Adaptive Robust Subspace Detection Based on GLRT, Rao, Wald, Gradient, and Durbin Tests

The current paper investigates the issue of designing adaptive robust subspace detectors in Gaussian noise whose covariance matrix is unknown. The original problem is revised by importing a fictitious signal with a given structure within the signal-plus-noise hypothesis to collect leakage signals around the subspace, thus increasing the credibility of this hypothesis in situations involving mismatch. To solve the issue described above, we utilize the generalized likelihood ratio test, Rao, Wald, Gradient, and Durbin tests to derive five adaptive subspace detectors. Both theoretical proofs and Monte Carlo simulation results suggest that these proposed detectors possess the constant false alarm rate properties. Numerical examples reveal the effectiveness of these proposed detectors and show their varying degrees of robustness under mismatch scenarios.