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.

在本文中，我们重新考虑了在未知高斯噪声中检测矩阵值的秩一信号的问题，该问题先前已在足够的训练数据的情况下得到解决。对于训练数据有限的情况，我们放宽了上述假设。我们基于对测试数据的某些unit变换，重新推导相应的广义似然比检验（GLRT）和两步GLRT（2S–GLRT）。结果表明，重新衍生的检测器可以在低样品支持率下工作。此外，在样品丰富的环境中，重新推导的GLRT与先前提出的GLRT相同，并且重新推导的2S–GLRT具有比先前提议的2S–GLRT更好的检测性能。提供了数值示例，以证明重新派生的检测器的有效性。