The unitary symmetric matrix manifold is geometrically characterized with tangent space, retraction, and geodesics, enabling Riemannian line-search and phase-optimization algorithms that outperform prior BD-RIS methods and exploit low-rank structure when elements exceed antennas.
A tutorial on beyond- diagonal reconfigurable intelligent surfaces: Modeling, architectures, system design and optimization, and applications,
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A depth-first tree search algorithm is proposed for BD-RIS configuration in MU-MISO systems to achieve a performance-complexity trade-off in channel strength maximization.
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The manifold of unitary and symmetric matrices: characterization, Riemannian optimization and application to BD-RIS design
The unitary symmetric matrix manifold is geometrically characterized with tangent space, retraction, and geodesics, enabling Riemannian line-search and phase-optimization algorithms that outperform prior BD-RIS methods and exploit low-rank structure when elements exceed antennas.
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Tree Search Algorithms Applied to the BD-RIS Configuration in MU-MISO Communication Systems
A depth-first tree search algorithm is proposed for BD-RIS configuration in MU-MISO systems to achieve a performance-complexity trade-off in channel strength maximization.