that exploits the non-circularity of the sources and already includes forward-backward averaging. Moreover, appropriate spatial smoothing techniques are introduced. Completely real-valued implementations of 1-D and 2-D Unitary ESPRIT for non-circular sources are presented as examples. In these cases, NC Unitary ESPRIT improves the resolution capability and the noise robustness of standard ESPRIT as well as Unitary ESPRIT and
can handle more sources than sensors.

## Book chapters

### 2013

F. Römer and M. Haardt, Efficient joint azimuth and elevation estimation using hexagonal antenna arrays, in The Digital Signal Processing Handbook, 2nd edition, V. K. Madisetti and D. B. Williams, CRC Press and IEEE Press, Boca Raton, FL, Jan 2013.

@INBOOK{RH:13, author = {F. Römer and M. Haardt}, title = {Efficient joint azimuth and elevation estimation using hexagonal antenna arrays}, booktitle = {The Digital Signal Processing Handbook, 2nd edition}, editor = {V. K. Madisetti and D. B. Williams}, publisher = {CRC Press and IEEE Press, Boca Raton, FL}, month = Jan, year = 2013 }

### 2012

M. Haardt, F. Römer, M. Pesavento, and M. N. El Korso, Subspace methods and exploitation of special array structures, in Electronic Reference in Signal Processing: Array Processing, vol. 3, A. M. Zoubir, M. Viberg, R. Chellappa, and S. Theodoridis, Elsevier Ltd, pp. 651 – 717, Apr 2012.

@INBOOK{HRPE:12, author = {M. Haardt and F. Römer and M. Pesavento and M. N. {El Korso}}, title = {Subspace methods and exploitation of special array structures}, booktitle = {Electronic Reference in Signal Processing: Array Processing, vol. 3}, editor = {A. M. Zoubir, M. Viberg, R. Chellappa, and S. Theodoridis}, publisher = {Elsevier Ltd}, pages = {651 -- 717}, month = Apr, year = 2012 }

### 2010

F. Römer, E. Jorswieck, and M. Haardt, Efficient spatial processing and resource allocation for amplify and forward two-way relaying, in Cross Layer Designs in WLAN Systems, N. Zorba, C. Skianis, and C. Verikoukis, Troubador Publishing Ltd, Leicester, UK, pp. 93 – 131, Sep 2010.

@INBOOK{RJH:10, author = {F. Römer and E. Jorswieck and M. Haardt}, title = {Efficient spatial processing and resource allocation for amplify and forward two-way relaying}, booktitle = {Cross Layer Designs in WLAN Systems}, editor = {N. Zorba, C. Skianis, and C. Verikoukis}, publisher = {Troubador Publishing Ltd, Leicester, UK}, pages = {93 -- 131}, month = Sep, year = 2010 }

### 2008

V. Stankovic, M. Haardt, F. Römer, S. Gale, and A. Jeffries, Multi-user MIMO systems, in Technologies for the Wireless Future: Wireless World Research Forum (WWRF), Volume 3, K. David, John Wiley & Sons, Ltd, Chichester, England, pp. 234 – 242, Sep 2008.

@INBOOK{SHRGJ:08, author = {V. Stankovic and M. Haardt and F. Römer and S. Gale and A. Jeffries}, title = {Multi-user {MIMO} systems}, booktitle = {Technologies for the Wireless Future: Wireless World Research Forum (WWRF), Volume 3}, editor = {K. David}, publisher = {John Wiley & Sons, Ltd, Chichester, England}, pages = {234 -- 242}, month = Sep, year = 2008 }

## Patents

### 2015

G. Del Galdo, F. Römer, A. Ihlow, A. Osman, B. Valeske, R. Hanke, and W. Bähr, Ultrasonic Measurements for Reconstructing an Image of an Object, WO2017028920, pending, Aug 2015.

@PATENT{DRIOVHB:15, author = {G. {Del Galdo} and F. Römer and A. Ihlow and A. Osman and B. Valeske and R. Hanke and W. Bähr}, title = {Ultrasonic Measurements for Reconstructing an Image of an Object}, number = {WO2017028920}, type = {pending}, month = Aug, year = 2015 }

Abstract – Teachings disclosed herein provide a method for performing multiple measurements of an object. The first method comprises the step of providing a plurality of non-focused excitation signals, receiving a plurality of response signals and reconstructing image based on the received signals. A second method serves for a reconstruction of an image of an object based on received signals and prior knowledge, wherein information available twice within the prior knowledge and the received signals are removed before reconstructing. A third method refers to the performing of multiple measurements of an object. This third method comprises the steps of performing a first measurement starting with reconstruction based on the first measurement, performing a second measurement and continuing the reconstruction based on the first and second measurement. A fourth aspect refers to a combiner comprising a plurality of interfaces for a plurality of ultrasonic transducers, a computer interface and a mixer.

### 2014

G. Del Galdo, S. Oeckl, T. Schön, M. Großmann, and F. Römer, Exploiting residual projection data and reference data for processing data produced by imaging modality, EP2922028, WO15140177, published, Mar 2014.

@PATENT{DOSGR:14, author = {G. {Del Galdo} and S. Oeckl and T. Schön and M. Großmann and F. Römer}, title = {Exploiting residual projection data and reference data for processing data produced by imaging modality}, number = {EP2922028, WO15140177}, type = {published}, month = Mar, year = 2014 }

Abstract – Apparatus which can be used in a context of image reconstruction on the basis of projection data produced by an imaging modality, such as computer tomography or magnetic resonance imaging comprises a residual projection data processor (101; 201; 301) and an image reconstruction unit (102; 202; 302). The residual projection data processor (101; 201; 301) is configured to determine residual projection data by cancelling reference projection data from measured projection data. The measured projection data represents a measured projection of a test object under examination obtained by an imaging modality. The reference projection data represents a projection of a reference object. The image reconstruction unit (102; 202; 302) is configured to reconstruct a resulting residual image on the basis of the residual projection data by solving an inverse projection transformation problem that links the residual projection data to the resulting residual image. The resulting residual image represents differences between the reference object and the test object under examination. A corresponding method is also described.

G. Del Galdo, M. Großmann, F. Römer, H. Neubauer, M. Schöberl, and F. Uhrmann, Apparatus and method for providing an image, EP2985992, published, Aug 2014.

@PATENT{DGRNSU:14, author = {G. {Del Galdo} and M. Großmann and F. Römer and H. Neubauer and M. Schöberl and F. Uhrmann}, title = {Apparatus and method for providing an image}, number = {EP2985992}, type = {published}, month = Aug, year = 2014 }

Abstract – An apparatus for providing an image is provided. The apparatus comprises a sensor (110) comprising a plurality of sensor pixels, wherein each of the sensor pixels of the sensor (110) comprises one or more photosensitive elements, wherein each of the one or more photosensitive elements comprises a photosensitive area, wherein the sensor (110) is configured to provide image data comprising a plurality of first image pixels, and wherein 10 each of the sensor pixels is configured to provide one of the first image pixels of the image data. Moreover, the apparatus comprises an image reconstructor (120; 220) for providing the image, wherein the image comprises a plurality of second image pixels, wherein the image reconstructor (120; 220) is configured to generate the second image pixels of the image depending on the first image pixels of the image data, wherein the number of the 15 first image pixels of the image data is smaller than the number of the second image pixels of the image data, wherein the image reconstructor (120; 220) is configured to generate each of a group of one or more of the second image pixels depending on at least two of the first image pixels. At least one of the sensor pixels of the sensor (110) comprises two or more photosensitive elements being connected such that said one of the first image 20 pixels provided by said sensor pixel depends on each of the two or more photosensitive elements. Or, the photosensitive area of a first one of the photosensitive elements of the sensor pixels of the sensor (110) has a first shape being different from a second shape of the photosensitive area of a second one of the photosensitive elements of the sensor pixels, wherein said first shape is concave.

### 2013

Y. Cheng, M. Dong, M. Haardt, S. Li, F. Römer, B. Song, and J. Zhang, Linear precoding method and device for communication system, CN102957502, WO13029561, granted, Mar 2013.

@PATENT{CDHLRSZ:13, author = {Y. Cheng and M. Dong and M. Haardt and S. Li and F. Römer and B. Song and J. Zhang}, title = {Linear precoding method and device for communication system}, number = {CN102957502, WO13029561}, type = {granted}, month = Mar, year = 2013 }

Y. Cheng, M. Dong, F. Römer, M. Haardt, S. Li, and J. Zhang, Method and apparatus for linear precoding in multi-user multiple-input multiple-output system, CN102983934, US2014185700, WO13034088, granted, Mar 2013.

@PATENT{CDRHLZ:13, author = {Y. Cheng and M. Dong and F. Römer and M. Haardt and S. Li and J. Zhang}, title = {Method and apparatus for linear precoding in multi-user multiple-input multiple-output system}, number = {CN102983934, US2014185700, WO13034088}, type = {granted}, month = Mar, year = 2013 }

Y. Cheng, M. Dong, F. Römer, M. Haardt, S. Li, and J. Zhang, Method for SDMA transmission in multicarrier MU MIMO system and base station, CN102983949, US9363815, WO13034093, granted, Mar 2013.

@PATENT{CDRHLZ:13, author = {Y. Cheng and M. Dong and F. Römer and M. Haardt and S. Li and J. Zhang}, title = {Method for {SDMA} transmission in multicarrier {MU} {MIMO} system and base station}, number = {CN102983949, US9363815, WO13034093}, type = {granted}, month = Mar, year = 2013 }

### 2008

F. Römer and M. Haardt, Verfahren zur Kanalschätzung in Two-Way-Relaying-Systemen mit Amplify and Forward-Relays, DE 102009033720, published, Jul 2008.

@PATENT{RH:08, author = {F. Römer and M. Haardt}, title = {Verfahren zur Kanalschätzung in {Two-Way-Relaying-Systemen} mit Amplify and {Forward-Relays}}, number = {DE 102009033720}, type = {published}, month = Jul, year = 2008 }

## Links

You can find me on google scholar.

I do have a Researcher-ID (it is J-8508-2013).

I also have an ORCID (which is 0000-0002-6403-6489).

You can find me on ResearchGate as well.

I am also on Mendeley.

And I have an arXiv.org profile.

Now also on publons.

I may be seen on math.stackexchange and stackoverflow occasionally.

## Statistics

A total of 26 journal papers in 7 journals (4 as first author), 124 conference papers at 84 conferences (28 as first author), 4 book chapters, and 7 patents in 16 years (10.1 publications per year) with 146 co-authors from 48 different affiliations.

### Top Co-authors:

Co-Author | Joint publications | |
---|---|---|

Martin Haardt | 98 | |

Giovanni Del Galdo | 62 | |

Joao Paulo Carvalho Lustosa Da Costa | 21 | |

Reiner S Thomä | 19 | |

Jens Steinwandt | 16 | |

Jan Kirchhof | 15 | |

Fabian Krieg | 14 | |

Anastasia Lavrenko | 14 | |

Jianshu Zhang | 14 | |

Mohamed Ibrahim | 13 |