  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.
