Reconfigurable intelligent surface (RIS) has entered the public consciousness as a promising technology for enhancing the performance of future wireless communication systems by dynamically constructing the wireless channels. In this letter, we study a double-RIS aided downlink multi-user multiple-input multiple-output (MIMO) communication system. We investigate the mean-square-error (MSE) minimization problem by jointly optimizing the active transmit beamforming, the receive equalizer and the passive beamforming at each RIS. Different from prior works, for the sake of reducing both communication overhead and signal processing complexity, we assume that the two RISs utilize the common reflection pattern. Under this assumption, the coupling of the variables becomes tighter, thereby making the optimization problem more challenging to solve. To effectively address this issue, we propose a majorization-minimization (MM)-based alternating optimization (AO) algorithm.Numerical results show that in high signal-to-noise ratio (SNR) region, the double-RIS with common reflection pattern can achieve nearly the same performance as that with separate reflection pattern whereas the complexity is only half of the latter. Thus, our proposed design enables an effective tradeoff between the performance and the implementation complexity of the considered system.

翻译：重新配置的智能表面(RIS)已进入公众意识,成为通过动态建设无线频道来提高未来无线通信系统性能的一种有希望的技术。在本信中,我们研究了一种双RIS辅助的低链接多用户多投入多输出输出(MIIMO)通信系统。我们通过联合优化每个RIS的主动传输光束、接收平衡器和被动波束,调查了平均平流(MSE)最小化问题。与以往不同,为了减少通信间接费用和信号处理复杂程度,我们假定两个RIS利用了共同的反射模式。根据这一假设,变数的组合变得更为紧密,从而使优化问题更难以解决。为了有效解决这一问题,我们提议了一种基于主要最小化(MM)的交替优化(AO)算法。Numeric结果显示,在高信号对噪声率(SNR)区域,具有共同反射模式的双RIS可以实现几乎相同的性能,以不同的反射模式进行不同的反射,而复杂度则只能使所设想的贸易系统得到有效的执行。</s>