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：可重构智能表面（RIS）作为一种通过动态构建无线信道来提升未来无线通信系统性能的前沿技术，已进入公众视野。本文研究双RIS辅助的下行多用户多输入多输出（MIMO）通信系统。我们通过联合优化主动发射波束成形、接收均衡器以及每个RIS处的被动波束成形，探讨均方误差（MSE）最小化问题。与以往研究不同，为降低通信开销和信号处理复杂度，我们假设两个RIS采用公共反射模式。在该假设下，变量间的耦合性增强，从而使得优化问题更具挑战性。为有效应对这一难题，我们提出了一种基于多数最小化（MM）的交替优化（AO）算法。数值结果表明，在高信噪比（SNR）区域，采用公共反射模式的双RIS系统性能与采用独立反射模式系统几乎相同，而复杂度仅为后者的一半。因此，本文所提出的设计方案能够有效权衡所考虑系统的性能与实现复杂度。