Compressive sensing (CS) has attracted significant attention as a technique that under-samples high dimensional signals and accurately recovers them exploiting the sparsity of these signals. There are several ingredients of the CS algorithm. The first is the structure of the sparse signal. By exploiting additional signal structures in addition to the simple sparsity, additional performance gains can be obtained. How to choose a flexible yet tractable sparse prior to capture various sophisticated structured sparsity in specific application would be one of the challenges for the CS algorithm design. Another important ingredient that would affect the CS recovery performance is the measurement matrix. Different applications may result in measurement matrices with different features....[ Read more ]

Compressive sensing (CS) has attracted significant attention as a technique that under-samples high dimensional signals and accurately recovers them exploiting the sparsity of these signals. There are several ingredients of the CS algorithm. The first is the structure of the sparse signal. By exploiting additional signal structures in addition to the simple sparsity, additional performance gains can be obtained. How to choose a flexible yet tractable sparse prior to capture various sophisticated structured sparsity in specific application would be one of the challenges for the CS algorithm design. Another important ingredient that would affect the CS recovery performance is the measurement matrix. Different applications may result in measurement matrices with different features. How to handle a general measurement matrix would be another challenge for the CS algorithm design. In wireless communication system, due to the limited number of scatterers in the environment, the massive multi-input multi-output (MIMO) channel can be quite sparse under an appropriate spatial basis. Besides the channel sparsity, the massive MIMO channel further exhibits additional structures. In this thesis, we focus on the CS algorithm designs with applications to massive MIMO systems to exploit the possible structured sparsity and handle specific measurement requirement under different application contexts.

First, we consider channel support side information (CSSI) is available at base station, which can be exploited to enhance the channel estimation performance and reduce the pilot overhead. We propose a weighted LASSO algorithm to fully exploit the CSSI and propose an optimal weight policy to optimize the recovery performance. We also derive the closed-form accurate expression for the minimum asymptotic normalized squared error and characterize the minimum number of measurements required to achieve stable recovery.

Then, we consider a channel tracking problem in downlink frequency-division duplexing (FDD) massive MIMO system. We propose a two-dimensional Markov model to capture the two-dimensional (2D) dynamic sparsity of massive MIMO channels. We derive an effective message passing algorithm to recursively track the dynamic massive MIMO channels exploiting the 2D dynamic sparsity.

Besides the above works, we further propose a more general CS algorithm to solve the problem of recovering a structured sparse signal from a linear measurement model with uncertain measurement matrix. The proposed general framework can be utilized to provide highly accurate user location tracking in massive MIMO systems. Specifically, a three-layer hierarchical structured sparse prior model is proposed to capture complicated structured sparsities. By combining the message passing and variational Bayesian inference (VBI) approaches via the turbo framework, the proposed Turbo-VBI algorithm is able to fully exploit the structured sparsity for robust recovery of structured sparse signals under an uncertain measurement matrix.