Reduced-control antenna arrays reduce the number of controls required for beamforming while maintaining a given array aperture. A reduced-control array for direction finding (DF), inspired by the concept of compressive sensing (CS), was recently proposed which uses random compression weights for combining antenna-element signals into fewer measurements. However, this compressive array had not been studied in terms of traditional characteristics such as directivity, sidelobe level (SLL) or beamwidth. In this work, random compression weights are shown to be suboptimal and a need for the optimisation of compressive arrays is expressed. Existing codebook optimisation algorithms prove to be the best starting point for the optimisation of compressive arrays, but are computationally complex. A computationally efficient codebook optimisation algorithm is proposed to address this problem, which inspires the compressive-array optimisation algorithm to follow. Compressive antenna arrays are formulated as a generalisation of reduced-control arrays and a framework is presented for their optimisation in terms of SLL. By allowing arbitrary compression weights, compressive arrays are shown to improve on existing reduced-control techniques. A feed network consisting of interconnected couplers and fixed phase shifters is proposed, enabling the implementation of compressive arrays in microwave hardware. The practical feasibility of compressive arrays is illustrated by successfully manufacturing a 3-GHz prototype compressive array with integrated antenna elements. / Thesis (PhD)--University of Pretoria, 2020. / Electrical, Electronic and Computer Engineering / PhD / Unrestricted

In large antenna systems, traditional channel estimation is costly and infeasible in some situations. Compressive sensing was proposed to estimate the channel with fewer measurements. Most of the previous work uses a predefined discrete Fourier transform matrix or overcomplete Fourier transform matrix to approximate the channel. Then, a learned dictionary trained by K-singular value decomposition (K-SVD) was proposed and was proved superiority using orthogonal matching pursuit (OMP) to reconstruct the sparse channel. However, with the development of compressive sensing, there are plenty of dictionary learning algorithms and sparse recovery algorithms. It is important to identify the effect and the performance of different algorithms when transforming the high dimensional channel vectors to low dimensional representations. In this thesis, we use a spatial channel model to generate channel vectors. Dictionaries are trained by K-SVD and method of optimal directions (MOD). Several sparse recovery algorithms are used to find the sparse approximation of the channel like OMP and gradient descent with sparsification (GraDeS). We present simulation results and discuss the performance of the various algorithms in terms of accuracy, sparsity, and complexity. We find that predefined dictionaries works with most of the algorithms in sparse recovery but learned dictionaries only work with pursuit algorithms, and only show superiority when the algorithm coincides with the algorithm in the sparse coding stage. / I stora antennsystem är traditionell kanaluppskattning kostsam och omöjlig i vissa situationer. Kompressionsavkänning föreslogs för att uppskatta kanalen med färre mätningar. Det mesta av det tidigare arbetet använder en fördefinierad diskret Fourier transformmatris eller överkompletterad Fourier -transformmatris för att approximera kanalen. Därefter föreslogs en inlärd ordbok som utbildats av K-SVD och bevisades överlägsen med hjälp av OMP för att rekonstruera den glesa kanalen. Men med utvecklingen av komprimerad avkänning finns det gott om algoritmer för inlärning av ordlistor och glesa återställningsalgoritmer. Det är viktigt att identifiera effekten och prestandan hos olika algoritmer när de högdimensionella kanalvektorerna omvandlas till lågdimensionella representationer. I denna avhandling använder vi en rumslig kanalmodell för att generera kanalvektorer. Ordböcker tränas av K-SVD och MOD. Flera glesa återställningsalgoritmer används för att hitta den glesa approximationen av kanalen som OMP och GraDeS. Vi presenterar simuleringsresultat och diskuterar prestanda för de olika algoritmerna när det gäller noggrannhet, sparsamhet och komplexitet. Vi finner att fördefinierade ordböcker fungerar med de flesta algoritmerna i gles återhämtning, men inlärda ordböcker fungerar bara med jaktalgoritmer och visar bara överlägsenhet när algoritmen sammanfaller med algoritmen i det glesa kodningsstadiet.

Exploiting signal sparsity has recently received considerable attention in a variety of areas including signal and image processing, compressive sensing, machine learning and so on. Many of these applications involve optimization models that are regularized by certain sparsity-promoting metrics. Two most popular regularizers are based on the l1 norm that approximates sparsity of vectorized signals and the total variation (TV) norm that serves as a measure of gradient sparsity of an image. Nevertheless, the l1 and TV terms are merely two representative measures of sparsity. To explore the matter of sparsity further, in this thesis we investigate relaxations of the regularizers to nonconvex terms such as lp and TVp "norms" with 0 <= p < 1. The contributions of the thesis are two-fold. First, several methods to approach globally optimal solutions of related nonconvex problems for improved signal/image reconstruction quality have been proposed. Most algorithms studied in the thesis fall into the category of iterative reweighting schemes for which nonconvex problems are reduced to a series of convex sub-problems. In this regard, the second main contribution of this thesis has to do with complexity improvement of the l1/TV-regularized methodology for which accelerated algorithms are developed. Along with these investigations, new techniques are proposed to address practical implementation issues. These include the development of an lp-related solver that is easily parallelizable, and a matrix-based analysis that facilitates implementation for TV-related optimizations. Computer simulations are presented to demonstrate merits of the proposed models and algorithms as well as their applications for solving general linear inverse problems in the area of signal and image denoising, signal sparse representation, compressive sensing, and compressive imaging. / Graduate

In this dissertation, sparse processing of signals for directions-of-arrival (DoAs) estimation is addressed in the framework of Compressive Sensing (CS). In particular, DoAs estimation problem for different types of sources, systems, and applications are formulated in the CS paradigm. In addition, the fundamental conditions related to the ``Sparsity'' and ``Linearity'' are carefully exploited in order to apply confidently the CS-based methodologies. Moreover, innovative strategies for various systems and applications are developed, validated numerically, and analyzed extensively for different scenarios including signal to noise ratio (SNR), mutual coupling, and polarization loss. The more realistic data from electromagnetic (EM) simulators are often considered for various analysis to validate the potentialities of the proposed approaches. The performances of the proposed estimators are analyzed in terms of standard root-mean-square error (RMSE) with respect to different degrees-of-freedom (DoFs) of DoAs estimation problem including number of elements, number of signals, and signal properties. The outcomes reported in this thesis suggest that the proposed estimators are computationally efficient (i.e., appropriate for real time estimations), robust (i.e., appropriate for different heterogeneous scenarios), and versatile (i.e., easily adaptable for different systems).