Adaptive Detection of a Rank-One Signal Based on Wald Test

This paper considers the problem of detecting a matrix-valued rank-one signal when there is uncertainty in the target's spatial steering vector and temporal steering vector. To account for the above uncertainty, the target spatial steering vector and temporal steering vector are both assumed to lie in certain subspaces, but the corresponding coordinates are unknown. We design two adaptive detectors according to the criterion of Wald test. The one-step Wald test can provide better detection performance in some scenarios, compared with the existing one-step generalized likelihood ratio test (GLRT), while the two-step Wald test is equivalent to the two-step GLRT.