# Radar as range detector between cars-static sender vs dynamic sender

#### marellasunny

Say I have a radar transmitter on a car,used to detect its distance from a car in front of it by measuring the doppler shift on the reflected wave.
i.e Car 1 is the source, its wave gets reflected by Car 2 in front of it.

My book splits the problem of calculating the Doppler shift by computing the frequencies w.r.t relative velocity.

1.When the source emits(Car1),take it as stationary by considering the receiver to move at relative velocity.

2.When the receiver reflects(Car2),take it as stationary by considering the source to move at relative velocity.

The book goes on to give the following statements:

1.If the sender moves relative to a static receiver,the wavelength changes.The received frequency now will be:
$$f_{receiver}=\frac{c_{sent}}{\lambda_{receiver}}=\frac{{c_{sent}}}{\lambda-\frac{v_{rel}}{f}}$$

2.If the receiver moves relative to a static sender,the propagation velocity changes**(but not the wavelength??)**.The received frequency now will be:
$$f_{receiver}=\frac{c_{receiver}}{\lambda}=\frac{c_{sent}+v_{relative}}{\lambda}$$

Q***Shouldn't the wavelength also change when the waves get reflected back by the moving receiver?*** The above equation no.2 says it doesn't.

I can't attach images because I just joined.

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#### mrspeedybob

2.If the receiver moves relative to a static sender,the propagation velocity changes.
Your book is wrong. Take it back to wherever you bought it and get your money back. The propagation velocity can only change in direction, not magnitude. Any suggestion that the speed of light is anything but constant is crack-pot thinking.

#### Bobbywhy

Gold Member
Agree with mrspeedybob: take your book back and demand your money back! One point of difference, however: your opening statement is false. "...Say I have a radar transmitter on a car,used to detect its distance from a car in front of it by measuring the doppler shift on the reflected wave."

You cannot measure the distance to the car in front by using the Doppler shift. You can only measure the relative opening or closing velocity.

To measure the distance you must send a pulse, wait for it to go to the other car (target), be reflected, and travel back. The radar set will measure the time required for the pulse to return and that will be proportional to the distance. Just for reference: One "radar range nautical mile" (that is, round trip) is equal to around 12.36 microseconds.

#### marellasunny

To measure the distance you must send a pulse, wait for it to go to the other car (target), be reflected, and travel back. The radar set will measure the time required for the pulse to return and that will be proportional to the distance. Just for reference: One "radar range nautical mile" (that is, round trip) is equal to around 12.36 microseconds.
So,then its 2 doppler shifts occurring over the entire pulse lifetime right?-one at the observer and another back at the source. What would be the doppler shift in frequency after the wave gets reflected back and reaches back at the source?

total doppler shift in frequency=
(frequency of the initial pulse sent out from source)-(frequency of the pulse reflected back,now back at source)

I want to write the above equation in $f=\frac{c}{\lambda}$ form. Can you please guide me?
I've attached the text from the book.

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#### Bobbywhy

Gold Member
marellasunny, Excuse me, I was mistaken in my post number 3. Those limitations do not apply to your project. Now I understand you are working with an FMCW Radar system.

As for your specific question(s) I can only refer you to these three sources, where I think you can find the answer(s) you need:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3673098/

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#### marellasunny

The papers use the 'phase difference' to measure the range between target and source. But, they don't say if the second case is validated in FMCW i.e If the target moves relative to a static source,the propagation velocity changes. Is it true in FMCW and why? Thanks for the papers and replies.

#### Bobbywhy

Gold Member
The papers use the 'phase difference' to measure the range between target and source. But, they don't say if the second case is validated in FMCW i.e If the target moves relative to a static source,the propagation velocity changes. Is it true in FMCW and why? Thanks for the papers and replies.
I'm not sure I understand exactly what is your question. If when using FMCW radar to measure the range to a target and that target moves radially with respect to a static source/receiver, then yes, the received signal will be Doppler shifted by some proportional amount. This may cause some error in the range measuring calculation (not sure about that). But, the "propagation velocity" never changes! It remains constant and is known as "c".

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