Weighted Codebook Scheme for RIS-Assisted Point-to-Point MIMO Communications

Reconfigurable intelligent surfaces (RIS) can reshape the characteristics of wireless channels by intelligently regulating the phase shifts of reflecting elements. Recently, various codebook schemes have been utilized to optimize the reflection coefficients (RCs); however, the selection of the optimal codeword is usually obtained by evaluating a metric of interest. In this letter, we propose a novel weighted design on the discrete Fourier transform (DFT) codebook to obtain the optimal RCs for RIS-assisted point-to-point multiple-input multiple-output (MIMO) systems. Specifically, we first introduce a channel training protocol where we configure the RIS RCs using the DFT codebook to obtain a set of observations through the uplink training process. Secondly, based on these observed samples, the Lagrange multiplier method is utilized to optimize the weights in an iterative manner, which could result in a higher channel capacity for assisting in the downlink data transmission. Thirdly, we investigate the effect of different codeword configuration orders on system performance and design an efficient codeword configuration method based on statistical channel state information (CSI). Finally, numerical simulations are provided to demonstrate the performance of the proposed scheme.