Adaptive detection of distributed targets in partially-homogeneous environment

This paper deals with adaptive detection of range-spread targets (with unknown amplitudes) embedded in Gaussian noise with unknown covariance matrix. For estimation purposes, we assume that a secondary data set, free of signal components, is available. All of data vectors share the same structure of the covariance matrix, but the (common) power level of the secondary data can be different from that of the cells under test. We resort to the GLRT and come up with adaptive detectors that able to operate in this partially-homogeneous scenario. In particular, we investigate the suitability of one-step and two-step GLRT-based detectors. A one-step receiver performs the GLRT over the totality of data while the design of a two-step detector assumes that the covariance matrix (or its structure only) is known; a fully adaptive structure is obtained by substituting the sample covariance, based upon secondary data, in place of the unknown matrix. Remarkably, both procedures lead to detectors ensuring the CFAR property with respect to the noise statistics. The performance assessment shows that the one-step GLRT and one of the two-step GLRTs, achieve the same performance under situations of relevant interest. Hence, the two-step approach is to be preferred since it leads to a simplified structure without loss of performance. Finally, such a detector is compared with a receiver which assumes a knowledge of the covariance matrix of the noise; the comparison confirms the suitability of the GLRT approach for operating in real radar scenarios.