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 technique. 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.

I. Introduction

Wireless technologies have gone through a series of notable improvement over the past few decades [1], [2], [3]. Most recently, the fifth-generation (5G) has been standardized, and massive multiple-input multiple-output (MIMO) has been one of its key enabling technologies [4]. The 5G wireless can attain substantial spectral and energy efficiency gains by virtue of large spatial multiplexing gains offered by massive antenna arrays [4]. Currently, novel candidate wireless technologies are being researched for beyond 5G (B5G) and sixth-generation (6G). Reconfigurable intelligent surfaces (RISs) have emerged as a promising physical layer technology owing to the recent advancements in metasurfaces and metamaterials [3], [5]. With the invention of RISs, the propagation environment may be perceived as passively controllable from the wireless designer’s perspective [3], [5]. Intelligently controllable phase-shifts can be introduced to the impinging electromagnetic (EM) waves off RISs to obtain passive beamforming gains at the desired directions to improve the end-to-end performance metrics through constructive signal combining. By meticulously designing passive phase-shift matrices, the RISs can also mitigate interference in the undesired directions via destructive combining of the EM signals [3], [5].