A CFAR Adaptive Subspace Detector Based on a Single Observation in System-Dependent Clutter Background

In this paper, the problem of detecting target in system-dependent clutter (SDC) background with a single observation from the test cell is researched. Classical detectors, such as the generalized likelihood ratio detectors (GLRDs) and the adaptive matched filters (AMFs), etc., usually deal with the clutter and the noise as a whole. The low rank detectors (LRDs) make use of the low rank property of the clutter to improve the detection performance. However, the performance of LRDs degrades when the signal is not orthogonal with respect to (w.r.t.) the clutter. In this paper, an adaptive subspace detector for SDC (SDC-ASD) background which deals with the clutter and the noise separately is proposed. The SDC-ASD designs the test statistic by replacing the signal and the clutter covariance matrix with their maximum likelihood estimations (MLEs). Its theoretical false alarm probability and detection probability are analytically deduced. Analytical results show that the test statistic has the form of non-central $F$ distribution. Besides, it is shown that the SDC-ASD has constant false alarm rate (CFAR) performance w.r.t. the clutter and the noise. Numerical experiments are provided to validate the detection performance of the SDC-ASD in dealing with the target detection in SDC background.