Maximally Sparse, Steerable, and Nonsuperdirective Array Antennas via Convex Optimizations

Achieving the minimum number of radiating elements in the active electronically scanned array synthesis represents a key problem in those applications where the power consumption, the weight, and the hardware/software complexity of the radiating system have a strong impact on the system cost. In this paper, a new method for the synthesis of planar, nonsuperdirective, maximally sparse, and steerable arrays is proposed and tested on several benchmarks available in the open literature. The method optimizes simultaneously the weight coefficients and sensor positions of a planar array without using global optimization schemes, properly exploiting convex optimization based algorithms. The resulting arrays are able to radiate a steerable beam pattern, satisfying a prescribed power mask and avoid to constraint the fitting of any a priori assigned reference field pattern. Several tests are presented to show the high efficiency in achieving the desired steerable radiation pattern with the minimum number of antenna elements.