Detection Performance of a Forward Scatter Radar Using a Crystal Video Detector

The forward scatter radar (FSR) configuration is especially appealing for the detection of low-observable targets since it provides well-known properties for the radar cross section, which includes enhancements with respect to the monostatic and/or moderate bistatic configurations, as well as robustness to the target material and detailed geometrical characteristics. Due to the separation of a transmitter and a receiver, it is customary to use a detection scheme based on a square-law envelope detector followed by an appropriate matched filter, which we address as a crystal video detector (CVD) based on traditional terminology. This paper provides an accurate analytical expression for the detection performance of the FSR target detection using the CVD in terms of both the probability of false alarm <inline-formula><tex-math notation="LaTeX">$(P_{{\rm{fa}}})$</tex-math></inline-formula> and the probability of detection <inline-formula><tex-math notation="LaTeX">$(P_{{\rm{d}}})$</tex-math></inline-formula> in order to support performance prediction and FSR system design. The derived expressions are validated by comparison to Monte Carlo simulations under two different geometrical scenarios. Moreover, the comparison of the CVD performance to an ideal optimum detector (upper bound for the FSR achievable detection performance) shows the geometrical conditions, where the CVD suffers significant detection losses so that alternative detectors should be investigated. Finally, to remove the need to operate the CVD with a fixed detection threshold, two fully adaptive detectors are derived, based on the structure of the CVD scheme, which are shown to provide a constant false alarm rate (CFAR). The performance of these CFAR detectors in terms of <inline-formula><tex-math notation="LaTeX">$P_{{\rm{fa}}}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$P_{{\rm{d}}}$</tex-math></inline-formula> are provided in closed form and validated through Monte Carlo simulations, showing quite small losses with respect to the fixed-threshold CVD. The application to real data acquired by a passive FSR based on frequency-modulated signals is used to show the practical effectiveness and consistency.