Synthesis of Nonuniformly Spaced Arrays With Frequency-Invariant Shaped Patterns by Sequential Convex Optimization

In this letter, a novel synthesis method for nonuniformly spaced linear and planar arrays with frequency-invariant shaped patterns is proposed. This method consists of two steps. In the first step, we acquire the array excitation weights for all frequency sampling points through a sequence of weighted ${\boldsymbol{l}_1}$ convex optimizations. In the optimization process, conjugate symmetric array excitation weights are assumed so that the nonconvex lower bound constraints on the shaped patterns are convex. In the second step, we make use of the analytical method to design the finite impulse response (FIR) filters corresponding to each sensor to ensure that the frequency responses of filters approximate the weights of antenna elements.