Synthesis of non-regular arrays using an FFT-based calculation of the cost function gradient

An efficient gradient-based optimization method was recently proposed for the array synthesis problems with free antenna positions. It relies on the use of a cost function that averages sidelobe levels using a (weighted) p-norm. We show how the gradient of this cost function can be evaluated using a Fourier transform, and hence computed quickly. We provide details about the FFT implementation of this computation. Numerical results for arrays comprising about 256 elements with constant magnitudes are reported, and the effects of mutual coupling between elements are demonstrated.