Decentralized Cooperative Beamforming for BDRIS-Assisted Cell-Free MIMO OFDM Systems

Abstract: In this paper, a wideband cell-free multi-stream multi-user Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) system is considered operating within a smart wireless environment enabled by multiple Beyond Diagonal Reconfigurable Intelligent Surfaces (BDRISs). A novel decentralized active and passive beamforming framework, robust to imperfect channel state availability and with minimal cooperation among the system's multiple Base Stations (BSs) for deciding the final configurations of the shared BDRISs, is proposed, which aims to substantially reduce the overhead inherent in centralized solutions necessitating a central processing unit of high computational power. By considering a Dynamic Group-Connected (DGC) BDRIS architecture with frequency-selective responses per unit element, we formulate the system's sum-rate maximization problem with respect to the tunable capacitances and permutation matrices of the BDRISs as well as the precoding matrices of the BSs, which is solved via successive concave approximation and alternating projections as well as consensus-based updates for the BDRISs' design. Through extensive simulation results, it is showcased that the proposed robust decentralized cooperative approach with diverse BDRIS architectures outperforms non-cooperation benchmarks. It is also demonstrated that the considered DGC BDRIS architecture is able to provide sum-rate performance gains sufficiently close to the more complex fully-connected BDRIS structure.