Beampattern Synthesis via First-Order Iterative Convex Approximation

This letter deals with a shaped beampattern synthesis problem through controlling the mainlobe ripple and the output filter energy based on the minimization of the peak sidelobe level in the spatial region of interest. To tackle the challenging optimization problem with nonconvex constraints, a novel first-order iterative convex approximation (FOICA) procedure that handles the nonconvex constraints with their convex upper bound functions resorting to the first-order Taylor expansion is developed. Hence, in each iteration, the original problem is approximated through a convex problem globally solved via a polynomial time method. Additionally, a nonnegative slack variable to ensure a decreasing trend in the objective function during the iteration is introduced. Finally, the numerical simulations are provided to verify that the proposed algorithm outperforms the state-of-the-art algorithms in terms of achieved beampattern performance.