Knowledge-Aided Adaptive Coherence Estimator in Stochastic Partially Homogeneous Environments

This letter introduces a stochastic partially homogeneous model for adaptive signal detection. In this model, the disturbance covariance matrix of training signals, ${\bf R}$ , is assumed to be a random matrix with some a priori information, while the disturbance covariance matrix of the test signal, ${\bf R}_{0}$ , is assumed to be equal to $\lambda {\bf R}$ , i.e., ${\bf R}_{0}=\lambda {\bf R}$ . On one hand, this model extends the stochastic homogeneous model by introducing an unknown power scaling factor $\lambda$ between the test and training signals. On the other hand, it can be considered as a generalization of the standard partially homogeneous model to the stochastic Bayesian framework, which treats the covariance matrix as a random matrix. According to the stochastic partially homogeneous model, a scale-invariant generalized likelihood ratio test (GLRT) for the adaptive signal detection is developed, which is a knowledge-aided version of the well-known adaptive coherence estimator (ACE). The resulting knowledge-aided ACE (KA-ACE) employs a colored loading step utilizing the a priori knowledge and the sample covariance matrix. Various simulation results and comparison with respect to other detectors confirm the scale-invariance and the effectiveness of the KA-ACE.