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.