Joint Beamforming Design for RIS-Assisted Cell-Free Network with Discrete Phase Shifts

Deploying reconfigurable intelligent surface (RIS) in cell-free network can significantly increase network capacity. Compared with continuous RIS beamforming, existing studies on discrete beamforming lag, mostly the discrete problem is relaxed into a continuous problem for solving, which will lead to poor performance and high complexity. In this paper, a joint optimization algorithm is proposed. The central processing unit (CPU) is responsible for active beamforming and the RIS independently handles passive beamforming in the algorithm. The aim is to maximize the sum-rate of users under constraints of the transmit power of access points and the discrete phase shifts of the RIS. Firstly, Lagrangian dual reformulation and multidimensional complex quadratic transformation are used to obtain the active beamforming matrix. Secondly, a statistical learning method is employed to find optimal discrete phase shifts. The proposed algorithm compensates for the performance deficiency, as existing algorithms only select the phase closest to the selectable phase as the optimal phase shifts. Simulation results demonstrate that the proposed joint optimization algorithm is better than the existing algorithms.