Bayesian Algorithms for Kronecker-structured Sparse Vector Recovery With Application to IRS-MIMO Channel Estimation

TL;DR

This paper introduces two algorithms within a Bayesian framework for recovering Kronecker-structured sparse vectors, with applications to IRS-MIMO channel estimation, demonstrating improved efficiency and accuracy over existing methods.

Contribution

It develops two novel algorithms for Kronecker-structured sparse recovery using Bayesian learning, with convergence guarantees and application to wireless channel estimation.

Findings

SVD-based method is more efficient and accurate.

Kronecker structure reduces local minima in the cost function.

Algorithms outperform state-of-the-art in numerical tests.

Abstract

We study the sparse recovery problem with an underdetermined linear system characterized by a Kronecker-structured dictionary and a Kronecker-supported sparse vector. We cast this problem into the sparse Bayesian learning (SBL) framework and rely on the expectation-maximization method for a solution. To this end, we model the Kronecker-structured support with a hierarchical Gaussian prior distribution parameterized by a Kronecker-structured hyperparameter, leading to a non-convex optimization problem. The optimization problem is solved using the alternating minimization (AM) method and a singular value decomposition (SVD)-based method, resulting in two algorithms. Further, we analytically guarantee that the AM-based method converges to the stationary point of the SBL cost function. The SVD-based method, though it adopts approximations, is empirically shown to be more efficient and accurate. We then apply our algorithm to estimate the uplink wireless channel in an intelligent reflecting surface-aided MIMO system and extend the AM-based algorithm to address block sparsity in the channel. We also study the SBL cost to show that the minima of the cost function are achieved at sparse solutions and that incorporating the Kronecker structure reduces the number of local minima of the SBL cost function. Our numerical results demonstrate the effectiveness of our algorithms compared to the state-of-the-art.