A COVARIANCE (COHERENCY) MATRIX FOR BACKSCATTERED AND SPATIAL ELECTROMAGNETIC NOISE

Abstract

The covariance (coherency) matrix for both a backscattered electromagnetic process and a spatial-noise process is formulated. The elements of the matrix are the covariance and cross-covariance functions between orthogonal components of the electric field vector at right angles to the direction of propagation.First a backscattered model is developed. The time-varying covariance function for each component of the electric field vector is determined. An approximation is made in order to obtain an expression for the power spectrum of each component of the process. The component covariance function and the component power spectrum are both functions of the probability density that a scatterer will be at range r and time t as well as the transmitted pulse shape. This implies that in order to minimize the component (or total) power, the transmitted signal pulse may not be wide band, but is affected by the probability distribution of the scatterers.Next a stochastic representation for a general polarized, nonisotropic noise process is formulated. The formulation accounts for the three-dimensional aspects of the noise field. The purpose of the formulation is to determine the covariance matrix of the noise.