Analytic Expressions of Some Statistics in Radar Target Recognition Based on Late Time Representation

Abstract

In this paper, we consider the projection of the late time response of an unknown radar target onto the column space and the left null space of the matrix whose entries are from the natural frequencies of the specific radar target. We get explicit expressions for the projection onto the column space, the projection onto the left null space, the square of projection onto the column space and the square of the projection onto the left null space. Also, we note that the norm of the defined projection onto the column space and the norm of the defined projection onto the left null space are Ricean distributed, and that the square of the norm of the projection onto the column space and the square of the norm of the projection onto the left null space are chi-square distributed. Accordingly, we give analytic expressions of the mean and the variance of the Ricean distribution and those of the chi-square distribution.