Applications of Various Space-time Transformations to Determine Radar Signal Distortion Caused by a Moving Target Having Constant Velocity and Acceleration

TL;DR

This paper investigates how different space-time transformations affect radar signal distortion caused by a moving target with constant velocity and acceleration, comparing classical, Lorentz, Galilean, and Hsu transformations.

Contribution

It introduces a comprehensive analysis of multiple space-time transformations to model radar signal distortion from moving targets, emphasizing the use of Hsu transformation for accelerating frames.

Findings

Hsu transformation effectively models target acceleration effects.

Lorentz and Galilean transformations are recovered as special cases.

Different transformations lead to distinct waveform distortions.

Abstract

The effects of target motion on the distortion of radar signals are investigated using five transformations, namely, Hsu, Lorentz, Galilean, Reference, and Classical transformation equations. Hsu transformation is used as a primary transformation since it expresses the temporal and spatial transformations between an inertial reference frame and accelerating frame where the origin of the accelerating frame has an initial velocity and acceleration with respect to the inertial frame. Additionally, as the acceleration approach zero and infinity, respectively, the Lorentz and Galilean transformations are obtained. These transformations are used to express the transmitted waveforms in the radar reference frame variables to that of the target reference frame variables, and the reflected waveform from the target in its reference frame variable to that of the radar reference frame variables, leading to the distorted waveform received at the radar receiver due to the motion of the target.