Adaptive Radar Detection Using Two Sets of Training Data

This paper deals with adaptive radar detection of a point-like target in a homogeneous environment characterized by the presence of clutter, jamming, and radar internal noise. At the design stage, two training datasets, whose gathering is carefully motivated in the paper, are considered to get receiver adaptation. Hence, the maximum likelihood estimator of the interference covariance matrix for the cell under test is computed exploiting both the available secondary sets. This estimate is then used to build two adaptive decision rules based on the two-step generalized likelihood ratio test and Rao test criteria. Remarkably, they are not limited by the conventional constraint on the cardinality of the classic training dataset. At the analysis stage, the detection performances of the newly proposed detectors are compared with those of the analogous conventional counterparts and the interplay among the different parameters of the problem is thoroughly studied.

I. Introduction

In radar detection based upon array of sensors or pulse trains [1] –[3], the Interference Covariance Matrix (ICM) might comprise several contributions associated with different interference sources. The most common sources are •

the electronic devices generating thermal noise, which is always present and leads to an ICM component modeled as , where is the thermal noise power and is the identity matrix;

•

the specific operating environment, whose backscattering gives rise to the clutter component;

•

jamming systems which can significantly modify the ICM depending on the jamming type and the radar signal processing. More precisely, if the radar performs spatial processing using sensors, then barrage noise jammers [4] illuminating the victim radar from the angle of arrival , , would yield the following ICM component $$\begin{equation} \sum _{k=1}^{K_J}\sigma _{J,k}^2 {\boldsymbol {v}}(\theta _{J,k}){\boldsymbol {v}}^{\dagger }(\theta _{J,k}), \end{equation}$$ where denotes conjugate transpose, and $$\begin{equation} {\boldsymbol {v}}(\theta _{J,k})=[1 \quad e^{j2 \pi \nu _s(\theta _{J,k})} \quad \ldots \quad e^{j2 \pi \nu _s(\theta _{J,k})(N-1)}]^T \end{equation}$$ are the power and the spatial steering vector of the -th jammer. In the last equation, denotes transpose and is the spatial frequency and is a function of . In the case of temporal processing, a noise jammer usually produces an ICM contribution equal to , where is the overall jammer power. Finally, still in the context of temporal processing, equation (1) can be modified to account for the effect of multi-tone continuous-wave jammers replacing with $$\begin{equation} {\boldsymbol {v}}(\nu _{J,k})=[1 \quad e^{j 2 \pi \nu _{J,k}} \quad \ldots \quad e^{j 2 \pi \nu _{J,k}(N-1)}]^T, \end{equation}$$ where is the number of transmitted tones and is the normalized Doppler frequency of the th tone. Such jammers can emulate the radar cross section of Swerling 1 targets.