Bayesian Inference Methods for Sparse Channel Estimation

This thesis deals with sparse Bayesian learning (SBL) with application to radio channel estimation.
As opposed to the classical approach for sparse signal representation, we focus on the problem of inferring complex signals. Our investigations within SBL constitute the basis for the development of Bayesian inference algorithms for sparse channel estimation.
Sparse inference methods aim at finding the sparse representation of a signal given in some overcomplete dictionary of basis vectors. Within this context, one of our main contributions to the field of SBL is a hierarchical representation of sparsity-inducing prior distributions for complex variables. The complex prior representation is rooted in complex Gaussian scale mixture models and encompasses as special cases the modeling of several sparsity-inducing
penalty functions previously introduced for real variables. We present a thorough analysis of the complex prior representation, where we show that the ability to induce sparse estimates of a given prior heavily depends on the inference method used and, interestingly, whether real or complex variables are inferred. We also show that the Bayesian estimators derived from the proposed complex prior representation achieve improved sparsity representations in low signalto-
noise ratio as opposed to state-of-the-art sparse estimators. This result is of particular importance for the applicability of the algorithms in the field of channel estimation.
We then derive various iterative inference algorithms based on the proposed prior representation for sparse channel estimation in orthogonal frequency-division multiplexing receivers.
The inference algorithms, which are mainly obtained from variational Bayesian methods, exploit the underlying sparse structure of wireless channel responses. Among the algorithms, we highlight our approach using generalized mean field inference. Within this framework, we derive different low complexity versions of a variety of SBL algorithms, where each version of the algorithm represents a different compromise between accuracy of the channel estimate and
computational complexity. We also analyze the impact of transceiver filters on the sparseness of the channel response, and propose a dictionary design that permits the deployment of sparse inference methods in conditions of low bandwidth.