My dissertation is entitled "Advanced Algebraic Concepts for Efficient Multi-Channel Signal Processing". I am showing that by simple tools in linear algebra (as well as their multidimensional extensions) we can find efficient algebraic solutions in various areas of digital signal processing. Such algebraic solutions are often suboptimal, however, they have some significant practical advantages. This could for instance be a deterministic (instead of a data-dependent) complexity, a more straightforward implementation (since they build on standard tools in signal processing) or a better understanding of the performance of the algorithms (e.g., analytical expressions for the achievable accuracy).
To this end, the first part of the thesis collects the most relevant tools of linear and multilinear (tensor) algebra, presents them in a systematic fashion, and provides some own additions. In three subsequent parts the application of these tools in three different areas are discussed. Firstly, the efficient decomposition of a given multidimensional signal into rank-one components (known as Canonical Polyadic Decomposition (CPD), PARAFAC analysis or CANDECOMP). Secondly, the subspace-based multidimensional high-resolution parameter estimation (e.g., via R-D Standard Tensor-ESPRIT or R-D Unitary Tensor-ESPRIT). Thirdly, the bidirectional exchange of information between two nodes via a relay station operating in the Two-Way Relaying mode.
The dissertation was submitted to the faculty on July 12, 2012 and successfully defended on October 04, 2012. It received the overall grade summa cum laude (with distinction).
I publish my dissertation under a Creative Commons Attribution Noncommercial-No Derivative Works 3.0 license. This means you are free to copy, share, and distribute it, provided that (a) the author (me) is properly attributed; (b) it is not used commercially; (c) it is not edited or otherwise altered.
The electronic version of the dissertation can be obtained from the following sources: