Optimum Array Processing and Characterization of Inhomogeneous Random Fields

Abstract

Characterization of second-order inhomogeneous random fields (four dimensional generalization of nonstationary stochastic processes) is of fundamental importance to the design of optimum array processors for reception of multipath signals in anisotropic and nonstationary noise fields. We review and establish interrelations between four second-order characterizations of inhomogeneous random fields. These are covariance functions, 2n-dimensional spectral density functions, Wigner distributions and complex ambiguity functions. We show that continuous parameter inner products on the reproducing kernel Hilbert space can be used to calculate detection indices for either distributed sensor or discrete optimum array processors. Discrete array processor is a special case of the continuous field formulation. Expressions for detection indices are derived in terms of Wigner distributions of signals and inverse kernels. Use of Wigner distribution in array processing is illustrated by specific examples.