Variational Learning Algorithms For Channel Estimation in RIS-assisted mmWave Systems

We consider the problem of estimating the channel in reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) systems. We propose two variational expectation maximization (VEM) based algorithms for channel estimation in RIS-aided wireless systems. The first algorithm is a structured mean field-based sparse Bayesian learning (SM-SBL) algorithm that exploits the doubly-structured sparsity and the individual sparsity of the elements of the channel. To exploit the sparsities, we propose a column-wise coupled Gaussian prior. We next design the factorized mean field-based algorithm based on the prior we propose. This algorithm called the factorized mean field SBL (FM-SBL) algorithm, addresses the time complexities of the SM-SBL algorithm without sacrificing channel estimation accuracy. We show using extensive numerical investigations that the i) proposed SM-SBL and FM-SBL algorithms outperform several existing algorithms and ii) FM-SBL has lower time complexity than the SM-SBL algorithm.