Achievable Rate Analysis for Multi-Cell RIS-Aided Massive MIMO with Statistical CSI-Based Optimizations

The achievable rates and computationally efficient statistical channel state information (CSI) based phase-shift and transmit power optimization techniques are investigated for multi-cell reconfigurable intelligent surface (RIS)-aided multi-user massive multiple-input multiple-output (MIMO). The uplink effective composite channels are estimated via linear minimum mean square error techniques. The channel covariance matrices are adopted to optimize the RIS phase-shifts to maximize the average sum power gains of the composite channels pertaining to all users, while minimizing the inter-cell interference. The proposed transmit power control algorithm maximizes the minimum user rate across all cells to achieve a common rate, while ensuring user-fairness by negating near-far effects. The performance of these techniques is evaluated by deriving the achievable user rates in closed-form by presenting two lemmas and two corollaries. These new results can be useful in accurate performance analysis of RIS-aided massive MIMO without invoking typical approximations based on the central limit theorem and moment matching with Gamma distribution. The achievable user rate analysis can also be used to evaluate the impact of spatially correlated fading, erroneously estimated CSI, intra-cell co-channel interference, pilot contamination, and statistical CSI-based user signal decoding. The pilot overhead and computational complexity of the proposed techniques are quantified. Thereby, we reveal that the proposed phase-shift optimization technique is both computationally efficient and scalable with large numbers of reflective elements and BS antennas. Our achievable rate analysis and convergence of the optimization algorithms are validated through Monte-Carlo simulations and numerical results.