Synthesis of small planar antenna arrays using collapsed distributions

This work presents an enhanced synthesis methodology for compact planar antenna arrays based on the principle of collapsed distributions. The proposed approach exploits the equivalence between azimuthal cuts of a planar radiation pattern and the patterns of corresponding linear arrays, enabling multidirectional radiation control under geometrical constraints. A 32-element planar array with square-grid geometry, circular boundary, and octant symmetry was synthesized by imposing Dolph–Chebyshev sidelobe specifications of $$-20$$ dB and $$-25$$ dB along the $$\phi = 0^\circ$$ and $$\phi = 45^\circ$$ cuts, respectively. The resulting overdetermined system was reformulated as a weighted optimization problem and solved using Particle Swarm Optimization (PSO), allowing flexible weighting between controlled directions. For comparison purposes, Genetic Algorithm (GA), Simulated Annealing (SA), and a Singular Value Decomposition (SVD)-based least-squares solution were also evaluated. Numerical results demonstrate that PSO significantly improves pattern accuracy and reduces residual error compared with the alternative approaches. Additional intermediate azimuthal cuts confirm the global angular stability of the synthesized radiation pattern. The proposed framework therefore constitutes an effective and robust methodology for the synthesis of compact planar arrays for modern beamforming and wireless communication applications.