CFAR adaptive detection of distributed signals

We consider the problem of detecting distributed signals described by the second order Gaussian models in the presence of noise whose covariance structure and level are both unknown. Such a detection problem is often called the "Gauss-Gauss" problem in that both the signal and the noise are assumed to have Gaussian distributions. We derive an adaptive detector for the second order Gaussian (SOG) model signals based on multiple observations. The detector is derived in a manner similar to that of the generalized likelihood ratio test (GLRT), but the unknown covariance structure is replaced by sample covariance matrix based on training data. The proposed detector is a constant false alarm rate (CFAR) detector. We give an approximate closed form of the probability of detection and false alarm and compute performance curves.