Compressive Subspace Detectors Based on Sparse Representation in Multistatic Passive Radar Systems

This paper considers the problem of target detection by using compressive observations in a multistatic passive radar system (MS-PRS) consisting of one non-cooperative illuminator of opportunity, one reference channel, and multiple receivers. We first jointly design the measurement matrix for each receiver to obtain the compressive observations, thus making the echo signals at different receivers corresponding to the same target share the same target support indices (SSIs). Following this, a generalized likelihood ratio test (GLRT) based complex-valued compressive subspace detector (CSD) is provided given the prior of receiver noise variance. To further improve the detection performance, we develop a linear-fusion based CSD (LFCSD) by designing a set of weights at the fusion center. For the scenario of unknown noise variance, we continue to derive two GLRT-based unknown-noise CSDs (UNCSD). Specifically, we consider two cases based on whether the noise variance of each receiver is equal, referred to as the UNCSD1 and UNCSD2, respectively. Besides, we provide closed-form expressions of the probability of false alarm and detection of the proposed detectors. It is shown that the proposed UNCSD1 and UNCSD2 have constant false alarm rate (CFAR) properties. Finally, numerical simulation results show that the proposed detectors outperform the generalized coherence correlation (GCC) detector and the energy detector (ED) in low and moderate signal-to-noise ratio (SNR) regions.