Sparsity and random projections in time-frequency-based communication systems: Theory and algorithm design for the OFDM physical layer

The topic of this thesis lies in the intersection of two disciplines in applied mathematics and communications engineering. It focuses on sparse reconstruction and sparse modeling methods from the recently established theory of Compressed Sensing, applied to communication systems using orthogonal frequency-division multiplexing (OFDM). This class of transmission systems involves an inherent time-frequency model, which makes it possible to apply theory and methods from Compressed Sensing involving frequency measurements for the estimation of sparse time-domain signals.
The focus is on the algorithm design for solving problems that are inherent to OFDM systems, while targeting those that can be modeled as a sparse reconstruction problem. Rather than aiming at replacing traditional methods, techniques are developed that can assist or be combined with the classical ones.
In this context, a number of possibilities are studied to implement a specific sparse reconstruction algorithm in a cost-efficient way.
As an outlook, the thesis contains an excursus on a different kind of sparsity, namely parametric sparsity, for which a different approach can be applied.
In addition, the concept of Compressed Sensing is compared to the idea of sparse coding in machine learning, pointing out differences and commonalities. Using ideas well known in the communications engineering community, a number of machine learning algorithms are extended to the field of complex numbers. This includes the sparse coding approach, as well as the class of generalized learning vector quantization algorithms and kernelized extensions thereof.