Differential frequency dependence on range and velocity refined equation for frequency chirp modulation signal
Radiolocation and radio navigation
Science Research Institute for Long Distance Radio communication, NIIDAR, 10, build.5, 8 March str., Moscow, 127083, Russia
The paper outlines the differential frequency refined equation derivation for correlation-filter processing of a linear frequency chirp modulation signal. The signal with linear frequency chirp modulation commonly used for radar-location. Single slope linear frequency chirp modulation is considered. The universally accepted formula does not provide the necessary accuracy of the differential frequency measurement processing for large time-bandwidth signals and high-speed spacecraft. The refined equation provides range referencing to the emission commence and accounts for target offset during exposure time. The accounting for the signal propagation in this equation provides exact targets’ range and range rate time reference. The refined equation accounts for range and range rate time variations on the interval between emission commence and signal reflection at the target. The target offset during emission time leads to Doppler’s dispersion effect, which can be accounted for in the equation. This effect should be considered while forming heterodyne signal parameters. Neglect of this effects results in residual linear modulation while signal compression.
The authors obtained the complete equation derivation and carried out numerical analysis of the summands for long-range radar parameters. The refined equation is reduced to classical formula, used for the low-speed targets and small time-bandwidth signals. The summands additional to the classic equation cannot be omitted for the signals with linear frequency modulation and large time-bandwidth. The refined equation is more flexible to account for transmitter and receiver parameters values. Such an approach can be implemented for more compound signals. The range acceleration should be taken into account for super-large time-bandwidth signals, or the targets with high radial acceleration value. The paper considers the practical features of the obtained equation, and suggests an approach to obtaining derivative transformations.
Keywords:linear frequency chirp modulation signal, Doppler shift, Doppler shift distortion
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