Robust Joint Beamforming Optimization for RISs-Empowered Cell-Free Networks

Abstract

Reconfigurable intelligent surfaces (RISs) have emerged as a promising economical solution to implement cell-free networks. In this paper, the joint active and passive beamforming optimization of access points (APs) and RISs for the RISs-empowered cell-free network in the presence of channel state information (CSI) estimation errors is investigated. By taking the CSI estimation errors into account, we start with deriving the expression of a tight lower bound on the exact sum-rate, which is taken as the optimization criteria. Then, a robust joint beamforming optimization algorithm is proposed to obtain the highest sum-rate by using the lower bound, so as to obtain the best result out of the worst-case. In addition, a counter-intuitive but interesting result can be concluded via rigorous mathematical derivations that CSI estimation errors always impact the optimization of active transmitting beamforming matrices of APs, but surprisingly have no impact on the optimization of passive reflecting beamforming matrices of RISs when the covariance matrices of CSI estimation errors seen from two sides of each channel are proportional to an identity matrix. Simulation results demonstrate that RISs can considerably improve the sum-rate of the conventional cell-free network, and confirm the resilience of the proposed algorithm against CSI uncertainty.