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In this letter, we focus on the hybrid precoding (HP) design for the reconfigurable intelligent surface (RIS) aided multi-user (MU) millimeter wave (mmWave) communication systems. Specifically, we aim to minimize the mean-squared-error (MSE) between the received symbols and the transmitted symbols by jointly optimizing the analog-digital HP at the base-station (BS) and the phase shifts (PSs) at the RIS, where the non-convex element-wise constant-modulus constraints for the analog precoding and the PSs are tackled by resorting to the gradient-projection (GP) method. We analytically prove the convergence of the proposed algorithm and demonstrate the desirable performance gain for the proposed design through numerical results.
Pradhan et al. (2020) studied this question.