Multichannel Signal Detection Based on Wald Test in Subspace Interference and Gaussian Noise

This paper investigates the problem of detecting a multichannel signal embedded in subspace interference and Gaussian noise. The interference lies in a known subspace but with unknown coordinates, while the noise, in the general sense, consisting of thermal noise and clutter, has an unknown covariance matrix. To estimate the covariance matrix, it is assumed that there are sufficient signal-free training data. Two cases are considered, namely, the homogeneous environment (HE) and partially HE (PHE). The test and training data in the HE have the same noise covariance matrix, while the test and training data in the PHE share the same noise covariance matrix up to an unknown scaling factor. We derive the corresponding Wald tests both in the HE and PHE. Remarkably, these two detectors reject the clutter by using the sample covariance matrix, and then reject interference and integrate signal simultaneously through the oblique projection. Numerical examples show that the two proposed detectors can provide better detection performance than existing detectors in some situations.