Thinned Array Beampattern Synthesis by Iterative Soft-Thresholding-Based Optimization Algorithms

In this paper, we cast thinned array beampattern synthesis as a linear inverse problem (LIP) and apply three iterative soft-thresholding based optimization algorithms to solve it effectively. We combine synthesis algorithms with beampattern error reweighting and beampattern phase adjustment to achieve accurate approximation of the desired reference pattern. The proposed methods can be used to synthesize arbitrarily shaped beam-patterns, including multibeam forming and radiation suppression within several angular regions. These methods offer a number of advantages in regard to array scale, beampattern specifics and computational time compared to existing methods. Since this paper focuses on synthesizing receiver arrays, there are no explicit constraints applied to the excitation weights. Numerical results demonstrate the efficiency of three proposed approaches for designing non-uniformly spaced arrays. In particular, the fast iterative soft-thresholding algorithm can synthesize of up to a few hundred antennas.