Glrt-Based Outlier Prediction and Cure in Under-Sampled Training Conditions using a Singular Likelihood Ratio

For cases where the number of training samples T does not exceed the number of antenna elements M, we consider a detection-estimation problem for Gaussian sources occupying a low-rank m-dimensioned signal subspace within the associated covariance matrix (m < T < M). We derive a likelihood ratio that for the null hypothesis is described by a probability function that does not depend on a scenario, and investigate a (non-trivial) correspondence between the likelihood function and the derived likelihood ratio with respect to maximization performance. Practical application of this technique is illustrated for under-sampled (T < M) conditions for the purpose of MUSIC performance enhancement in the "threshold" region.