In this post we are going to review the main characteristics of radar signals and we are going to explain how to process them in Matlab by analyzing a practical case.

The attached CSV file (at the bottom of the page) contains the samples of a signal generated by a pulsed radar. This signal is formed by 4 pulses and the sampling period is 12 ns.

Exercise 1

Plot one pulse in the time domain (0≤t≤PRI) and in the frequency domain (showing the spectrum around +/- 3 MHz). Highlight the Pulse Width (PW) in the time domain plot. Figure 1. Radar signal: 1 pulse Figure 2. Radar signal: Fourier Transform of 1 pulse

Comment:

The spectrum signal can be also represented using the following code:

```f = linspace( fs/2*(1-N)/N,fs/2*(N-1)/N, N );  % this is the frequency content

figure;
plot( f/1e6, db(fft(v)) );
title( 'Signal Power' )
xlabel( 'MHz' );

```

This is the frequency representation centered on zero (note that in Figure 2, we have used the Matlab function shift).

In addition, the y-axis will show the power in dB: if the input contains voltage (energy) measurements, the output is:
dB=10 log10(V2/R)  where V is the absolute value of v. Figure 3. Radar signal: Fourier Transform of 1 pulse (alternative representation with power centered at 8.6785 MHz)

Exercise 2

Plot the 4 pulses of the signal in the time domain (0≤t≤4xPRI) and in the frequency domain (showing the spectrum around +/- 3 MHz). Highlight the Pulse Repetition Interval (PRI) in the time domain plot. Figure 3. Radar signal: 4 pulses Figure 4. Radar signal: Fourier Transform of 4 pulses

Exercise 3

a. What is the value of the PW?
b. What is the target resolution in meters?
c. What is the value of the PRI?
d. What is the maximum unambiguous range?
e. For that maximum unambiguous range, what is the received power reduction factor due to the distance?

a. The pulse width is PW= 1.35 µs = 1350 ns.
b. The target resolution in meters, for PW=1.35 µs is: c. The Pulse Repetition Interval (PRI), measuring in the graph is 10 µs or 104 ns.

d. The maximum unambiguous range is: e. The received power reduction factor due to the distance is: Comment:

The equation for the power at the input to the receiver is: where the terms in the equation are:

• Pr — Received power in watts.
• Pt — Peak transmit power in watts.
• Gt — Transmitter gain.
• λ — Radar operating frequency wavelength in meters.
• σ — Target’s nonfluctuating radar cross section in square meters.
• L — General loss factor to account for both system and propagation loss.
• Rt — Range from the transmitter to the target.
• Rr — Range from the receiver to the target. If the radar is monostatic, the transmitter and receiver ranges are identical.

This is a combination of the free-space path loss to the target following Friis equation and the scattering from the target and propagating back.

Therefore, the radar propagation loss equation is

L_Path = λ2 / ((4π3)x R4)

Which depends on R4, as you’ve noted, and on the wavelength.

Final conclusions and notes

As we have seen, the Pulse Width, PW, is proportional to the target resolution. In addition, in order to avoid ambiguity in the targets, we can limit the maximum range (which will also depends of the effective surface of them) so is smaller than the distance between pulses, Run<c/2·PRI, which can be achieved by reducing the PRI.

Finally, when designing this radar system, it’s also important that the receiver fidelity is enough so it can process up to the modulation frequencies 1/PW.

If you want to create your own radar pulses, you can use the Matlab function: chirp

We hope you found this tutorial useful! If radars is something that you are interested in, leave a comment below or send us an email to contact@18.169.179.26 and we will post more about it!
All the comments added in this tutorials were possible thanks to the contribution of William Buller, from Michigan Technological University, thank you, William!

Sources:

 Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005.

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