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