STAR Beyond Diagonal RISs with Amplification: Modeling and Optimization

TL;DR

This paper introduces a comprehensive model and optimization framework for a novel STAR BD-RIS with amplification, enabling enhanced signal control and significant sum-rate improvements over traditional passive RIS systems.

Contribution

It develops a physically consistent model for STAR BD-RIS with amplification, and proposes an efficient optimization algorithm with provable convergence for sum-rate maximization.

Findings

Achieves substantial sum-rate gains over passive BD-RIS.

Provides a closed-form solution for MMSE updates and a waterfilling-like beamformer update.

Ensures passivity and practical feasibility through Riemannian gradient steps.

Abstract

This paper develops a physically consistent signal model with hardware constraints for a simultaneous transmitting and reflecting beyond-diagonal RIS (STAR BD-RIS) endowed with per-element amplification and lossless power splitting. We explicitly decouple (i) amplification via a diagonal gain matrix, (ii) element-wise reflection/transmission splitting, and (iii) passive beyond-diagonal coupling on each branch, while enforcing practical feasibility through per-element emission caps and an aggregate RIS power budget under the operating covariance. Building on this model, we cast downlink sum-rate maximization as an equivalent weighted minimum mean-square error (WMMSE) problem and propose an alternating optimization framework with provable monotonic descent. The method admits closed-form updates for MMSE combiners and weights, waterfilling-like beamformer updates via a single dual variable, a per-element amplification update that satisfies emission constraints, and a STAR power-splitting update based on cyclic coordinate descent with a global acceptance test. For the beyond-diagonal coupling matrices, we derive Riemannian gradient steps on the complex Stiefel manifold with QR/polar retraction method, preserving passivity at every iterate. Furthermore, the proposed approach decouples the optimization of the reflective and transmissive responses of the BD-RIS, enabling efficient distributed implementation. Numerical results demonstrate substantial sum-rate gains compared to the conventional passive BD-RIS.