Parametric Rao test for multichannel adaptive detection of range-spread target in partially homogeneous environments

In this paper we deal with the problem of detecting a multi-channel signal of range-spread target in the presence of Gaussian disturbance with an unknown covariance matrix. In particular, we consider the so-called partially homogeneous environment, where the disturbances in both the cells under test (primary data) and the training samples (secondary data) share the same covariance matrix up to an unknown power scaling factor. To this end, we first model the disturbance as a multichannel autoregressive (AR) process, and then develop an adaptive detector resorting to the Rao test. Remarkably, the proposed detector attains asymptotically a constant false alarm rate (CFAR) independent of the disturbance covariance matrix as well as the power scaling factor. The performance assessment conducted by Monte Carlo simulation highlights that the new receiver significantly outperforms their traditional covariance matrix-based counterparts both in AR and non-AR modeled disturbance backgrounds. Meanwhile, it requires less secondary data and is computationally more efficient.