RIS-Aided Cell-Free Massive MIMO System: Joint Design of Transmit Beamforming and Phase Shifts

This article studies a reconfigurable intelligent surface (RIS)-aided cell-free massive multiple-input multiple-output system and formulate the max-min fairness problem that maximizes the minimum achievable rate among all the users by jointly optimizing the transmit beamforming at access points and the phase shifts at RISs. To address such a challenging problem, we first study the special single-user scenario and propose an algorithm that can transform the optimization problem into a semidefinite program (SDP) or an integer linear program for the cases of continuous or discrete phase shifts, respectively. Then, in order to solve the optimization problem for the multiuser scenario with continuous phase shifts, we propose an alternating optimization algorithm, which can alternately transform the problem into a second-order-cone program and an SDP. Finally, for the multiuser scenario with discrete phase shifts, we design a zero-forcing-based successive refinement algorithm, which can find the suboptimal transmit beamforming and phase shifts by means of alternating optimization. Numerical results show that compared with the benchmark schemes of random phase shifts and without using the RIS, the proposed algorithms can significantly increase the minimum achievable rate. It is also demonstrated that, compared with the case of programming continuous phase shifts, using 2-bit discrete phase shifts can practically achieve the same performance.