Joint Sparsity and Low-Rank Minimization for Reconfigurable Intelligent Surface-Assisted Channel Estimation

Reconfigurable intelligent surfaces (RISs) have attracted extensive attention in millimeter wave (mmWave) systems because of the capability of configuring the wireless propagation environment. However, due to the existence of a RIS between the transmitter and receiver, a large number of channel coefficients need to be estimated, resulting in more pilot overhead. In this paper, we propose a joint sparse and low-rank based two-stage channel estimation scheme for RIS-assisted mmWave systems. Specifically, we first establish a low-rank approximation model against the noisy channel, fitting in with the precondition of the compressed sensing theory for perfect signal recovery. To overcome the difficulty of solving the low-rank problem, we propose a trace operator to replace the traditional nuclear norm operator, which can better approximate the rank of a matrix. Furthermore, by utilizing the sparse characteristics of the mmWave channel, sparse recovery is carried out to estimate the RIS-assisted channel in the second stage. Simulation results show that the proposed scheme achieves significant performance gain in terms of estimation accuracy compared to the benchmark schemes.