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In this paper, optimal array synthesis of three-ring concentric circular antenna arrays (CCAA) without and with central element feeding are reported. For each optimal synthesis, optimal current excitation weights and optimal radii of the rings are determined having the objective of maximum Sidelobe Level (SLL) reduction. The optimization technique adopted is Particle Swarm Optimization with Constriction Factor Approach (PSOCFA). The extensive computational results show that the CCAA having central element feeding yield much more reduction in SLL as compared to the same not having central element feeding. Moreover, the particular CCAA containing 4, 6 and 8 number of elements in three successive rings along with central element feeding yields grand minimum SLL (−36.00 dB).