# Doppler Frequency Resolution for Radar

Doppler frequency is calculated by the formula $f_{d} = 2*v_{r}/\lambda$, where $v_{r}$ is the radial velocity and $\lambda$ is the radar wavelength.

Normally FFT is used to detect the doppler frequency(A bank of FFT filters is used for Doppler frequency estimation).

Assume that sampling frequency is fixed as $4*f_{max}$, where $f_{max}$ is the maximum $f_{d}$ corresponding to the maximum radial velocity.

Now I have to determine the number of FFT points to be employed in the FFT calculation. How can I determine this.

In other words, which target parameter determines the Doppler frequency resolution.

Doppler resolution usually depends on the dwell time $T_{dwell}$, i.e., the time for which the radar is going to stare (look) at the target. If the pulse/sweep repetition interval is given by $T_{PRI}$ then $N = T_{dwell}/T_{PRI}$ is the number of pulses/sweeps in one dwell, which is also the limit of your FFT size. Your maximum Doppler corresponds to $N/2$th bin, therefore the Doppler resolution is $f_d/(N/2)$. Note that more pulses you are able to send to the target, better is the Doppler resolution.

Depends on the resolution you want for doppler frequency. Doppler frequency resolution determines how well you can observe targets of different radial velocities. If you want to resolve targets that are closely spaced in radial velocities you will need to have higher doppler resolution measurement. That means you will have to have more number of points in your FFT calculation. That means you have to observe the signal for a longer time. Fsampling/N will give you the frequency bin resolution where N is the number of points in FFT and Fsampling is the sampling frequency.

• I want to connect the Doppler frequency resolution to a physical parameter of a target or the radar. – Vinod Aug 2 '14 at 10:25
• Doppler resolution is directly connected to the velocity measurement resolution of the target because as the doppler frequency and target velocity are related as given by you through the equation. – Seetha Rama Raju Sanapala Aug 2 '14 at 20:58

Similar to spectral estimation problems, if you need better resolution, (aka narrower mainlobe in your estimate), then you need to have a larger set of data to FFT. A larger set of data means you have a longer record, and thus, when FFT'd, your mainlobe becomes narrower.

The ability to discriminate between peaks of overlapping main lobes is what is commonly used as a metric for resolution.

If however you want to keep the frame size the same, but increase your frequency granularity, then you can zero-pad your data pre-FFT, (but post-windowed).

In pulse-doppler radar applications, that means you need more pulse-records whose constant-range samples are to be FFT'd across records. This in turn means you need to transmit more pulses. This also makes intuitive sense: If you want to estimate the velocity of a target, you need to probe it longer - aka - you need to send out more pulses - aka - more data, and thus, a larger record length.

• One should note that this processing assumes constant velocity of the target along the processing time. Which the longer you take, the less probable this assumption is. This is another trade off to remember. – Royi Sep 1 '14 at 21:19

The Doppler frequency resolution is not determined by any characteristic of the moving target. It is determined by the Radar system parameters. If you are using a FFT to to determine the Doppler shift, this assumes that you're transmitting a sinusoidal pulse. The length of the pulse then determines the Doppler resolution for that single pulse. This assumes the radial velocity of the target is relatively constant for the pulse - usually this is not too bad an assumption

You can increase the resolution by coherently integrating multiple pulses. There are design constraints on the Pulse Repetition Frequency (PRF). The PRF needs to be high enough to sample the Doppler frequency bandwidth of interest. PRF needs to be low enough to allow the pulse to propagate to the target range and back, or else you will suffer from pulse ambiguities. Note that at a fixed PRF you will also have blind velocities.

The number of pulses you integrate is referred to as the Coherent Processing Interval (CPI). As mentioned elsewhere, if your target does not maintain a constant radial velocity throughout the CPI, this will result is some spectral spreading across your FFT bins.