Fast Correlated SBL Algorithm for Estimating Correlated Sparse Millimeter Wave Channels

Abstract

Correlated sparse Bayesian learning (Corr-SBL) is a powerful framework for multi-user multiple input multiple-output millimeter wave (mmWave) channel estimation. It exploits the underlying sparsity and spatial correlation in a mmWave channel. Due to massive antennas at the base station in mmWave systems, this algorithm becomes computationally expensive. This is because it inverts a high-dimensional matrix while computing the covariance matrix of the channel estimate. We propose a novel fast Corr-SBL algorithm, which exploits the sparsity in the estimated covariance matrix, and then calculates it approximately with a much lesser time complexity. We show that the proposed algorithm, without significantly compromising the performance, estimates a correlated sparse vector with a reduced complexity.