HOME

FMCW Waveforms

This notebook tries to visualize the waveforms that are transmitted and received by a typical up-chirping FMCW radar. Be sure to play around with the slider values. Do note that you might see some aliasing effects at certain combinations of values because of the limited number of points.

First, we look at the amplitude over time of our transmitted chirp. We will focus on just a single chirp.

Chirp Time (T_C): ns

Chirp Start Frequency (f_0): MHz

Chirp Bandwidth (B_C): MHz

The chirp is reflected by a point target a certain range away from the radar. It appears at the receive antenna after a certain delay.

Target Delay (τ): ns

It passes through some amplification and filtering and so on and is finally mixed with our transmit chirp. You can see a monofrequent envelope on top of a higher frequency signal. When the target delay goes up, so does the low frequency component of the mixing result. The chrip rate is the proportionality factor for the IF frequency. The IF frequency does not depend on the initial frequency of the chirp.

We can also look at it in the frequency domain, which shows the high and low frequency components more clearly. The graph below shows the spectrum of the mixing result (IF) and that of the transmit signal as a reference. This signal can be low-pass filtered, sampled and used for frequency analysis to determine the target's range.

We have assumed that the received chirp will simply be a time-delayed version of the transmitted chirp. Of course, the received chirp will also be attenuated, but this is just a linear thing and for this demonstration, we can ignore it. Just know that the received waveform will have a much lower amplitude than shown here. Additionally, there will probably also be some dispersive effects due to the environment which is also not covered here.

What we also did not look at is an effect called range-doppler-coupling. In addition to the time delay and attenuation, there will be a doppler shift in the received waveform if the target is moving. This shift is, however, generally very small, but it does depend on the Radar parameters, especially when using low chirp rates. This leads to something called range-walk, an effect that makes it appear as though the range (IF-frequency) changes over our processing interval. For more information see this paper: doi.org/10.1109/RADAR54928.2023.10371098.

Target Velocity: m/s

However, do not confuse this with the actual change in IF-frequency due to the phase difference from the transmit-receive delay. Here, the return frequency does not change, only the frequency of the mixer product changes based on the delay. When we have range-doppler coupling, the actual frequencies of our received signal (used for mixing) are changing relative to our transmit signal due to the doppler effect. So this effect will be superimposed on the regular delay and result in an IF phase that is changing quadratically over time, proportional to the speed of the target (i.e. the IF will basically be an FMCW waveform itself). This causes the range estimation to be off, which assumes it to be linear over time (sinusoidal).