Derivative constrained optimum broad-band antenna arrays

The optimization problem corresponding to the design of a presteered broadband processor with maximally flat second-order spatial response in the look direction is discussed. The constraints corresponding to necessary and sufficient conditions for second-order flatness are presented. The nonlinearly constrained optimization approach is unable to consistently locate the global minimum. An approach to solving this problem that essentially converts the nonconvex optimization problem into a parameterized set of convex problems is presented. In the case of 2-D scenarios, the global optimum is determined by finding the roots of a cubic function. The characteristics of the constraints, including the minimum number required and the dependence on the choice of coordinate systems, are examined.>