Multi-RIS Aided Cell-Free MIMO Networks with Imperfect CSI

In the pursuit of an efficient 6G network that achieves an enhanced capacity with minimal power consumption, reconfigurable intelligent surfaces (RIS) and cell-free Multiple-Input-Multiple-Output (CF-MIMO) emerge as two key technologies. In this paper, a joint precoding algorithm is designed for a multi-RIS aided CF-MIMO network, where the objective is to maximize the weighted sum rate (WSR) in the presence of imperfect channel state information (CSI) at the users. This optimization problem is divided into subproblems to alternately design the access point (AP) precoders and the RISs' phase shift matrices. A feasible solution is then obtained through a combination of Lagrangian Dual Reformulation (LDR), Fractional Programming (FP), and multidimensional complex quadratic transform (MCQT).