Adaptive Detection of Gaussian Rank-One Signals Using Adaptively Whitened Data and Rao, Gradient and Durbin Tests

We address the problem of detecting a Gaussian rank-one signal using training samples to learn the covariance matrix of the noise present in the samples under test. Towards this end, we propose to use the latter after they have been whitened by the sample covariance matrix of the training samples. As an alternative to the generalized likelihood ratio test, we investigate three simpler alternatives, namely the Rao, gradient and Durbin tests. Closed-form expressions of the corresponding test statistics are derived and the detectors are shown to have a constant false alarm rate. Their performance is assessed via numerical simulations.