Statistical CSI Based Phase-Shift and Transmit Power Optimization for RIS-Aided Massive MIMO

We investigate statistical channel state information (CSI) based phase-shift and transmit power optimization techniques for the reconfigurable intelligent surface (RIS)-aided multi-user massive multiple-input multiple-output (MIMO) systems. Towards this end, the uplink composite channel at the massive MIMO base-station is estimated by using uplink pilots sent by the users via linear minimum mean square error estimation for an arbitrary phase-shift matrix at the RIS. Then, the RIS phase-shift matrix is iteratively optimized to maximize the sum of eigenvalues of the correlation matrix of the weakest user. Thereby, a maximal ratio transmission based precoder is designed by using the estimated composite channel together with the statistical CSI based optimal phase-shift matrix for the downlink payload transmission. Via the worst-case Gaussian technique, the downlink achievable user rates are derived in closed-form for correlated Rayleigh fading in the presence of imperfect CSI. A max-min based transmit power optimization algorithm is proposed to provide a common system-wide achievable user rate and thereby ensuring user-fairness while mitigating near-far effects. Monte-Carlo simulations are presented to validate our rate analysis, to exhibit the convergence of our proposed optimization algorithms, and to reveal system-design insights.