Search

This article addresses adaptive radar detection of $N$ pulses coherently backscattered by a prospective target in heterogeneous disturbance. As customary $K \geq N$ range cells adjacent to the one under test are used for estimation purposes. The disturbance in each range cell is described by a non-Gaussian model based on a mixture of $L < K$ Gaussian distributions. Gaussian components are characterized by an unknown low-rank matrix plus thermal noise with unknown power level. We first derive a detector inspired by the generalized likelihood ratio test that adaptively estimates the statistical properties of the disturbance from the observed data. To overcome the intractability of the involved maximum-likelihood estimation problem, a suitable approximate strategy based on the expectation-maximization algorithm is developed. This also allows us to classify the cell under test by selecting the “maximum a posteriori Gaussian distribution” for the disturbance (under both hypotheses). Accordingly, a likelihood ratio test is also proposed. An extensive performance analysis, conducted on synthetic data as well as on two different experimental datasets (PhaseOne and IPIX for land and sea radar returns, respectively), shows that the proposed approaches outperform state-of-the-art competitors in terms of both detection capabilities and false alarms control.

Characterization of the exceedance probability (EP) of the energy statistic (ES) plays a fundamental role in several signal processing applications, including radar (e.g., probability of false alarm) and communications (e.g., outage probability). However, manageable closed-form expressions are not available for general non-Gaussian models such as the $\eta$-$\mu$ distribution. In this letter, simple formulas for predicting the EP of the ES are provided, based on second- and third-order cumulant series expansion of the tightest Chernoff bound, coupled with low-complexity approximations of Hoyt moments. Results show that the proposed method significantly improves over earlier work based on different bounds, and outperforms the asymptotic approximation via the central limit theorem as well as the Generalized Pareto Distribution fitting of the distribution tail.