# Requirement on sampling rate for Doppler shift estimation

What is the requirement of sampling rate on channel impulse response (CIR) for Doppler shift estimation? Suppose that there is a bi-static radar system with perfect synchronization, the receiver samples the CIR and estimates the Doppler shift caused by the dynamic object in the targeted area.

Does the sampling rate have impact on Doppler shift estimation, and how?

• It does. Are you familiar with the Shannon-Nyquist sampling theorem? If so, have you tried applying it here? Where did you meet a problem? – Marcus Müller May 1 at 10:42
• @MarcusMüller. Do you mean the sampling frequency should be at least two times of the Doppler frequency shift? – Land May 1 at 12:25
• Well, now we're talking! So, the Sampling Theorem states your sampling rate must be higher than twice the signal bandwidth, right. Now, the CIR might only contain a doppler-shifted tone, in which case bandwidth = range of possible doppler shifts. However, more realistically, your radar signal has a bandwidth of its own, even after pulse compression, so you'll need to describe what kind of thing you're actually sampling when you say "it samples the CIR"! – Marcus Müller May 1 at 12:29
• @MarcusMüller. Well, for the common use cases (such as, radar-based car detection or human detection), the Doppler shift is small, at least far smaller than the bandwidth. For example, the Doppler casued by walking may be just tens of Herz, whereas the radar's bandwidth is at least the order of MHz, even GHz. Such that, the Sampling Theorem should be satisfied naturally in case of such a small Doppler. Correct? – Land May 1 at 12:42
• @Land how do you use CIR to estimate Doppler shift? – AlexTP May 1 at 14:14