SAR matched filters?

Started by Bo May 19, 2006
I'm TOTALLY new to RADAR world and am looking for some pointers/info in 
regards to SAR radar.

In particular, I am interested in finding out how matched filters can be 
implemented for X band SAR radars. I know that one method is through DSP of 
sampled data---but in our particular case, needing 500MHz- 1GHz bandwidth, I 
don't see that sampling I/Q data for those bandwidths is practical. (is 
it?). We may be used coded CDMA waveforms as well--which would as I 
understand it, even further widen our bandwidth requirements.

Could matched filters be done with analog or RF circuits? and CDMA coded 
matched filters? Can anyone point me to some good tutorials/ references, 
websites, or mfrs of these type filters?

Thanks,

Bo



See embedded answers below...

-- 
========
Armin Doerry
adoerry@yahoo.com


"Bo" <bo@cephus.com> wrote in message 
news:c349f$446e2ab4$18d6ec55$24115@KNOLOGY.NET...
> I'm TOTALLY new to RADAR world and am looking for some pointers/info in > regards to SAR radar. > > In particular, I am interested in finding out how matched filters can be > implemented for X band SAR radars.
*** Note that all (at least the useful and used ones) SAR processing algorithms attempt to implement a matched filter to the scene pixel locations. Where they fall short is in the approximations employed for efficient processing techniques - usually some kind of transforms. The specific assumptions and approximations made leading to specific techniques employed then distinguish the various image formation algorithms.
> I know that one method is through DSP of sampled data---but in our > particular case, needing 500MHz- 1GHz bandwidth, I don't see that sampling > I/Q data for those bandwidths is practical. (is it?).
*** As a matter of fact, this is posible with the latest A/D converters... This notwithstanding, a technique known as "stretch" processing for Linear FM chirps allows 'de-chirping' the echoes for substantial bandwidth reduction. This is how state-of-the-art radars can achieve 4-inch range resolution (>1.5 GHz of resolution bandwidth). Note that 'de-chirping' the echoes is in fact a partial compression scheme, that is, a partial implementation of a matched filter in analog RF.
> We may be used coded CDMA waveforms as well--which would as I understand > it, even further widen our bandwidth requirements. >
*** Note that the latest FPGA technology can operate at clock frequencies greater than 1 GHz.
> > Could matched filters be done with analog or RF circuits?
*** Yes... LFM chirp range compression with SAW filters is well known...
>and CDMA coded matched filters?
*** I suspect this requires at least some minimal digitization of the signals, but I don't know...
> Can anyone point me to some good tutorials/ references, websites, or mfrs > of these type filters? > > Thanks, > > Bo > > >
On Fri, 19 May 2006 15:30:02 -0500, "Bo" <bo@cephus.com> wrote:

>I'm TOTALLY new to RADAR world and am looking for some pointers/info in >regards to SAR radar. > >In particular, I am interested in finding out how matched filters can be >implemented for X band SAR radars. I know that one method is through DSP of >sampled data---but in our particular case, needing 500MHz- 1GHz bandwidth, I >don't see that sampling I/Q data for those bandwidths is practical. (is >it?). We may be used coded CDMA waveforms as well--which would as I >understand it, even further widen our bandwidth requirements. > >Could matched filters be done with analog or RF circuits?
SAR (and radar in general) has been around for a long time and the original processors were analog. In the range dimension dispersive filters were sometimes used which matched the FM rate of the chirp signal. Optical processors (analog optical processing) were all the rage until the late 70s or 80s. Range and cross-range matched filters were done with Fourier transform lenses and screens. Motion compensation was done by slightly adjusting the lenses as the signal was processed. Pretty cool stuff...
> and CDMA coded >matched filters? Can anyone point me to some good tutorials/ references, >websites, or mfrs of these type filters?
As was mentioned, SAW filters are often used for this sort of thing. There are probably other methods, too. Digital processing at these rates is certainly possible, though. Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org
Please see follow-up questions below.

"Armin Doerry" <adoerry@yahoo.com> wrote in message 
news:_NKdnfOSkJsRr_PZnZ2dnUVZ_u-dnZ2d@comcast.com...
> See embedded answers below... > > "Bo" <bo@cephus.com> wrote in message > news:c349f$446e2ab4$18d6ec55$24115@KNOLOGY.NET... >> I'm TOTALLY new to RADAR world and am looking for some pointers/info in >> regards to SAR radar. >> >> In particular, I am interested in finding out how matched filters can be >> implemented for X band SAR radars. > > *** Note that all (at least the useful and used ones) SAR processing > algorithms attempt to implement a matched filter to the scene pixel > locations. Where they fall short is in the approximations employed for > efficient processing techniques - usually some kind of transforms. The > specific assumptions and approximations made leading to specific > techniques employed then distinguish the various image formation > algorithms. > >> I know that one method is through DSP of sampled data---but in our >> particular case, needing 500MHz- 1GHz bandwidth, I don't see that >> sampling I/Q data for those bandwidths is practical. (is it?). > > *** As a matter of fact, this is posible with the latest A/D converters...
I know there are 3GHz 8bit ADCs available--but that leads to further questions---like 1) will 8 bits provide enough SNR? 2) re-iterating the earlier thread questions about I/Q sampling---how could one use these 8b 3GHz ADCs to perform I/Q sampling? 3) if 8 bit is too low for system SNR, how could this be improved? 4) I assume that at these data rates all, or almost all, processing algorithms to implement a matched filter would *have* to be implemented in an FPGA--that not even the fastest DSPs from TI/Analog Devices could process data this quickly? Is this a valid viewpoint? I don't know the length/types of coding that will be employed on this SAR yet--but discussion is leaning toward digital encoding of perhaps length 32 or 64 PN codes. How much (ballpark) would such PN codes spread the bandwidth of say a nominal 1GHz BW LFM chirp?
> This notwithstanding, a technique known as "stretch" processing for Linear > FM chirps allows 'de-chirping' the echoes for substantial bandwidth > reduction. This is how state-of-the-art radars can achieve 4-inch range > resolution (>1.5 GHz of resolution bandwidth). Note that 'de-chirping' > the echoes is in fact a partial compression scheme, that is, a partial > implementation of a matched filter in analog RF.
Can you explain what 'partial compression' means in this context? Or provide any links on the method or available HW for analog RF matched filter?
> >> We may be used coded CDMA waveforms as well--which would as I understand >> it, even further widen our bandwidth requirements. >> > > *** Note that the latest FPGA technology can operate at clock frequencies > greater than 1 GHz.
Point taken.
> >> >> Could matched filters be done with analog or RF circuits? > > *** Yes... LFM chirp range compression with SAW filters is well known...
And by using these SAW filters for matching, I could then beat the SAW output signal down to baseband for sampling/processing?
> >>and CDMA coded matched filters? > > *** I suspect this requires at least some minimal digitization of the > signals, but I don't know... >
Thanks again, Bo
See answers embedded below...

Armin

========
Armin Doerry
adoerry@yahoo.com


"Bo" <bo@cephus.com> wrote in message 
news:c7059$4471c507$18d6ec55$10839@KNOLOGY.NET...
> Please see follow-up questions below. > > "Armin Doerry" <adoerry@yahoo.com> wrote in message > news:_NKdnfOSkJsRr_PZnZ2dnUVZ_u-dnZ2d@comcast.com... >> See embedded answers below... >> >> "Bo" <bo@cephus.com> wrote in message >> news:c349f$446e2ab4$18d6ec55$24115@KNOLOGY.NET... >>> I'm TOTALLY new to RADAR world and am looking for some pointers/info in >>> regards to SAR radar. >>> >>> In particular, I am interested in finding out how matched filters can be >>> implemented for X band SAR radars. >> >> *** Note that all (at least the useful and used ones) SAR processing >> algorithms attempt to implement a matched filter to the scene pixel >> locations. Where they fall short is in the approximations employed for >> efficient processing techniques - usually some kind of transforms. The >> specific assumptions and approximations made leading to specific >> techniques employed then distinguish the various image formation >> algorithms. >> >>> I know that one method is through DSP of sampled data---but in our >>> particular case, needing 500MHz- 1GHz bandwidth, I don't see that >>> sampling I/Q data for those bandwidths is practical. (is it?). >> >> *** As a matter of fact, this is posible with the latest A/D >> converters... > > I know there are 3GHz 8bit ADCs available--but that leads to further > questions---like > > 1) will 8 bits provide enough SNR?
*** generally, yes... The image dynamic range is the sum (in dB) of the processing SNR gain and the ADC dynamic range...
> 2) re-iterating the earlier thread questions about I/Q sampling---how > could one use these 8b 3GHz ADCs to perform I/Q sampling?
*** same as any other ADC... Look up quadrature demodulation... For example http://members.tripod.com/michaelgellis/mixerscom.html There are two basic techniques for achieving quadrature (I/Q) data 1) form analog I/Q channels and then sample each channel with separate ADCs 2) Sample the IF with a single ADC and do digital baseband conversion and formation of I/Q channels
> 3) if 8 bit is too low for system SNR, how could this be improved?
*** If you de-chirp (stretch processing) for LFM waveforms you will need more bits than if you do not de-chirp. The difference is due to the SNR gain of de-chirping.
> 4) I assume that at these data rates all, or almost all, processing > algorithms to implement a matched filter would *have* to be implemented in > an FPGA--that not even the fastest DSPs from TI/Analog Devices could > process data this quickly? Is this a valid viewpoint?
No... real-time SAR systems generating digital data and using DSP to form images were around before FPGAs... Remember that systems are often pulse-Doppler radars, and that a rate buffer can follow the ADC to slow the data rate from the burst rate of the ADCs.
>I don't know the length/types of coding that will be employed on this SAR >yet--but discussion is leaning toward digital encoding of perhaps length 32 >or 64 PN codes. How much (ballpark) would such PN codes spread the >bandwidth of say a nominal 1GHz BW LFM chirp? >
*** Why would you use a PN code on top of a LFM chirp? It is not necessary merely to achieve fine resolution.
> >> This notwithstanding, a technique known as "stretch" processing for >> Linear FM chirps allows 'de-chirping' the echoes for substantial >> bandwidth reduction. This is how state-of-the-art radars can achieve >> 4-inch range resolution (>1.5 GHz of resolution bandwidth). Note that >> 'de-chirping' the echoes is in fact a partial compression scheme, that >> is, a partial implementation of a matched filter in analog RF. > > Can you explain what 'partial compression' means in this context? Or > provide any links on the method or available HW for analog RF matched > filter?
*** mixing the received echoes with a local oscillator chirp removes the chirp characteristic from the received signals, thereby compressing its bandwidth with no loss of signal. This generates SNR gain in addition to bandwidth compression. The result is a partial compression along the way to a matched filter. A matched filter is the ultimate (in a minimum mean square error sense) compression of the signal, i.e. maximizing the SNR.
>> >>> We may be used coded CDMA waveforms as well--which would as I understand >>> it, even further widen our bandwidth requirements. >>>
*** resolution is the same function of bandwidth regardless of the waveform used. The system impulse response is the autocorrelation of the waveform, which is the Fourier transform of the power spectral density of the waveform, regardless of the exact signal itself. Check out the appendix in http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/2006/060821.pdf
>> >> *** Note that the latest FPGA technology can operate at clock frequencies >> greater than 1 GHz. > > Point taken. > >> >>> >>> Could matched filters be done with analog or RF circuits? >> >> *** Yes... LFM chirp range compression with SAW filters is well known... > > And by using these SAW filters for matching, I could then beat the SAW > output signal down to baseband for sampling/processing? > >> >>>and CDMA coded matched filters? >> >> *** I suspect this requires at least some minimal digitization of the >> signals, but I don't know... >> > > Thanks again, > > Bo >
If I may add one sentence to Armin Doerry's explanation

"...mixing the received echoes with a local oscillator chirp removes
the chirp characteristic from the received signals, thereby compressing
its bandwidth with no loss of signal.  This generates SNR gain in
addition to bandwidth compression.  The result is a partial compression
along the way to a matched filter. "

stretch becomes "matched filtering" when the resulting heterodyne tone
at th eoutput of the mixer is filtered by a bandpass filter whose
bandwidth is the reciprocal of the chirp length; the filtering is
usually done in an FFT that will immediately gives a bank of parallel
filters, so you can also estimate the frequency (range) not only detect
the target's presence. It is only approximately matched because the
impulse response of the resulting filter is not exactly a finite square
pulse.

Subtleties of signals having both finite time duration and finite bandwidth 
notwithstanding, the stretch-processed impulse response (IPR) is pretty darn 
close to a true matched filter... or at least can be...

A matched filter's output for the input signal to which it is matched is the 
signal's autocorrelation function, which is also the Fourier transform of 
the signal's Power Spectral Density (PSD).  A constant amplitude, finite 
duration, LFM chirp with large time-bandwidth product has a PSD that is very 
nearly a rectangle function.  Consequently, its IPR is very nearly a sinc() 
function, that is, sin(x)/x in character, especially near its mainlobe peak. 
Typical SAR systems operate with time-bandwidth products in the hundreds to 
the many ten-thousands for high-performance systems, e.g. in fact a 100 usec 
chirp with 1800 MHz bandwidth = 180000.

Deramping the received chirp echoes doesn't by itself lose any information. 
The received signal can always be reconstituted by adding back the chirp. 
If the sampling interval is long enough such that all echo energy from all 
ranges of interest is contained in the samples, then a deskewing (removing a 
residual video phase error) operation can align the deramped echoes in time, 
and superfluous time samples can be trimmed.  At this point then no energy 
has been lost.  A FFT applied will result in an IPR that is again very much 
like a sinc() function, especially in its mainlobe, to within what the 
digital sampling will allow (i.e.  more samples make the mainlobe more 
sinc()-like)...

The bottom line is that for large time-bandwidth LFM chirps, the IPR in the 
region of its mainlobe will have inconsequential differences.  Both will 
exhibit essentially sinc() behavior in their IPR.

I apologize for being too wordy...  radar design and analysis is actually 
fun for me... so I get carried away sometimes... ;-)

Armin

-- 
========
Armin Doerry
adoerry@yahoo.com

"rge11x" <rge11x@netscape.net> wrote in message 
news:1148729655.788217.58990@j55g2000cwa.googlegroups.com...
> If I may add one sentence to Armin Doerry's explanation > > "...mixing the received echoes with a local oscillator chirp removes > the chirp characteristic from the received signals, thereby compressing > its bandwidth with no loss of signal. This generates SNR gain in > addition to bandwidth compression. The result is a partial compression > along the way to a matched filter. " > > stretch becomes "matched filtering" when the resulting heterodyne tone > at th eoutput of the mixer is filtered by a bandpass filter whose > bandwidth is the reciprocal of the chirp length; the filtering is > usually done in an FFT that will immediately gives a bank of parallel > filters, so you can also estimate the frequency (range) not only detect > the target's presence. It is only approximately matched because the > impulse response of the resulting filter is not exactly a finite square > pulse. >
You are not too wordy, on the contrary. I think we should all be
thankful to you for the rare effort in usenet to write coherent
explanation at all levels of readership. Most of sci.phys and sci.math
are by now have become nearly unreadable drivel. While this newsgroup
is not as widely read as those, we should be, and I certainly am
always, glad to read your opinions.

Armin,

Thanks for the reply. I've been out a few days and am just getting back to 
this--see my replies below.


>>> "Bo" <bo@cephus.com> wrote in message >>> news:c349f$446e2ab4$18d6ec55$24115@KNOLOGY.NET... >>>> I'm TOTALLY new to RADAR world and am looking for some pointers/info in >>>> regards to SAR radar. >>>> >>>> In particular, I am interested in finding out how matched filters can >>>> be implemented for X band SAR radars. >>> >>> *** Note that all (at least the useful and used ones) SAR processing >>> algorithms attempt to implement a matched filter to the scene pixel >>> locations. Where they fall short is in the approximations employed for >>> efficient processing techniques - usually some kind of transforms. The >>> specific assumptions and approximations made leading to specific >>> techniques employed then distinguish the various image formation >>> algorithms. >>> >>>> I know that one method is through DSP of sampled data---but in our >>>> particular case, needing 500MHz- 1GHz bandwidth, I don't see that >>>> sampling I/Q data for those bandwidths is practical. (is it?). >>> >>> *** As a matter of fact, this is posible with the latest A/D >>> converters... >> >> I know there are 3GHz 8bit ADCs available--but that leads to further >> questions---like >> >> 1) will 8 bits provide enough SNR? > > *** generally, yes... The image dynamic range is the sum (in dB) of the > processing SNR gain and the ADC dynamic range... > >> 2) re-iterating the earlier thread questions about I/Q sampling---how >> could one use these 8b 3GHz ADCs to perform I/Q sampling? > > *** same as any other ADC... Look up quadrature demodulation... For > example > http://members.tripod.com/michaelgellis/mixerscom.html > There are two basic techniques for achieving quadrature (I/Q) data > 1) form analog I/Q channels and then sample each channel with separate > ADCs > 2) Sample the IF with a single ADC and do digital baseband conversion and > formation of I/Q channels > >> 3) if 8 bit is too low for system SNR, how could this be improved? > > *** If you de-chirp (stretch processing) for LFM waveforms you will need > more bits than if you do not de-chirp. The difference is due to the SNR > gain of de-chirping. > >> 4) I assume that at these data rates all, or almost all, processing >> algorithms to implement a matched filter would *have* to be implemented >> in an FPGA--that not even the fastest DSPs from TI/Analog Devices could >> process data this quickly? Is this a valid viewpoint? > > No... real-time SAR systems generating digital data and using DSP to form > images were around before FPGAs... Remember that systems are often > pulse-Doppler radars, and that a rate buffer can follow the ADC to slow > the data rate from the burst rate of the ADCs. > >>I don't know the length/types of coding that will be employed on this SAR >>yet--but discussion is leaning toward digital encoding of perhaps length >>32 or 64 PN codes. How much (ballpark) would such PN codes spread the >>bandwidth of say a nominal 1GHz BW LFM chirp? >> > > *** Why would you use a PN code on top of a LFM chirp? It is not > necessary merely to achieve fine resolution.
Because this is not a single radar-- but rather N radars and we are contemplating use of PN codes to allow each radar to distinguish the other radar's returns. Either that or find a way to sync the radars very precisely so that only one transmits at a given time. The final signal coding/LFM/combo scheme is very much up for grabs right now. I'm looking into the +/- of each type and how one can implement the system once the decision is made.
> >> >>> This notwithstanding, a technique known as "stretch" processing for >>> Linear FM chirps allows 'de-chirping' the echoes for substantial >>> bandwidth reduction. This is how state-of-the-art radars can achieve >>> 4-inch range resolution (>1.5 GHz of resolution bandwidth). Note that >>> 'de-chirping' the echoes is in fact a partial compression scheme, that >>> is, a partial implementation of a matched filter in analog RF. >> >> Can you explain what 'partial compression' means in this context? Or >> provide any links on the method or available HW for analog RF matched >> filter? > > *** mixing the received echoes with a local oscillator chirp removes the > chirp characteristic from the received signals, thereby compressing its > bandwidth with no loss of signal. This generates SNR gain in addition to > bandwidth compression. The result is a partial compression along the way > to a matched filter. A matched filter is the ultimate (in a minimum mean > square error sense) compression of the signal, i.e. maximizing the SNR. > >>> >>>> We may be used coded CDMA waveforms as well--which would as I >>>> understand it, even further widen our bandwidth requirements. >>>> > > *** resolution is the same function of bandwidth regardless of the > waveform used. The system impulse response is the autocorrelation of the > waveform, which is the Fourier transform of the power spectral density of > the waveform, regardless of the exact signal itself. > Check out the appendix in > http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/2006/060821.pdf > >
Is it _possible_ to implement a matched filter for CDMA in an analog fashion? I'm thinking not. Which leads me to the question-- _must_ a CDMA signal be directly sampled---or can it be sampled after mix down to IF?
>>>> Could matched filters be done with analog or RF circuits? >>> >>> *** Yes... LFM chirp range compression with SAW filters is well >>> known... >> >> And by using these SAW filters for matching, I could then beat the SAW >> output signal down to baseband for sampling/processing?
I looked into SAW filters after your reply--but could find nothing available beyond the 2-4GHz range. The ones I found also had fairly limited bandwidth as well. Perhaps one existed for X band I have not yet found...(?)
>>>>and CDMA coded matched filters? >>> >>> *** I suspect this requires at least some minimal digitization of the >>> signals, but I don't know...
Thanks again, Bo
"rge11x" <rge11x@netscape.net> wrote in message 
news:1148863301.929369.264130@u72g2000cwu.googlegroups.com...
> You are not too wordy, on the contrary. I think we should all be > thankful to you for the rare effort in usenet to write coherent > explanation at all levels of readership. Most of sci.phys and sci.math > are by now have become nearly unreadable drivel. While this newsgroup > is not as widely read as those, we should be, and I certainly am > always, glad to read your opinions. >
Well put. Thanks again for the responses. Being new to radar I am still struggling to digest all of what has been said and am sure to have some more follow-up questions. Best regards, Bo