{'fraction_non_alphanumeric': 0.021756647864625302, 'fraction_numerical': 0.0016116035455278, 'mean_word_length': 5.241206030150754, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Doppler correction for high-velocity targets using a relativistic approach

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.