Manifold Optimization Based Multi-user Rate Maximization Aided by Intelligent Reflecting Surface

TL;DR

This paper introduces novel manifold optimization algorithms for multi-user rate maximization in IRS-assisted systems, effectively leveraging geometric structures to enhance performance and address practical constraints.

Contribution

It proposes the DOMALO and S-DOMALO algorithms based on manifold theory for weighted sum-rate and minimal-rate maximization, respectively, with practical IRS considerations.

Findings

Algorithms outperform benchmark schemes significantly.

Effective handling of IRS phase shift resolution limitations.

Enhanced cooperative beamforming gains demonstrated.

Abstract

In this work, two problems associated with a downlink multi-user system are considered with the aid of intelligent reflecting surface (IRS): weighted sum-rate maximization and weighted minimal-rate maximization. For the first problem, a novel DOuble Manifold ALternating Optimization (DOMALO) algorithm is proposed by exploiting the matrix manifold theory and introducing the beamforming matrix and reflection vector using complex sphere manifold and complex oblique manifold, respectively, which incorporate the inherent geometrical structure and the required constraint. A smooth double manifold alternating optimization (S-DOMALO) algorithm is then developed based on the Dinkelbach-type algorithm and smooth exponential penalty function for the second problem. Finally, possible cooperative beamforming gain between IRSs and the IRS phase shift with limited resolution is studied, providing a reference for practical implementation. Numerical results show that our proposed algorithms can significantly outperform the benchmark schemes.