In this letter, we investigate the signal-to-interference-plus-noise-ratio (SINR) maximization problem in a multi-user massive multiple-input-multiple-output (massive MIMO) system enabled with multiple reconfigurable intelligent surfaces (RISs). We examine two zero-forcing (ZF) beamforming approaches for interference management namely BS-UE-ZF and BS-RIS-ZF that enforce the interference to zero at the users (UEs) and the RISs, respectively.Then, for each case, we resolve the SINR maximization problem to find the optimal phase shifts of the elements of the RISs. Also, we evaluate the asymptotic expressions for the optimal phase shifts and the maximum SINRs when the number of the base station (BS) antennas tends to infinity. We show that if the channels of the RIS elements are independent and the number of the BS antennas tends to infinity, random phase shifts achieve the maximum SINR using the BS-UE-ZF beamforming approach. The simulation results illustrate that by employing the BS-RIS-ZF beamforming approach, the asymptotic expressions of the phase shifts and maximum SINRs achieve the rate obtained by the optimal phase shifts even for a small number of the BS antennas.

翻译：本文研究了多可重构智能表面（RIS）辅助的多用户大规模多输入多输出（massive MIMO）系统中的信干噪比（SINR）最大化问题。我们考察了两种用于干扰管理的迫零（ZF）波束成形方法，即BS-UE-ZF和BS-RIS-ZF，这两种方法分别使用户端（UE）和RIS端的干扰为零。针对每种情况，我们通过求解SINR最大化问题来寻找RIS元件的最优相移。此外，当基站（BS）天线数趋于无穷大时，我们评估了最优相移和最大SINR的渐近表达式。研究表明，若RIS元件信道独立且BS天线数趋于无穷大，采用BS-UE-ZF波束成形方法时，随机相移可达到最大SINR。仿真结果表明，即便BS天线数量较少，采用BS-RIS-ZF波束成形方法时，相移与最大SINR的渐近表达式仍能达到由最优相移所获得的速率。