Adaptive Double Subspace Signal Detection in Gaussian Background-Part II: Partially Homogeneous Environments

In this part of the paper, we continue to study the problem of detecting a double subspace signal in Gaussian noise. Precisely, we address the detection problem in partially homogeneous environments, where the primary and secondary data share the same covariance matrix up to an unknown scaling factor. We derive the generalized likelihood ratio test (GLRT), Rao test, Wald test, and their two-step versions. We also introduce three spectral norm tests (SNTs). All these detectors possess the constant false alarm rate (CFAR) property. Moreover, various kinds of special cases of these detectors are given. At the stage of performance evaluation, we consider two cases. One is the case of no signal mismatch. The other is more general, namely, the case of signal mismatch, including the column-space signal mismatch and row-space signal mismatch.