Effects of using a first-order approximation to compensate the Doppler on large time-bandwidth product signals

Abstract

Current generation radars employ a first order approximation to compensate the frequency shift due to target's velocity. This approach is inadequate when high velocity targets are considered; however, real targets do not possess such high velocities. For that reason, this research analyzes how the increment of the Time-Bandwidth (TBW) product and the target velocity would impact the analysis of radar signals when a first order approximation is implemented to compensate the Doppler shift. The common approach to improved resolution and performance of radar system is to increase the time-bandwidth product of the transmitted signal. The problem of using the first order approximation to compensate the Doppler is that it is limited only to the first two terms of a power series expansion of a full Doppler compensation. As a consequence, an increment on the target's velocity or the time-bandwidth product of the transmitted signal will result in a significant error at the output of the matched filter. On this research a Linear FM (chirp) signal with a large TBW is considered as the transmitted signal. First, to observe the effects of increasing the time-bandwidth product and target velocity the received signal is modeled using a full Doppler compensation and a first order approximation. Second, each signal is applied to the input of one matched filter in which the transmitted signal is used as a reference. Finally, the outputs from both matched filters are analyzed in order to observe the effects of using the first order approximation to model the Doppler induced on the reflected signal. This analysis was performed assuming that the target was moving at a constant velocity. By increasing the time-bandwidth product of the transmitted signal the output of both matched filters are compared and analyzed to observe the differences between modeling the reflected signal using the first order compensation and the full Doppler compensation. The simulation results showed that, by increasing the time-bandwidth product of the transmitted signal the output of the matched filter using the first order approximation deviates significantly with respect to the matched filter that contains the signal modeled using the full Doppler compensation. From these results it is concluded that a dramatic increase in time-bandwidth product of the received signal, results in a significant error at the output of the matched filter if the first order approximation is used to model the reflected signal instead of the Full Doppler compensation.