Paper
STAR Beyond Diagonal RISs with Amplification: Modeling and Optimization
Authors
Chandan Kumar Sheemar, Giovanni Iacovelli, Wali Ullah Khan, George C. Alexandropoulos, Stefano Tomasin, Symeon Chatzinotas
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.06020v1</id>\n <title>STAR Beyond Diagonal RISs with Amplification: Modeling and Optimization</title>\n <updated>2026-03-06T08:13:40Z</updated>\n <link href='https://arxiv.org/abs/2603.06020v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.06020v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.IT'/>\n <category scheme='http://arxiv.org/schemas/atom' term='eess.SP'/>\n <published>2026-03-06T08:13:40Z</published>\n <arxiv:primary_category term='cs.IT'/>\n <author>\n <name>Chandan Kumar Sheemar</name>\n </author>\n <author>\n <name>Giovanni Iacovelli</name>\n </author>\n <author>\n <name>Wali Ullah Khan</name>\n </author>\n <author>\n <name>George C. Alexandropoulos</name>\n </author>\n <author>\n <name>Stefano Tomasin</name>\n </author>\n <author>\n <name>Symeon Chatzinotas</name>\n </author>\n </entry>"
}