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：在这份信函中，我们研究了使用多重可重构智能表面(RISs)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。我们研究了两种用于干扰管理的零强制(ZF)波束成形方法，即基站-用户设备-ZF和基站-RIS-ZF，分别在用户(UEs)和RISs强制干扰为零。然后，针对每种情况，我们解决了SINR最大化问题，找到了RIS中元素的最优相位移位。此外，我们评估了当基站(BS)天线数量趋于无穷大时，最优相位移位和最大SINR的渐近表达式。我们表明，如果RIS元素的信道是独立的，且基站天线的数目趋近无限大，则随机相位移位使用基站-用户设备-ZF波束成形方法能够实现最大SINR。仿真结果表明，通过使用基站-RIS-ZF波束成形方法，相位移位和最大SINR的渐近表达式即使在基站天线数量较少的情况下，也可以达到最优相位移位所获得的速率。