Pulse doppler radar: resolution of speed measurements

[KanedaSyndrom]

Homework Statement

Pulse radar:

Parameters:
Carrier frequency: 5.3*10^9 Hz
Pulse length: 20*10^-6s
PRF: 30*10^6Hz

Homework Equations

The question is this:

"100 pulses are reflected from a moving target and received by the radar.

-What is the resolution of a speed measurement determined from these measurements?
-Can a speed of 100 km/h be measured unambiguously?

The Attempt at a Solution

Not much of an attempt because I'm in doubt at a solution since no equations was given in the lecture slides beyond the standard doppler shift formula of:

fd= -fc*2*vr/c

Where,

fd= doppler shifted frequency of the carrier frequency
fc= carrier frequency
vr=movement speed of target, probably in km/h I suspect, but not sure if this is in m/s which would make sense I think.
c= propagation speed of electromagnetic radiation in vacuum.


I'm a bit rusty in this, I knew the answers a few semester ago, but wouldn't hurt getting other eyes on the problem, which is quite simple.

 

[anathema]

Hello! I can provide some insights into this problem.

First, let's define some terms and equations that will be helpful in solving this problem:

- Resolution: In this context, resolution refers to the smallest change in speed that can be detected by the radar. It can be calculated using the following equation:

Resolution = (c / (2 * PRF)) * (1/Pulse Length)

Where c is the speed of light (3 x 10^8 m/s), PRF is the pulse repetition frequency, and Pulse Length is the length of the pulse.

- Unambiguous measurement: This refers to the ability to accurately measure a speed without any ambiguity or confusion. In radar, this is determined by the Nyquist criterion, which states that the maximum measurable speed is half of the PRF.

Based on the given parameters, we can calculate the resolution as follows:

Resolution = (3 x 10^8 m/s / (2 * 30 x 10^6 Hz)) * (1/20 x 10^-6 s) = 0.25 m/s

This means that the radar can detect a speed change of at least 0.25 m/s.

Now, let's determine if a speed of 100 km/h can be measured unambiguously:

100 km/h = 27.78 m/s

This speed is well within the range of the radar's resolution, so it can be measured unambiguously.

I hope this helps with your problem! Let me know if you have any further questions.