Principal Angle Detector For Subspace Signal With Structured Unknown Interference

Detecting subspace signals is an important problem in radar and sonar signal processing, hyperspectral image processing, wireless communication, and other fields. Among these problems, a typical scenario is that one needs to detect a signal lying in a given target subspace, contaminated by interferences that also lie in some subspaces. Most classical works in this aspect treated only the cases where the interfering subspace is known a priori, but in practice the interfering subspace is often unknown. Recently, the arise of Volume Correlation Detector allows to detect subspace signals when the interfering subspace is unknown, but it does not work in the case where the target subspace overlaps with the interfering subspace. Moreover, previous literature only gives flawed technical analysis for Volume Correlation Detector. In this paper, we propose a new detector, called Principal Angle Detector (PAD), based on principal angles between subspaces. Our new detector is robust against overlapping target subspace and interfering subspace, and some other model mismatches. To provide a correct and reasonable theoretical result, we borrow from the literature of numerical linear algebra the tool of affine-invariant covariance estimation, which could be of potential use for related problems in signal processing.