EAPSI: Computation of Wishart Eigenvalue Distributions for Multi-Channel Passive Radar Detection

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Passive radars seek to perform the same detection and characterization of targets as an active radar, with the key difference that passive systems do not transmit a signal. Instead, passive radars rely on electromagnetic radiation already present in the environment to illuminate targets, typically from sources such as radio, cellular, and television transmitters. In order for the system to decide if there is a target traveling at a particular velocity at a given angle and range, sophisticated models of the target and noise signals are employed to construct an optimal test statistic. This research seeks to use analytic and geometric methods to enable computation of noise models in multiple receiver passive radar systems in collaboration with Professor Vaughan Clarkson at the University of Queensland, who has significant experience in the areas of detection and estimation theory. The University of Queensland also offers the unique opportunity to test these models with data drawn from a single frequency network, in which area Professor Clarkson's group has particular expertise.In a multiple channel passive radar system, data vectors are measured at each receiver. When no signal is present, it is assumed that the data is identically distributed zero mean complex white Gaussian noise; this noise is considered additively in the case of a present signal. It has been shown that the optimal test statistic for presence of a rank one signal in such a system is the largest eigenvalue of the Grammian matrix constructed from the measured data. This Grammian matrix has a complex Wishart distribution, and closed form expressions exist for the largest eigenvalue distribution. However, expressions for the CDF involve taking the determinant of matrices with terms taking the form of ratios of gamma functions with large integer arguments, which overwhelm floating point representations for cases of practical interest. This project will utilize results expansions in terms of partial inner products with orthogonal polynomials to produce a factorization of this matrix to make computation tractable. Following completion of the theoretical portions of the work, single frequency network data gathered by the University of Queensland will be used for experimental tests.This award under the East Asia and Pacific Summer Institutes program supports summer research by a U.S. graduate student and is jointly funded by NSF and the Australian Academy of Science.