Rao and Wald Tests for Target Detection in Coherent Interference

Interference can degrade the detection performance of a detector. Previously, several detectors were proposed according to the criteria of Rao and Wald tests in the presence of coherent interference. However, these detectors were derived by using incorrect Fisher information matrices (FIMs). This article considers the problems of subspace target detection in the presence of three cases of coherent interference. We redefine the complex parameter sets and correct the FIMs as well as the corresponding Rao and Wald tests. It is shown that some corrected detectors are new, some coincide with existing ones, and some are the subspace generalization of an existing one. There is no reasonable Rao or Wald test for a kind of coherent interference. Moreover, we derive the statistical performance of one corrected detector, including the analytical expressions for probability of detection and probability of false alarm. We also show the statistical distributions of another corrected detector which is the subspace generalization of an existing one. Numerical examples are provided to evaluate the performance of the corrected detectors. The results show that two Rao test-based detectors have good selectivity with signal mismatch, and a Wald test-based detector is robust for mismatch signals.