CFAR Detection of High-Accelerating Targets: A Study of the Probability of False Alarm

Fast accelerating targets feature a non-negligible time-varying Doppler shift which induces a drop in Signal to Noise Ratio (SNR) at the output of a classical range-Doppler radar detector. The optimal detector against fast accelerating targets retrieves the maximum available SNR by a three-dimensional search to match the target echo to the target range, Doppler and acceleration. This operation, however, modifies the statistical properties (probability density function and the correlation) of background white Gaussian noise at the output of the filter and, ultimately, impacts the receiver probability of false alarm and how this can be robustly controlled. In this paper, we study the statistical properties of white Gaussian background noise at the output of the optimal processor and propose a modified one-parametric Largest Exponential Value (LEV) distribution to fit the receiver noise before the detection threshold. Two Constant False Alarm Rate (CFAR) schemes are proposed and developed based on the modified LEV distribution and their performance is characterised analytically and compared with simulated data and experimental data collected at C-band. Results show the distribution parameter of the modified LEV converges to a fixed value as the number of filters in the acceleration domain increases. This yields detection performance that is independent of the relevant detection parameters. CFAR results demonstrate the probability of false alarm can be robustly controlled with the proposed solution on simulated and real experimental data.