Fractional Programming and Manifold Optimization for Reciprocal BD-RIS Scattering Matrix Design

TL;DR

This paper introduces a novel optimization framework combining fractional programming and manifold optimization to enhance the sum-rate performance of BD-RIS-assisted MU-MISO systems, demonstrating reduced complexity and improved results.

Contribution

It presents a new method integrating fractional programming and manifold optimization for BD-RIS scattering matrix design, outperforming existing techniques.

Findings

Reduced computational complexity compared to state-of-the-art methods

Significant sum-rate performance improvements in simulations

Effective optimization of the scattering matrix for MU-MISO systems

Abstract

We investigate the problem of maximizing the sum-rate performance of a beyond-diagonal reconfigurable intelligent surface (BD-RIS)-aided multi-user (MU)-multiple-input single-output (MISO) system using fractional programming (FP) techniques. More specifically, we leverage the Lagrangian Dual Transform (LDT) and Quadratic Transform (QT) to derive an equivalent objective function which is then solved iteratively via a manifold optimization framework. It is shown that these techniques reduce the complexity of the optimization problem for the scattering matrix solution, while also providing notable performance gains compared to state-of-the-art (SotA) methods under the same system conditions. Simulation results confirm the effectiveness of the proposed method in improving sum-rate performance.