Subset selection in signal processing using sparsity-inducing norms
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...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/456819 |
| Acceso en línea: | http://hdl.handle.net/10803/456819 https://dx.doi.org/10.5821/dissertation-2117-111229 |
| Access Level: | acceso abierto |
| Palabra clave: | Àrees temàtiques de la UPC::Enginyeria de la telecomunicació 621.3 |
| Sumario: | 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. Different mathematical relaxations are proposed with the aim of obtaining algorithms that approximately solve the proposed problems with a tractable computational cost. 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 and its optimization. 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. Dealing with the multiple relay selection in an ad-hoc wireless network with one source-destination, a new algorithm is proposed for finding the best subset of cooperative relays, and their beamforming weights, so that the SNR is maximized at the destination terminal. This problem is addressed taking into account per-relay power constraints and second-order channel state information. In this context, a sub-optimal method, based on a semidefinite programming relaxation, is proposed. It achieves a near-optimal performance with a reduced computational complexity. The joint relay assignment and distributed beamforming optimization in multi-user wireless relay networks deserves a special attention. Two major problems are addressed: i) the selection of the minimum number of cooperative nodes that guarantees some predefined Quality of Service (QoS) requirements at the destination nodes and; ii) the selection of the best subset of K relays that minimizes the total relay transmit power, satisfying QoS constraints at the destinations. The mathematical formulations of these problems involve non-convex objective functions coupled with non-convex constraints. They are fit into the DC optimization framework and solved using novel path-following methods based on the penalty convex-concave procedure. The proposed techniques exhibit a low complexity and are able to achieve high-quality solutions close to the global optimum. |
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