Order-Statistic Based Target Detection with Compressive Measurements in Single-Frequency Multistatic Passive Radar

This paper considers the problem of compressive target detection with direct-path interference (DPI) and clutter in a single-frequency network (SFN) based multistatic passive radar system (MS-PRS). Specifically, a measurement matrix is designed to jointly obtain compressive observations and remove the DPI and clutter. We first analyze a compressive subspace detector which assumes the target support is known. When the target supports cannot be accurately obtained, an order-statistic (OS) based detector, referred to as the OSOMP, is proposed by using the orthogonal matching pursuit (OMP) algorithm to estimate the target support, and then projecting the compressive observations into the estimated subspace. Since OMP applies an iterative ranking process to select the components/atoms of the dictionary, the OSOMP test variable is an order statistic, which has a non-convergent distribution. To cope with this problem, a modified test statistic for the OSOMP detector is presented and an analytical expression for the probability of false alarm is obtained. We further discuss the minimum number of iterations required by the OSOMP algorithm to achieve the desired probability of detection and false alarm. Numerical simulations are conducted to verify the theoretical analysis and illustrate the performance of the proposed detector relative to several benchmark detectors.