Showing papers on "Complex normal distribution published in 1971"

Complex Gaussian noise moments

Abstract: The problem of the computation of moments of nonzero mean circularly complex Gaussian noise is treated. The noise need not be symmetric about the carrier frequency. In particular, the second-order moments are computed, and expansions are given. The necessary univariate and bivariate complex Hermite polynomials are discussed. The means of some rational functions useful in FM theory are given. This paper extends work of Rice, Middleton, and Zadeh to complex Gaussian noise with nonzero mean and nonsymmetrical power spectrum.

A Canonical Form of the Likelihood Detector for Gaussian Random Vectors

Abstract: In this paper, the likelihood ratio detector for zero‐mean complex Gaussian vector signals in zero‐mean complex Gaussian vector noise is considered. The receiving apparatus is assumed to be spatially distributed, and only a single frequency of interest is treated. By simultaneous diagonalization of the signal and noise spatial covariance matrices, say S and N, a canonical form is found for the familiar detector appropriate to this problem. Using this canonical form, a number of special cases follow easily. First, for small signals such that all eigenvalues of SN−1 are less than 1, we obtain the approximate detector. We then obtain the usual matched filter and threshold for the plane‐wave signal case, and a generalization to the case of a signal which is a superposition of plane waves. Finally, for signals such that the smallest nonzero eigenvalue of SN−1 is greater than 1, we obtain the asymptotic detector. Few of the results presented are new, but it is hoped that their derivation in a unified way from t...

Some Inference Problems Associated with the Complex Multivariate Normal Distribution

Abstract: : Consider k = q+1 complex multivariate normal populations with the same variance-covariance matrix but with different means. The problem of the number of discriminant functions needed to discriminate among the k-populations is considered and shown to be equivalent to the rank of the mean-space. A test for this dimensionality being R is presented. Also developed is the statistic for testing the goodness of fit of a single hypothetical discriminant function. As in the case of the real normal populations, the test statistic for this single hypothetical function is presented as the product of two independent factors, whose distributions are given; one measuring the direction aspect of the hypothetical function, and the other measures the collinearity aspect that is the necessity of only one function. Also included is the Bartlett decomposition of a complex Wishart matrix and some results pertaining to the coherence of complex random variables.