CONSTRAINTS FOR MAXIMALLY FLAT OPTIMUM BROAD-BAND ANTENNA-ARRAYS

Frequency response shaping for the direct form pre-steered broadband ( PB) antenna array processor is often achieved by imposing look directi on constraints on the weights of the processor. This results in a line arly constrained optimization problem. To ensure a maximally flat spat ial response of a specified order in tbe look direction of the PB proc essor, additional constraints known as derivative constraints can be f urther imposed on the weights. In general, derivative constraints corr esponding to necessary and sufficient (NS) conditions for a maximally flat spatial power response can result in a quadratic equality constra ined optimization problem. In this paper, we transform the quadratic N S derivative constraints to parameterized linear forms. These paramete rized linear forms allow the global optimum of the quadratic equality constrained optimization problem to be obtained easily. They also prov ide a general framework for deriving new sets of derivative constraint s which correspond only to sufficient conditions for a maximally flat spatial power response. These sufficient derivative constraints are us eful for real-time processing because of their reduced computational r equirements and because they can deliver performance comparable to the NS derivative constraints.