# What is doppler tolerance

Can anybody explain the meaning of Doppler tolerance for the waveforms(Linear frequency modulated, Barker code, Polyphase codes) used for Pulse compression.

The Doppler frequency shift $f_{d}$ due to a moving target of velocity $v_{r}$ is given by

$f_{d} = 2*v_{r}/\lambda$ where $\lambda$ is the wavelength of the transmitted signal.

Polyphase codes are known to be having high Doppler tolerance compared to LFM waveforms. Can anybody explain this fact in simple terms.

## 1 Answer

In pulse radars you perform matched filtering in receiver where you compute cross-correlation of the received waveform and reference one. Due to Doppler shift matched filter performance will decrease. It's like decreasing of correlation function with increasing of time delay between waveforms. Doppler tolerance defines the maximum available Doppler shift for given waveform such that you can still achieve correlation peak bigger than some threshold (SNR is assumed high enough to produce such a correlation).

There is fundamental property of all waveforms used in Radar (and other apps): ambiguity function. Look https://en.wikipedia.org/wiki/Ambiguity_function. In a few words this function determines how correlation between 2 identical waveforms changes with time delay and also with doppler shift. Some waveforms have very narrow ambiguity function, while others - more spreading.

For example maximum length sequences have narrow AF both in time and frequency shifts. LFM has slightly wide AF especially in frequency shift. They are actually very tolerable to Doppler shift. COZAC sequences (used in LTE) have narrow AF in time axe but wide in frequency one.

So if you are choosing waveform for your application you should refer to its AF at first.