Joint Compressed Signal Recovery and RIS Diagnosis via Double-Sparsity Optimization

Compressive Sensing (CS) technology, which handles large amounts of data in its low-dimensional form, has been shown to enjoy 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 be damaged and 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 failure. For the scenarios with and without Channel State Information (CSI) at the receiver, Double-Sparsity based algorithm (DS), and Atomic norm and Double-Sparsity based algorithm (ADS) exploiting Alternating Direction Method of Multipliers (ADMM) framework are proposed respectively. Additionally, a novel ℓB,B norm is incorporated to further constrain the block and binary characteristics of RIS failures, and the resulting improved versions of DS and ADS are termed as Binary and Block-Sparsity based algorithm (BBS) and Atomic norm, Binary and Block-Sparsity based algorithm (ABBS). Simulations verify the effectiveness and robustness of the proposed algorithms, and show the improved performance of the BBS and ABBS algorithms compared with the DS and ADS algorithms.