Sparse Bayesian Learning for Joint Channel Estimation and Data Detection in OFDM Systems

Bayesian approaches for sparse signal recovery have enjoyed a long-standing history in signal processing and machine learning literature. Among the Bayesian techniques, the expectation maximization based Sparse Bayesian Learning (SBL) approach is an iterative procedure with global convergence guarantee to a local optimum, which uses a parameterized prior that encourages sparsity under an evidence maximization framework. SBL has been successfully employed in a wide range of applications ranging from image processing to communications. In this thesis, we propose novel, efficient and low-complexity SBL-based algorithms that exploit structured sparsity in the presence of fully/partially known measurement matrices. We apply the proposed algorithms to the problem of channel estimation and data detection in Orthogonal Frequency Division Multiplexing (OFDM) systems. Further, we derive Cramér Rao type lower Bounds (CRB) for the single and multiple measurement vector SBL problem of estimating compressible vectors and their prior distribution parameters. The main contributions of the thesis are as follows: • We derive Hybrid, Bayesian and Marginalized Cramér Rao lower bounds for the problem of estimating compressible vectors drawn from a Student-t prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error (MSE) in the estimates. Through simulations, we demonstrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector. • OFDM is a well-known multi-carrier modulation technique that provides high spectral efficiency and resilience to multi-path distortion of the wireless channel. iii