Randomly perturbed array processing with optimum integral nulling approach

Pattern integral synthesis is used in an optimal sense to achieve a broadband gain response in a linear array with equispaced isotropic sensors which is subject to random variations of array weights and sensor positions. The expectations of integrals of array space-frequency and power responses are analyzed and used to find an optimum weight vector which generates a broadband gain response in a specified spatial region. A set of narrowband gains within a specified region, pattern derivative, or integral is used to achieve a broadband gain response. Without loss of generality, it is assumed that the expected sensor positions are confined to a one-dimensional space, the directions of incoming signals are confined to a two-dimensional space, and the sensor positions vary randomly in a three-dimensional space