Synthesis of circular isophoric sparse arrays by using compressive-sensing

A design approach for large-scale sparse arrays based on Compressive Sensing has been recently introduced in the literature and extended to include complex EM effects and scan performance. However, that approach cannot directly control the number of excitation amplitudes. Here, we apply a two-step procedure that first synthesizes continuous rings with unconstrained amplitudes using an iterative ℓ1-norm minimization approach, and then replaces them with a circular isophoric ring array with a number of elements proportional to the original amplitude of each ring. The procedure is demonstrated for an isotropic array of a 10λ radius, for which a reference solution based on the analytical density-taper approach is available in the literature. Results show the capability of the proposed method to achieve a significant reduction of the array aperture (20%) with 25% less elements or 4dB lower peak side lobe level.