Theoretical Introduction

In this post we are going to study and practice the basis of the FMCW Radar: we will analyse a practical example in Matlab in which we will develop the main applications of it. For those who are unfamiliar with these types of radars, bear in mind that its importance comes from its use in applications such as traffic and sports monitoring.

Now, let’s start by recalling the main theoretical principles of the FMCW Radar: Figure 1. FMCW Radar: Operation Principle
In the picture above, you can see the main parameters that describe the FMCW operation:
• Sweep time: T=(2xR)/c. This parameters helps us to determine the distance to the target.
• The Doppler shift: fd. This frequency, in addition to the radar wavelength, helps us to determine the radial speed of the target.

Practical Case:

Now let’s assume we have a given transmitted and received radar signals with the following characteristics with a sampling time: Ts=200 ns, and the following FMCW signal characteristics:
• Minimum frequency (after base band processing): f1=1.1 MHz
• Maximum frequency (after base band processing): f2=2.1 MHz
• Sweep slope: Tc=100 μs
• Radar frequency: f= 40 GHz

Note: You can generate your own FMCW radar signals by following this Matlab tutorialAutomotive Adaptive Cruise Control Using FMCW Technology

Now, by using the spectrogram Matlab function we can represent the transmitted signal spectrogram (there is an example in the Matlab tutorialmentioned above): Figure 2. Transmitted Signal Spectrogram
Check that you understand the FMCW signal parameters represented in Figure 2 (feel free to contact us if you miss them!).
Now we are going to obtain the spectogram of the sum of the transmitted and received signals, as we saw in Figure 1, so we will be able to obtain the distance to the target and the target’s radial speed. Figure 3. Spectrogram of Tx and Rx Signal sum

From Figure 3, we can estimate the sweep time to the target from the equation T=(2xR)/c : The Doppler frequency is calculated as the shift between the transmitted and received signal; from the spectrogram in Figure 3 we can determinatefd=78 KHz.
Now, in order to calculate the target speed to determine the radar wavelength from its frequency:   1. 