# FMCW Radar: Matlab Tutorial

|## 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**:: T=(2xR)/c. This parameters helps us to determine the__Sweep time__**distance to the target**.: fd. This frequency, in addition to the radar wavelength, helps us to determine the radial**The Doppler shift****speed of the targe****t**.

## 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 tutorial**: Automotive 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 tutorial**mentioned 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 determinate

**fd=78 KHz**.Now, in order to calculate the target speed to determine the radar wavelength from its frequency:

Therefore, the

**target radial speed**with respect to the radar is:As the radial speed is

**negative**, the target is**approximating**to the radar.## Conclusions and Further Analysis

The FMCW radar have many applications, from the conventional radar altimeter and traffic radar to the very innovative people detectors in dark environments, used in the military field. In our example, for a frequency of 40 GHz (Ka band) and a speed of -292.5 m/s,

**this radar’s application could be a short range radar on earth or a pointing radar in an aircraft**. The theoretical accuracy that the signals can be measured with depends on the transmitted signal bandwidth and the signal to noise ratio at the receiver.These measurements are also affected by physical limitations such as the non linearity in the frequency sweep, that can be corrected with a closed-loop circuit that includes a PLL. We can also improve the spectra analysis by solving the aliasing and lateral lobes effects. Therefore,**the FMCW radar is considered by its high resolution in several applications**.We hope you have enjoyed this tutorial, and please, feel free to contact us or leave a comment if you want to ask or propose something. To start with, we are going to leave you a small question to think about:

**what would happen when considering two targets? How does the radar differentiate each target?****HINT**: have a look at the following images

Figures 3 and 5. Two targets case

Looking forward to hearing from you!