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In this paper, optimal designs of three-ring Concentric Circular Antenna Arrays (CCAA) without and with central element feeding are reported. For each optimal design, optimal current excitation weights and optimal radii are determined having the objective of maximum Sidelobe Level (SLL) reduction. The optimization technique adopted is Bacteria Foraging Optimization (BFO). 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 (-36.14 dB).