On the Joint Beamforming Design for Large-scale Downlink RIS-assisted Multiuser MIMO Systems

TL;DR

This paper introduces an efficient joint beamforming algorithm for large-scale RIS-assisted multi-user MIMO systems, significantly improving spectral efficiency with reduced complexity and practical scalability.

Contribution

It proposes a novel low-complexity algorithm for joint precoder and phase shift design in large-scale RIS-MIMO systems, leveraging an equivalent reformulation and advanced optimization techniques.

Findings

The proposed algorithm reduces computational complexity linearly with system size.

It achieves higher weighted sum rate than baseline methods.

Numerical results confirm efficiency and scalability of the approach.

Abstract

Reconfigurable intelligent surfaces (RISs) have huge potential to improve spectral and energy efficiency in future wireless systems at a minimal cost. However, early prototype results indicate that deploying hundreds or thousands of reflective elements is necessary for significant performance gains. Motivated by this, our study focuses on \emph{large-scale } RIS-assisted multi-user (MU) multiple-input multiple-output (MIMO) systems. In this context, we propose an efficient algorithm to jointly design the precoders at the base station (BS) and the phase shifts at the RIS to maximize the weighted sum rate (WSR). In particular, leveraging an equivalent lower-dimensional reformulation of the WSR maximization problem, we derive a closed-form solution to optimize the precoders using the successive convex approximation (SCA) framework. While the equivalent reformulation proves to be efficient for the precoder optimization, we offer numerical insights into why the original formulation of the WSR optimization problem is better suited for the phase shift optimization. Subsequently, we develop a scaled projected gradient method (SPGM) and a novel line search procedure to optimize RIS phase shifts. Notably, we show that the complexity of the proposed method \emph{scales linearly with the number of BS antennas and RIS reflective elements}. Extensive numerical experiments demonstrate that the proposed algorithm significantly reduces both time and computational complexity while achieving higher WSR compared to baseline algorithms.