Use of an under-sampled likelihood ratio for GLRT and AMF detection

In this paper we propose a modified GLRT and AMF adaptive detection framework for scenarios with a number of training samples that does not exceed the adaptive system (antenna) dimension, when the traditional maximum likelihood covariance matrix estimation, adopted in the current GLRT and AMF detectors, is not applicable. The introduced techniques rely upon the modified likelihood ratios recently suggested for testing covariance matrices with finite signal subspace dimension. We demonstrate that the modified framework provides theoretical justification and parameter selection for some known "under-sampled" techniques and is capable of suggesting new similarly efficient detectors.