Synthesis of Linear and Planar Arrays With Minimum Element Selection

A new method for the synthesis of linear and planar arrays having prescribed beamwidth and sidelobe levels and a minimum number of elements is proposed. In the method, the number of elements in an array is minimized while constraining the amplitude-response error in the mainlobe region, the attenuation in the sidelobe region, and the array dimensions. An iterative constrained optimization method is used where the amplitude-response error is linearly approximated at each iteration while concurrently minimizing a re-weighted L1 norm of the array coefficients. To ensure robustness of the array, we constrain a sensitivity parameter, namely, the white noise gain, to be above a prescribed level. Furthermore, the method also provides the additional flexibility of controlling the array dimensions, symmetry properties, and element positions of the array. Two variants have been developed: In the first variant, both the array coefficients and the positions of the elements are optimized; in the second variant, only the array coefficients are optimized while the elements are fixed at predefined positions. Experimental comparisons with several state-of-the-art competing methods show that the proposed method provides greater flexibility of controlling the robustness, beampattern response error, array dimensions, and element positions while at the same time the number of elements is less than or equal to that of the competing methods.