Adaptive CFAR detection of multidimensional signals

Adaptive detection of multidimensional signals in the presence of interference with unknown covariance matrix is an expanding topic in a variety of scenarios ranging from radar/sonar to digital communication systems. In this paper we attack the problem of detecting a multidimensional radar signal, modeled as an unknown matrix, embedded in Gaussian noise with unknown covariance matrix, with the ambition of devising receivers which yield the Constant False Alarm Rate (CFAR) property. We show that this aim can be achieved resorting to the principle of invariance, namely restricting our attention to hypothesis testing problems which remain unaltered under a proper group of transformations. Several detectors based on the maximal invariant statistic are studied and, in particular, the Generalized Likelihood Ratio Test (GLRT) is shown to belong to the class of invariant tests.