DERIVATIVE CONSTRAINED OPTIMUM BROAD-BAND ANTENNA-ARRAYS

In optimum broad-band antenna processing, conditions are frequently im posed for shaping the frequency and spatial response of the processors . For direct form presteered broad-band processors, frequency response shaping in the look direction results in a linearly constrained optim ization problem. However, the constraints corresponding to necessary a nd sufficient conditions for second-order spatial derivatives to be ze ro are in general nonlinear and the optimization problem is nonconvex. The conventional approach for this problem is unable to consistently locate the global optimum. In this paper, a new approach is presented for solving this nonlinear constrained optimization problem. The new a pproach essentially converts the nonconvex optimization problem into a parameterized set of convex problems. In the case of two-dimensional (2-D) scenarios, the global optimum is determined by finding the roots of a cubic function. The paper also examines the characteristics of t he constraints, including the minimum number required and the dependen ce on the choice of coordinate systems. Previous work on second-order derivative constraints has proposed linear constraints which are coord inate system dependent.