STAR Beyond Diagonal RISs with Amplification: Modeling and Optimization
This work addresses the problem of optimizing STAR BD-RIS performance for wireless communication systems, offering significant sum-rate gains for practitioners designing next-generation wireless networks.
This paper develops a physically consistent signal model for simultaneous transmitting and reflecting beyond-diagonal reconfigurable intelligent surfaces (STAR BD-RIS) with per-element amplification and lossless power splitting. The model incorporates practical constraints like emission caps and power budgets. Building on this, the authors propose an alternating optimization framework for downlink sum-rate maximization, demonstrating substantial sum-rate gains compared to conventional passive BD-RIS.
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.