Abstract
The uplink of a reconligurable intelligent surfaces (RIS)-aided cell-free massive multiple-input multiple-output (MIMO) system is analyzed, where the channel slate information (CSI) is estimated using uplink pilots. First, we derive analytical expressions for the achievable rate of the system with zero forcing (ZF) receiver, taking into account the effects of pilot contamination, channel estimation error and the distributed RISs. The max-min rale optimization problem is considered with per-user power constraints. To solve this non-convex problem, we propose to decouple the original optimization problem into two sub-problems, namely, phase shift design problem and power allocation problem. The power allocation problem is solved using a standard geometric programming (GP) whereas a semidefinite programming (SDP) is utilized to design the phase shifts. Moreover, the Taylor series approximation is used to convert the nonconvex constraints into a convex form. An iterative algorithm is proposed whereby at each iteration, one of the sub-problems is solved while the other design variable is fixed. The max-min user rate of the RIS-aided cell-free massive MIMO system is compared to that of conventional cell-free massive MIMO. Numerical results indicate the superiority of the proposed algorithm compared with a conventional cell-free massive MIMO system. Finally, the convergence of the proposed algorithm is investigated.