Optimum pattern derivative synthesis in randomly perturbed linear array

The concept of pattern derivative is introduced in an optimal sense in a randomly perturbed linear array with equispaced isotropic elements. The effects of the random variations of weights and element positions on the expectations of the first-order derivative of array space-frequency and power responses are analyzed and employed in optimum weight solutions. Without loss of generality, it is assumed that the expected positions of elements are confined to one-dimensional space; the directions of arrivals for the relevant signals are confined to two-dimensional space; and the element positions vary randomly in three-dimensional space. To illustrate the broadband null performance, an optimum point null and an optimum derivative null are combined to produce a deep null in a three-element linear array.<>