# Double-RIS Aided Multi-user MIMO Communications: Common Reflection Pattern and Joint Beamforming Design

## TL;DR

This paper proposes a joint beamforming design for double-RIS aided multi-user MIMO systems with a common reflection pattern, reducing complexity while maintaining high performance, especially at high SNR.

## Contribution

It introduces a novel optimization framework for double-RIS systems with shared reflection patterns, addressing the coupling challenge with a MM-based AO algorithm.

## Key findings

- Double-RIS with common reflection pattern achieves near the same performance as separate pattern at high SNR.
- The proposed method reduces complexity by half compared to separate reflection pattern systems.
- Numerical results validate the effectiveness of the joint beamforming design.

## Abstract

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.