On the Maximum Achievable Sum-rate of the RIS-aided MIMO Broadcast Channel

TL;DR

This paper investigates the maximum sum-rate achievable in RIS-assisted MIMO broadcast channels, proposing algorithms to optimize user covariance matrices and RIS phase shifts, demonstrating significant performance gains through simulations.

Contribution

It introduces new algorithms for joint optimization of covariance matrices and RIS phase shifts in RIS-assisted MIMO broadcast channels, leveraging duality and gradient methods.

Findings

Algorithms converge to similar sum-rate but differ in specific cases.

Gradient-based methods are more time-efficient.

Significant sum-rate gains are achievable with multiple RISs depending on placement.

Abstract

Reconfigurable intelligent surfaces (RISs) represent a new technology that can shape the radio wave propagation and thus offers a great variety of possible performance and implementation gains. Motivated by this, we investigate the achievable sum-rate optimization in a broadcast channel (BC) in the presence of RISs. We solve this problem by exploiting the well-known duality between the Gaussian multiple-input multiple-output (MIMO) BC and the multiple-access channel (MAC), and we correspondingly derive three algorithms which optimize the users' covariance matrices and the RIS phase shifts in the dual MAC. The users' covariance matrices are optimized by a dual decomposition method with block coordinate maximization (BCM), or by a gradient-based method. The RIS phase shifts are either optimized sequentially by using a closed-form expression, or are computed in parallel by using a gradient-based method. We present a computational complexity analysis for the proposed algorithms. Simulation results show that the proposed algorithms tend to converge to the same achievable sum-rate overall, but may produce different sum-rate performance for some specific situations, due to the non-convexity of the considered problem. Also, the gradient-based optimization methods are generally more time efficient. In addition, we demonstrate that the proposed algorithms can provide a significant gain in the RIS-assisted BC assisted by multiple RISs and that the gain depends on the placement of the RISs.