Abstract Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels are independent and contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue $\lambda_1$ of the Gram matrix formed from data. This Gram matrix has a Wishart distribution. Although exact expressions for the distribution of $\lambda_1$ are known under both hypotheses, numerically calculating values of these distribution fu... (more) 2019 Jones, Scott (Author) / Cochran, Douglas (Advisor) / Berisha, Visar (Committee member) / Bliss, Daniel (Committee member) / Kosut, Oliver (Committee member) / Richmond, Christ (Committee member) / Arizona State University (Publisher) Electrical engineering / Statistics / Applied mathematics / Multi-channel detection / Passive Radar / Wishart Doctoral Dissertation 114 pages English Doctoral Dissertation Electrical Engineering 2019 Graduate College / ASU Library MODS / OAI Dublin Core / RIS