STAR Beyond Diagonal RISs with Amplification: Modeling and Optimization

2026-03-06

AI Summary

This work addresses the physically consistent modeling and downlink sum-rate maximization for a STAR BD-RIS endowed with per-element amplification capability. By constructing a unified signal model that jointly incorporates per-element amplification, reflection/transmission power allocation, and passive non-diagonal coupling, the sum-rate maximization problem is reformulated as a weighted minimum mean square error (WMMSE) problem and solved via an alternating optimization framework. The key innovation lies in the first explicit decoupling of amplification, power allocation, and non-diagonal coupling, enabling distributed implementation while rigorously enforcing hardware constraints and passivity at each iteration. The algorithm integrates closed-form MMSE combiners, single-variable water-filling beamforming, cyclic coordinate descent for power allocation, and Riemannian gradient optimization over the complex Stiefel manifold with QR/polar decomposition retraction. Simulations demonstrate that the proposed method significantly outperforms conventional passive BD-RIS architectures.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Multiagent Systems: Mechanism Design
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Personalized, context-aware and across-device search
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• STAR RIS
• beyond-diagonal coupling
• per-element amplification
• sum-rate maximization
• hardware constraints

Innovation

• STAR RIS
• beyond-diagonal coupling
• per-element amplification
• WMMSE optimization
• Riemannian optimization