Exact Performance Analysis of an Adaptive Subspace Detector

The adaptive subspace detector (ASD), which is developed to handle detection problems in partially homogeneous environments where test and training data samples share the same noise covariance matrix up to an unknown scaling factor, has been evaluated in terms of probabilities of false alarm and detection. However, the probability of false alarm of the ASD is provided in an integral form. Moreover, the detection probability of the ASD is approximate in certain cases. In this correspondence, a finite-sum expression for the probability of false alarm of the ASD is obtained, and an exact expression for the detection probability of the ASD is also derived. These expressions are all validated using Monte Carlo simulations.