A Bayesian approach to orthogonal rejection tests

In this paper, we deal with the problem of adaptive radar detection of point-like targets in presence of noise with unknown spectral properties. As customary, we assume that a set of data sharing the same properties of the noise in the cell under test is available. A Bayesian framework is adopted at the design stage. More precisely, the noise is assumed conditionally complex normal, given the covariance matrix, that in turn is ruled by a complex inverse Wishart distribution. In addition, in order to come up with detectors with good rejection capabilities, the possible presence of a fictitious signal under the null hypothesis is modeled probabilistically, as opposite to the conventional ABORT-like approach. Two detectors are proposed, which reveal a good trade-off between detection power and selectivity even assuming a limited number of training data.