8 May 2006 Doppler correction for high-velocity targets using a relativistic approach
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Standard radar systems commonly use a first-order phase compensation to account for the Doppler effect. As target speed increases, higher-order phase terms are needed to compensate a large time-bandwidth product signal. For extremely high speeds, a relativistic scheme based on the Lorentz Transformation of the wave 4-vector is more desirable since it provides correct results. Since the echo location problem involves transmission of the signal from a stationary frame and signal reflection from a moving frame, the wave 4-vector must be transformed twice to simulate a round trip. We show that for relative motion in one direction, the round-trip Lorentz transformation is equivalent to compressing the instantaneous frequency of the signal. The frequency compression factor is a nonlinear function of speed v. The nonlinearity is apparent only for relativistic speeds. In this paper, we analyze the ambiguity surface of the linear FM (chirp) signal to compare first-order and relativistic (full) compensation, and demonstrate that at relativistic speeds the ambiguity surface of the fully compensated linear FM compensated shows a linear delay-Doppler coupling.
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Hector A. Ochoa, Hector A. Ochoa, Benjamin C. Flores, Benjamin C. Flores, } "Doppler correction for high-velocity targets using a relativistic approach", Proc. SPIE 6210, Radar Sensor Technology X, 62100F (8 May 2006); doi: 10.1117/12.666299; https://doi.org/10.1117/12.666299

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