Estimate chirp shift Doppler

Hello,
I have a question for you. I have to simulate the
signal received in a radar system by applying a time delay and a
doppler shift. By now I have delayed the original signal and I have
estimated the delay by correlating the original transmitted signal
with the received one and by picking the max. Now I have to estimate
the shift in frequency but I don't know how to proceed. I think I
should multiply the delayed signal for exp(-j*2pi*fd*t) but how can I
estimate the shift? The transmitted signal is a chirp, duration of 100
microsec sampled at 0.5 MHz (50 samples)
Thanks in advance!

Fox wrote:
> Hello,
> I have a question for you. I have to simulate the
> signal received in a radar system by applying a time delay and a
> doppler shift.
> By now I have delayed the original signal and I have
> estimated the delay by correlating the original transmitted signal
> with the received one and by picking the max. Now I have to estimate
> the shift in frequency but I don't know how to proceed. I think I
> should multiply the delayed signal for exp(-j*2pi*fd*t) but how can I
> estimate the shift?  The transmitted signal is a chirp, duration of 100
> microsec sampled at 0.5 MHz (50 samples)
> Thanks in advance!

For the linear chirp, the effect of the small frq. shift is 
indistinguishable from the shift in time. This is a well known property.

If the Doppler shift is comparable with the bandwidth of the chirp, then 
you can seek for the max. correlation both in time and frequency. This 
is rather heavy and nasty calculation.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Sorry if my question my sound naive ...

If your chirp starts at Fo and Fn, and your measured signal starts at
F1 and ends at Fm
can't you take the spectral shift as the average difference between
these two frequencies (ie, the edge frequencies)?

Fox wrote:
> Hello,
> I have a question for you. I have to simulate the
> signal received in a radar system by applying a time delay and a
> doppler shift. By now I have delayed the original signal and I have
> estimated the delay by correlating the original transmitted signal
> with the received one and by picking the max. Now I have to estimate
> the shift in frequency but I don't know how to proceed. I think I
> should multiply the delayed signal for exp(-j*2pi*fd*t) but how can I
> estimate the shift? The transmitted signal is a chirp, duration of 100
> microsec sampled at 0.5 MHz (50 samples)
> Thanks in advance!

Sorry if my question might sound naive ...

If your chirp starts at Fo and Fn, and your measured signal starts at
F1 and ends at Fm
can't you take the spectral shift as the average difference between
these two frequencies (ie, the edge frequencies)?


Fshift= 0.5*(F1-Fo + Fm-Fn);


That is offcourse assuming that the chirp is fairly bandlimited
compared to your recording bandwidth, and the the chirp has constant
amplitude....


> Fox wrote:
> > Hello,
> > I have a question for you. I have to simulate the
> > signal received in a radar system by applying a time delay and a
> > doppler shift. By now I have delayed the original signal and I have
> > estimated the delay by correlating the original transmitted signal
> > with the received one and by picking the max. Now I have to estimate
> > the shift in frequency but I don't know how to proceed. I think I
> > should multiply the delayed signal for exp(-j*2pi*fd*t) but how can I
> > estimate the shift? The transmitted signal is a chirp, duration of 100
> > microsec sampled at 0.5 MHz (50 samples)
> > Thanks in advance!

Ikaro wrote:

> Sorry if my question might sound naive ...
> 
> If your chirp starts at Fo and Fn, and your measured signal starts at
> F1 and ends at Fm
> can't you take the spectral shift as the average difference between
> these two frequencies (ie, the edge frequencies)?
> 
> 
> Fshift= 0.5*(F1-Fo + Fm-Fn);
> 
> 
> That is offcourse assuming that the chirp is fairly bandlimited
> compared to your recording bandwidth, and the the chirp has constant
> amplitude....

We are talking about the radars here. The SNR at the input may be as low 
as -20dB or less. Therefore you can't say anything about the signal 
until you compute the correlation.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

I agree with Vladimir.  The signal's ambiguity function and the
Cramer-Rao Bound can be computed for the SNR's of interest to convince
yourself that the estimation of doppler shift from a single return is
difficult at best.  Estimation of doppler is usually performed using
multiple coherent returns in a radar system.

Mike




Vladimir Vassilevsky wrote:
> Ikaro wrote:
>
> > Sorry if my question might sound naive ...
> >
> > If your chirp starts at Fo and Fn, and your measured signal starts at
> > F1 and ends at Fm
> > can't you take the spectral shift as the average difference between
> > these two frequencies (ie, the edge frequencies)?
> >
> >
> > Fshift= 0.5*(F1-Fo + Fm-Fn);
> >
> >
> > That is offcourse assuming that the chirp is fairly bandlimited
> > compared to your recording bandwidth, and the the chirp has constant
> > amplitude....
>
> We are talking about the radars here. The SNR at the input may be as low
> as -20dB or less. Therefore you can't say anything about the signal
> until you compute the correlation.
>
> Vladimir Vassilevsky
> 
> DSP and Mixed Signal Design Consultant
> 
> http://www.abvolt.com

"Ikaro" <ikarosilva@hotmail.com> wrote in message 
news:1158165965.508867.289920@m73g2000cwd.googlegroups.com...
> Sorry if my question might sound naive ...
>
> If your chirp starts at Fo and Fn, and your measured signal starts at
> F1 and ends at Fm
> can't you take the spectral shift as the average difference between
> these two frequencies (ie, the edge frequencies)?
>
>
> Fshift= 0.5*(F1-Fo + Fm-Fn);
>
>
> That is offcourse assuming that the chirp is fairly bandlimited
> compared to your recording bandwidth, and the the chirp has constant
> amplitude....
>

"compared to your recording bandwidth" is a key point.
To do what you suggest requires a couple of things:

1) High SNR so you can actually find the edges.

2) High bandwidth so you can actually find the edges in time accurately 
enough.

3) Long time processing so you can actually find the edges in time 
accurately enough.

So, yes, with infinite signal to noise ratio in a laboratory environment as 
with Matlab you could likely come up with processing that would do it.  But, 
in the real world where SNR is often not ideal then the processing you 
choose will probably not have the properties needed.

See "ambiguity function"  It's called that for a reason.  :-)

Fred 

Yes,  but I don't see how this answers the question...since in my post
the frequency shift can also apply to the powe spectral density.


> We are talking about the radars here. The SNR at the input may be as low
> as -20dB or less. Therefore you can't say anything about the signal
> until you compute the correlation.
>

> 1) High SNR so you can actually find the edges.

Correct, you can also estimate the noise power in a silent interval
(asssuming WN), and consider any edges by simple thresholding. Seems
like a common detection problem (at least if the noise is white, or
some of it's properties are known).

> 2) High bandwidth so you can actually find the edges in time accurately
> enough.

Agreed, but that's the typical trade-off between time vs frequency
resolution....
That why I suggested that the chirp's bandwidth bemuch smaller compared
to the channel's bandwidth (ie, the sampling frequency much higher than
say, 5*nyquist).
By selecting an appropiately high sampling frequency *and* *keeping the
desired time resolution constant  we approximately achieve the desired
spectral resolution (at the cost of more samples per second and cpu
time offcourse)

> 3) Long time processing so you can actually find the edges in time
> accurately enough.
I think you meant "edges in frequency" here...

> 1) High SNR so you can actually find the edges.

Correct. But with really low SNRs I doubt any technique will stand-out
unless we can exploit/assume properties on the type of noise.

Thus we might estimate the noise PSD in silents interval (asssuming
WN), and consider any edges by simple thresholding based on the average
noise power at silent intervals. Seems like a common detection problem
(at least if the noise is white, or some of it's properties are known).



> 2) High bandwidth so you can actually find the edges in time accurately
> enough.


Agreed, but that's the typical trade-off between time vs frequency
resolution....
That why I suggested that the chirp's bandwidth bemuch smaller compared

to the channel's bandwidth (ie, the sampling frequency much higher than

say, 5*nyquist).
By selecting an appropiately high sampling frequency *and* *keeping the

desired time resolution constant  we approximately achieve the desired
spectral resolution (at the cost of more samples per second and cpu
time offcourse)


> 3) Long time processing so you can actually find the edges in time
> accurately enough. 


I think you meant "edges in frequency" here...