Robust Beamforming Design for RIS-aided Cell-free Systems with CSI Uncertainties and Capacity-limited Backhaul

In this paper, we consider the robust beamforming design in a reconfigurable intelligent surface (RIS)-aided cell-free (CF) system considering channel state information (CSI) uncertainties of both direct channels and cascaded at transmitter with capacity-limited backhaul. We jointly optimize precoding access points (APs) phase shifts multiple RISs to maximize worst-case sum rate CF subject constraints maximum transmit power APs, unit-modulus shifts, limited backhaul capacity, bounded CSI errors. By applying series transformations, non-smoothness semi-infinite are tackled low-complexity manner that facilitates an alternating optimization (AO)-based iterative algorithm. The proposed algorithm divides considered problem into two subproblems. For RIS subproblem, exploit penalty convex-concave procedure (P-CCP) obtain stationary solution achieve effective initialization. successive convex approximation (SCA) is adopted convergence guarantee Karush-Kuhn-Tucker (KKT) solution. Numerical results demonstrate effectiveness design, which achieves superior performance low complexity. Moreover, importance shift for robustness advantages distributed further highlighted.