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

TL;DR

This paper proposes a robust beamforming design for RIS-aided cell-free systems that accounts for CSI uncertainties and limited backhaul, optimizing precoding and phase shifts to maximize worst-case sum rate with low complexity.

Contribution

It introduces an alternating optimization algorithm that jointly optimizes RIS phase shifts and precoding under CSI errors and backhaul constraints, with proven convergence and improved robustness.

Findings

Proposed algorithm outperforms existing methods in sum rate performance.

RIS phase shift optimization enhances robustness significantly.

Distributed RISs provide notable advantages in cell-free systems.

Abstract

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