Abstract

Compressive sensing (CS) is a revolutionary theory that has important applications in many engineering areas. Using CS, sparse or compressible signals can be recovered from incoherent measurements with far fewer samples than the conventional Nyquist rate. In wireless communication problems where the sparsity structure of the signals and the
channels can be explored and utilized, CS helps to significantly reduce the number of transmissions required to have an efficient and reliable data communication. The objective of this thesis is to study new methods of CS, both from theoretical and application perspectives, in various complex, multi-channel and large-scale wireless networks. Specifically, we explore new sparse signal and channel structures, and develop low-complexity CS-based algorithms to transmit and recover data over these networks more efficiently.

Starting from the theory of sparse vector approximation based on CS, a compressive multiple-channel estimation (CMCE) method is developed to estimate multiple sparse channels simultaneously. CMCE provides a reduction in the required overhead for the estimation of multiple channels, and can be applied to estimate the composite channels of
two-way relay channels (TWRCs) with sparse intersymbol interference (ISI). To improve end-to-end error performance of the networks, various iterative estimation and decoding
schemes based on CS for ISI-TWRC are proposed, for both modes of cooperative relaying: Amplify-and-Forward (AF) and Decode-and-Forward (DF). Theoretical results including
the Restricted Isometry Property (RIP) and low-coherent condition of the discrete pilot signaling matrix, the performance guarantees, and the convergence of the schemes are presented in this thesis. Numerical results suggest that the error performances of the system is significantly improved by the proposed CS-based methods, thanks to the awareness of the sparsity feature of the channels.

Low-rank matrix approximation, an extension of CS-based sparse vector recovery theory, is then studied in this research to address the channel estimation problem of large-scale (or massive) multiuser (MU) multiple-input multiple-output (MIMO) systems. A low-rank channel matrix estimation method based on nuclear-norm regularization is formulated and solved via a dual quadratic semi-definite programming (SDP) problem. An explicit choice of the regularization parameter and useful upper bounds of the error are presented to show the efficacy of the CS method in this case. After that, both the uplink channel estimation and a downlink data precoding of massive MIMO in the interference-limited multicell scenarios are considered, where a CS-based rank-q channel approximation
and multicell precoding method are proposed. The results in this work suggest that the proposed method can mitigate the effects of the pilot contamination and intercell interference, hence improves the achievable rates of the users in multicell massive MIMO systems. Finally, various low-complexity greedy techniques are then presented to confirm the efficacy and feasibility of the proposed approaches in practical applications.