Joint Optimization of Subarray Tiling and Rotation Angles for Circularly Polarized Multibeam Domino-Tiled Arrays Employing Generalized and Phase Dictionary Matrices

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This communication proposes a novel joint optimization method for subarray tiling and rotation angles in domino-tiled planar arrays to synthesize multi-beam circularly polarized (CP) patterns with constrained sidelobe level (SLL) and cross-polarization level (XPL). Unlike stepwise approaches that separately handle subarray tiling and rotation, the proposed joint optimization approach releases more degrees to enhance CP beam performance. To address the resulting coupled design challenge, two novel dictionary matrices are introduced: 1) A generalized dictionary matrix that represents candidate domino subarrays at discrete rotation angles, allowing distinction between subarrays sharing identical coordinates but distinct rotations; 2) A beam-specific phase dictionary matrix that encodes the required excitation phases, uniquely determined by each candidate’s coordinates and rotation angles, including both beam-scanning and polarization-compensation components. Then, a structured sparse vector incorporating rotation states is introduced to simultaneously determine subarray tiling and rotation from the proposed generalized dictionary, while retrieving the associated excitation phases from the phase dictionary. This sparse representation transforms the original coupled problem into a constrainedℓ1-minimization task. Simulation results demonstrate that the proposed joint optimization approach, relying on phase-only excitation, achieves CP beam performance comparable to amplitude-weighted stepwise methods, while consistently attaining lower SLLs under the same phase-only excitation strategy.

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