A Hybrid Method for the Optimal Synthesis of 3-D Patterns of Sparse Concentric Ring Arrays

A hybrid method is proposed for synthesizing sparse concentric ring arrays (CRAs) to get circularly symmetric and invariant three-dimensional (3-D) patterns over all-azimuth directions. The hybrid method involves a convex optimization approach and a determined approach together. Based on the Bessel function approximation of the circular array pattern and the compressed sensing (CS) theory, the synthesis of a sparse concentric current ring array can be formulated as a convex problem with the minimization of
$l_1$
-norm, and the corresponding array parameters including the number of concentric rings, the ring radii, and the current ring excitations can be determined simultaneously to satisfy the requirements on radiation pattern. In order to reconstruct the 3-D pattern accurately with discrete antenna elements in place of the current rings, a determined approach with or without radial amplitude weighting is proposed to define the number of elements equally distributed on each ring. The proposed hybrid method can be applied to synthesizing CRAs with 3-D pattern either matching a desired pattern or satisfying a prescribed power mask. Moreover, the method is very easy to implement, while has good numerical stability and computational efficiency. Numerical experiments are conducted to validate the flexibility and effectiveness of the proposed method.