Eigenvalue Tests and Distributions for Small Sample Order Determination for Complex Wishart Matrices
Abstract
This thesis looks at tests to determine how many signal sources exist in the medium when constrained to using only a few samples. It applies classical hypothesis testing assuming complex multivariate Gaussian random variables. The critical issue is the derivation of probability density functions of appropriate test statistics. This thesis includes a comprehensive development of the tools of statistics of complex variables for engineers and physicists. This includes complex matrix derivatives, changes of complex variables, and properties of the characteristic function of a complex multivariate random variable. Probability density functions are derived for: the set of eigenvalues satisfying the generalized eigenvalue problem of two complex Wishart matrices, the matrix complex Normal distribution, a joint distribution needed to derive the density for the sphericity test statistic, ratio of averages of disjoint sums of sequential eigenvalues of a complex Wishart matrix, and several tests based on the ratio of an arbitrary eigenvalue. Mathematical statistics, Probability, Hypothesis tests, Complex variables, Principal components analysis, Complex Wishart distribution, Eigen-structure signal processing
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 13, 1994
- Accession Number
- ADA283825
Entities
People
- Curtis I. Caldwell
Organizations
- Office of Naval Research