A Two-Stage Scheme for Efficient RIS-Assisted Massive MIMO Sparse Channel Representation and Recovery

To realize the full potential of reconfigurable intelligent surface (RIS)-assisted massive multiple-input multiple-output (MIMO) systems, the acquisition of accurate channel information is crucial. However, the high-dimensional cascaded channel considering its underlying structured sparsity makes efficient channel estimation scheme design a challenging task. This paper develops a novel two-stage scheme for efficient RIS-assisted massive MIMO channel estimation where the methods for sparse channel representation and recovery are respectively designed. For the former, we develop a random search orthogonal matching pursuit (RSOMP) algorithm to exactly estimate the common angles of arrival at the base station side, based on which the dimension of sparse representation dictionary for the high-dimensional cascaded channel can be significantly reduced. The remarkable thing is that it can efficiently cope with the off-grid error caused by direction mismatch between the fixed sampling grids and the random directions of angles. For the latter, to relieve the high-computational complexity involving matrix inversion when calculating the posterior of channels, we develop a pattern-coupled covariance free expectation maximization (PC-CoFEM) algorithm, which simultaneously exploits the underlying block-structured sparsity of channels. Simulation results demonstrate that our proposed schemes can achieve superior performance to comparison schemes as well as illustrate the effectiveness for sparse channel representation and recovery.