Signal detection in compound-Gaussian noise: Neyman-Pearson and CFAR detectors

This paper handles the problem of detecting signals with known signature and unknown or random amplitude and phase in the presence of compound-Gaussian disturbance with known spectral density. Two alternative approaches are investigated: the Neyman–Pearson criterion and the generalized likelihood ratio strategy. The first approach leads to a hardly implementable detector but provides an upper bound for the performance of any other detector. The generalized likelihood ratio strategy, instead, leads to a canonical detector, whose structure is independent of the disturbance amplitude probability density function. Based on this result, the threshold setting, which is itself independent on both the noise distribution and the signal parameters, ensures a constant false alarm rate. Unluckily, this receiver requires the averaging of infinitely many components of the received waveform. This is not really a drawback since a close approximation can be found for a practical implementation of the receiver. The performance analysis shows that the generalized likelihood ratio test (GLRT) detector suffers a quite small loss with respect to the optimum Neyman–Pearson receiver (less than 1 dB in the case of random amplitude) and largely outperforms the conventional square-law detector.