Knowledge-Aided Covariance Matrix Estimation and Adaptive Detection in Compound-Gaussian Noise

We address the problem of adaptive detection of a signal of interest embedded in colored noise modeled in terms of a compound-Gaussian process. The covariance matrices of the primary and the secondary data share a common structure while having different power levels. A Bayesian approach is proposed here, where both the power levels and the structure are assumed to be random, with some appropriate distributions. Within this framework we propose MMSE and MAP estimators of the covariance structure and their application to adaptive detection using the NMF test statistic and an optimized GLRT herein derived. Some results, also in comparison with existing algorithms, are presented to illustrate the performances of the proposed detectors. The relevant result is that the solutions presented herein allows to improve the performance over conventional ones, especially in presence of a small number of training data.