Common structured sparsity based multi-user channel estimation for double-RIS assisted millimeter wave systems

Compared to a single reconfigurable intelligent surface (RIS) system, a double RIS system can achieve better passive beamforming gain, while requiring more accurate channel state information (CSI). However, due to the presence of double-reflection links, channel estimation with low pilot overhead is quite challenging. In this paper, we investigate channel estimation of double-RIS assisted multi-user millimeter wave (mmWave) communication systems. Firstly, the channel estimation problem for double-reflection links is formulated as a sparse signal recovery problem. Then, we analyze and exploit the common structured sparsity of the cascaded channel among multiple users, i.e., the common row and column sparsity in the angular channel matrix, and the corresponding common sparsity after being transformed into the channel vector. Inspired by this, we further propose a novel common structured sparsity based orthogonal matching pursuit (CSS-OMP) algorithm for multi-user joint channel estimation. Simulation results show that CSS-OMP algorithm can provide more accurate channel estimation with reduced pilot overhead compared to the conventional OMP algorithm.