Parametric Rao Tests for Multichannel Adaptive Detection in Partially Homogeneous Environment

This paper considers the problem of detecting a multichannel signal in partially homogeneous environments, where the disturbances in both test signal and training signals share the same covariance matrix up to an unknown power scaling factor. Two different parametric Rao tests, referred to as the normalized parametric Rao (NPRao) test and the scale-invariant parametric Rao (SI-PRao) test, respectively, are developed by modeling the disturbance as a multichannel autoregressive (AR) process. The NPRao and SI-PRao tests entail reduced training requirements and computational efficiency, compared with conventional fully adaptive, covariance matrix based solutions. The SI-PRao test attains asymptotically a constant false alarm rate (CFAR) that is independent of the covariance matrix and power scaling factor of the disturbance. Comparisons with the covariance matrix based, scale-invariant generalized likelihood ratio test (GLRT), also known as the adaptive coherence estimator (ACE), are included. Numerical results show that the parametric Rao detectors, in particular the SI-PRao test, attain considerably better detection performance and use significantly less training than the ACE detector.