Sparse Signal Recovery and RIS Diagnosis: Double-Sparsity Based Algorithms

Compressive sensing (CS) technology, which handles large amounts of data in its low-dimensional form, enjoys excellent transmission and storage efficiency. To further improve the stability and robustness of CS-based wireless communication system, reconfigurable intelligent surface (RIS) technology has been introduced to enhance the transmission link connectivity. Current researches generally assume perfect RIS; however, some of its elements may fail to work, which degrades the sparse signal recovery. Therefore, this paper establishes a double-sparsity optimization model to jointly recover the sparse signal and diagnose the RIS element state. A double-sparsity based algorithm (DS) exploiting Alternating Direction Method of Multiplier framework is proposed as the solution. Additionally, a novel
$\ell_{B,B}$
norm is incorporated to further constrain the block and binary characteristics of RIS failures, and the resulting improved version of DS is termed as the binary and block-sparsity based algorithm (BBS). Simulations verify the effectiveness and robustness of the proposed algorithms, and show the improved performance of the BBS algorithm compared with the DS algorithm.