Generalized direction detectors in sample-starved environments

This paper investigates the problem of generalized direction detection in unknown Gaussian noise in sample-starved environment where the training data are insufficient such that the original sample covariance matrix is singular. To devise effective detectors, we first perform a unitary matrix transformation to the test data, which results in a signal-free data set, denoted as the virtual training data set. Then we use the true and virtual training data as the total training data, and adopt the principle of the generalized likelihood ratio test (GLRT) and two-step GLRT to design detectors, which has superior detection performance to the existing detectors. A dominant characteristic of the proposed detectors is that they can work in the aforementioned sample-starved environment.