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The material discussed can be divided into two parts. In the first part, an iteration method is presented for calculating the distances between the elements of a symmetrical nonuniformly spaced linear array antenna for sidelobe reduction. The amplitude of the excitation is assumed to be constant. The iteration method is applied to linear array consisting of 24 elements. After a few iterations, the sidelobe-to-mainlobe power ratio was reduced to over 22 dB from its value of 13.2 dB for uniform array spacing. In the second part, several symmetrical nonuniformly spaced planar array antennas have been designed, using the nonuniform linear array spacings of part one. The planar arrays include square-shaped and circular structures, with the number of elements ranging from 284 to 576. The iteration method discussed can be applied to linear arrays with any number of elements to obtain nonuniform grid spacings for sidelobe reduction. A number of planar grid structures can be constructed using the nonuniform linear grids. The nonuniform linear and planar arrays utilize fewer radiating elements and result in desirable sidelobe structures.