EFFICIENT AND SCALABLE OPTIMIZATION ALGORITHMS FOR MULTIANTENNA SIGNAL PROCESSING

Multiantenna signal processing (MASP) is indispensable in many applications like wireless communications, radar, seismology, etc. Large-scale antenna arrays (LSAAs) are envisioned for future wireless communication systems to improve the range, power, and spectral efficiency (SE) of existing systems. Thus, for a practical multiantenna wireless communication system, efficient and scalable signal processing (SP) algorithms are essential to optimize system operations. In this thesis, we address several facets of such system optimization including beampattern matching, SE maximization among others. These are formulated as nonconvex optimization problems and the thesis proposes novel, efficient, and scalable optimization algorithms with theoretical convergence guarantees. We first consider the problem of transmit analog beamforming (or phase-only beamforming) design by solving a beampattern matching problem. We formulate variants of the unit-modulus/constant-modulus least-squares problem. To attempt at solving these NP-hard problems, we propose efficient and scalable algorithms based on different optimization frameworks including alternating minimization, majorization-minimization (MM), and cyclic coordinate descent (CCD). The proposed algorithms are theoretically shown to converge to a Karush–Kuhn–Tucker (KKT) point of the corresponding optimization problem while offering superior performance. We also provide a use case in satellite communications where a desired two-dimensional beampattern is approximated using a planar array by designing the analog beamforming system. Building on the previous problem, we consider a joint array design and beampattern matching perspective and formulate variants of sparse unit-modulus or sparse constant-modulus least-squares. The optimization problems are solved using combinations of different optimization frameworks such as variable projection/elimination, MM, and block/alternating MM.

Next, we consider the problem of hybrid transceiver design for a single user point-to-point multiple-input multiple-output (MIMO) system employing LSAAs. We solve this problem based on the variable projection/elimination and MM frameworks. The proposed algorithms are shown to converge to a stationary point. We also study the applications of the proposed algorithms for hybrid precoding design for satellite communications. We then generalize convergence proofs from the earlier sections by providing a unified convergence proof for solving a generic block-structured optimization problem over nonconvex constraints. Finally, we consider the problem of localizing sources in the far-field of a spatio-temporal array formed by a single moving sensor along a known trajectory. We provide a novel signal model capturing the incoherency in the measurements sampled by the moving sensor. We establish different Cramér-Rao bounds for the considered system model by exploiting varying degrees of information, propose and study various direction of arrival (DOA) estimators. The thesis concludes by summarizing the main contributions and some open research problems.