Beyond the Stop-and-Go Assumption in Pulse-Doppler Radar Sensors

Coherent radars have multiple applications; among them, they can obtain images of targets. Unfortunately, the image quality can be seriously compromised for highly maneuvering targets, since the commonly adopted stop-and-go assumption is no longer valid for them. An approximated conventional explicit model for the signal delay, being proportional to the time-dependent target range, is usually employed to evaluate the violation of the stop-and-go simplification in these scenarios. Nevertheless, even this model can lead to radar-based measurement inaccuracies for extreme situations; for example, those involving very fast relative dynamics between the platform and target or for radars exploiting long-time-pulse waveforms. In this paper, an implicit function is proposed as the exact model for the radar echo time delay. Solutions for the conventional and exact models in the case of first- and second-order range polynomials are provided, and pertinent comparisons between them are accomplished. The main conclusion of this paper is that the conventional model is generally a good approximation to the exact solutions, but there may be extreme cases for which it does not give insight into the real appearing effects. Thus, the application of the exact model for the derivation of the radar round-trip delay could enable the conception of advanced radar-sensor algorithms, which improve the image quality for highly maneuvering targets. Simulated results of 1-D range profiles for a linear frequency-modulated continuous-wave radar example are also presented for verification of the expounded analytical equations.