PhD thesis Defense: Subset selection in signal processing using sparsity-inducing norms
In the context of this PhD thesis defense, Luis Blanco presents his work realized at CTTC.
This dissertation deals with different subset selection problems in wireless communications systems. These type of problems have a combinatorial nature, which makes them computationally intractable for medium and large-scale sizes. In particular, two different types of problems are addressed in this thesis: cardinality minimization and cardinality-constrained problems.
The first part of the dissertation deals with the angle of arrival estimation in an antenna array and falls within the so-called sparse signal representation framework. A simple, fast and accurate algorithm is proposed for finding the angles of arrival of multiple sources that impinge on an array of antennas. In contrast to other methods in the literature, the considered technique is not based on ad-hoc hyperparameters and does not require the previous knowledge of the number of incoming sources or a previous initialization.
The second part of the thesis addresses the selection of the appropriate subset of cooperative nodes in dense relay-assisted wireless networks and constitutes the main focus of the research activities carried out in this thesis. In order to cope with the huge data traffic in the next generation of wireless networks, the number of access nodes and communication links will be densified, having as a result, an increase of the network complexity. Within this framework, subset selection problems naturally arise to reduce the overall system management. The activation of many relay links, in dense relay-assisted wireless networks, is impractical due to the communications and processing overhead required to maintain the synchronization amongst all the spatially distributed nodes in the wireless network, which makes the network complexity unaffordable. The selection of the most suitable subset of spatially distributed relays, in this context, is a key issue, since it has a dramatic effect in the overall system performance. In particular, the thesis addresses the joint distributed beamforming optimization and relay subset assignment in a multi-user scenario with non-orthogonal transmission and in a scenario with a single source-destination pair. Different design criteria are analyzed, all of them lead to challenging combinatorial nonlinear problems, which are non-convex and non-smooth.
In order to deal with the combinatorial nature of the subset selection problems presented in this dissertation, different mathematical relaxations are proposed with the aim of obtaining algorithms that approximately solve the proposed problems with a tractable computational cost. Namely, to address the NP-hardness of the problems addressed in the thesis, different mathematical frameworks are considered, such as, for instance, semidefinite programming relaxations, Difference-of-Convex-functions (DC) programming, reweighted norms and the LARS/homotopy algorithm.