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In this paper, an achievable rate analysis is presented for the downlink and uplink (UL) of reconfigurable intelligent surface (RIS)-aided massive multiple-input multiple-output (MIMO) non-orthogonal multiple-access (NOMA) systems. A linear minimum mean square error estimation technique is used to estimate the UL composite channels at the massive MIMO base-station via the user pilots for a given RIS phase-shift matrix. A statistical channel state information (CSI)-based RIS phase-shift optimization technique is adopted by leveraging the effective covariance matrices of the composite channels pertaining to NOMA clusters with distinct spatial signatures. Since channel statistics vary at a much slower rate compared to the channel coherence interval, the proposed RIS-aided NOMA system design is benefited by a much lower pilot overhead and computational complexity than the instantaneous CSI-based joint phase-shift and precoder optimization techniques. The achievable sum rates are derived in closed-form for the maximum ratio transmission/combining based linear precoder/detector in the presence of practical impediments, including spatially correlated fading, erroneously estimated CSI, intra-cluster pilot contamination, imperfect successive interference cancellation, and hardware impairments by leveraging the statistical CSI-based optimal RIS phase-shift matrix. The pilot overhead, computational complexity, and convergence of the proposed phase-shift optimization are investigated and compared against the baseline techniques that use instantaneous CSI-aided optimization with semi-definite relaxation techniques. Monte-Carlo simulations/numerical results are used to validate our achievable sum rate analysis and to investigate the rate gains of the proposed system design over the orthogonal multiple access based counterparts.
Jayasinghe et al. (Mon,) studied this question.