Detection of a rank-one signal with limited training data

In this paper, we reconsider the problem of detecting a matrix-valued rank-one signal in unknown Gaussian noise, which was previously addressed for case sufficient training data. We relax above assumption to limited re-derive corresponding generalized likelihood ratio test (GLRT) and two-step GLRT (2S–GLRT) based on certain unitary transformation It is shown that re-derived detectors can work with low sample support. Moreover, sample-abundant environments same as proposed 2S–GLRT has better detection performance than 2S–GLRT. Numerical examples are provided demonstrate effectiveness detectors.