Building a dual-polarization mode for my USRP/GnuRadio RA receiver

[Marcus D. Leech]

Since we'll be working with a dual-polarization feed system, I decided
that it was time to upgrade the RA receiver code
to handle this.

What I ended up doing was to compute the complex cross-power between H
and V like so:

power = avg(H(I)*V(I) + H(Q)*V(Q))

This has the effect (like in a well-balanced correlation interferometer)
of tending towards zero when there's no coherent input
between the polarizations. I think this is correct.

Comments?

--
Marcus Leech
Principal Investigator, Shirleys Bay Radio Astronomy Consortium
http://www.sbrac.org

[Marko Cebokli]

Hello,

without an input signal, this will be zero, provided that your LNA's noises
are uncorrelated. They could be a little correlated however, because of
antenna crosstalk, power supply noise etc.

The problem is, that when you DO have an incoming signal, correlation is not
certain.
Most natural sources are very weakly polarized, and won't give you much
correlation.
Even for a fully polarized signal, if it happens to be so polarized, to be
matched to one of your polarizations and orthogonal to the other, you will
have no correlation (no signal in the second antenna!)
Also, if you only use the real part of the correlation (your formula), if the
signal gives you a 90 degree phase shift between channels (circ pol on two
lin chans), your output will be zero.

What I think you could do is:

1. for weakly polarized natural sources, just make two total power
(radiometer) channels and add their outputs. This will give you 1.5dB of
sensitivity boost (twice the bandwidth).

2. make a real polarization analyzer. Even a non-calibrated one would give you
discrimination against strongly polarized signals (QRM, SETI).
To measure the weak polarization of natural sources, you would have to make a
calibrated polarimeter.

Marko Cebokli

[Matt Ettus]

Polarization is analyzed with the Stokes parameters:

http://en.wikipedia.org/wiki/Stokes_parameters

Matt

[oxl...@att.net]

Marcus

As you will likely observe, the perfect polarized signal is non existant. The sources that we observe are random polarized in most cases. In addition, they have a random component even when a polarized signal is present.

 

The random signal would add on a 10 Log basis. If there is any component that is coherent in both polarities, it would add on a 20 log basis. Thus the cross product approach is good for looking for this type of component.

 

Non-random sources would include any motion of the object creating the signal, any interferometer type of signal where there is a spatial difference of the same signal and other effects such as the focusing of a beam through a medium (gravitational lensing).

 

It appears that the cross product is a good tool to have, but for most cases where you are looking for total power, it would be insignificant.

 

Paul

-------------- Original message from "Marcus D. Leech" <mar...@propulsionpolymers.com>: --------------

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[oxl...@att.net]

Matt

The "Stokes" parameters are useful to describe the signal in a three dimensional environment such as free space or over the face of an antenna. However, I dont think they would be very useful in analyzing a signal that has been captured by an antenna and represented by two signals.

Paul

-------------- Original message from "Matt Ettus" <boys...@gmail.com>: --------------

>
> Polarization is analyzed with the Stokes parameters:
>
> http://en.wikipedia.org/wiki/Stokes_parameters
>
> Matt
>
> On Fri, Aug 15, 2008 at 8:39 PM, Marcus D. Leech

> wrote:
> >
> > Since we'll be working with a dual-polarization feed system, I decided
> > that it was time to upgrade the RA receiver code
> > to handle this.
> >
> > What I ended up doing was to compute the complex cross-power between H
> > and V like so:
> >
> > power = avg(H(I)*V(I) + H(Q)*V(Q))
> >
> > This has the effect (like in a well-balanced correlation interferometer)
> > of tending towards zero when there's no coherent input
> > between the polarizations. I think this is correct.
> >
> > Comments?
> >
> > --
> > Marcus Leech
> > Principal Investigator, Shirleys Bay Radio Astronomy Consortium
> > http://www.sbrac.org
> >
> >
> > >
> >
>

[Marcus D. Leech]

Marko Cebokli wrote:
> Hello,
>
> without an input signal, this will be zero, provided that your LNA's noises
> are uncorrelated. They could be a little correlated however, because of
> antenna crosstalk, power supply noise etc.
>
> The problem is, that when you DO have an incoming signal, correlation is not
> certain.
> Most natural sources are very weakly polarized, and won't give you much
> correlation.
> Even for a fully polarized signal, if it happens to be so polarized, to be
> matched to one of your polarizations and orthogonal to the other, you will
> have no correlation (no signal in the second antenna!)
> Also, if you only use the real part of the correlation (your formula), if the
> signal gives you a 90 degree phase shift between channels (circ pol on two
> lin chans), your output will be zero.
>
> What I think you could do is:
>
> 1. for weakly polarized natural sources, just make two total power
> (radiometer) channels and add their outputs. This will give you 1.5dB of
> sensitivity boost (twice the bandwidth).
>

Changed the code, and here's what I'm now doing:

IIR_FILTER { H(I)*H(I) + H(Q)*H(Q) +V(I)*V(I) + V(Q)*V(Q) }

By changing to 8-bit samples across the USB bus, I can do both channels
at 8Mhz, giving me 16Mhz bandwidth into
the radiometer. Sweet!

Cheers

[Luis Cupido]

Paul,

On the contrary, stokes parameters is in fact
what comes out of the polarimeter back-ends on
radioastronomy.

Old times analog versions use mixers, delays sums and subtractions
to compute the various stokes parameters.

Modern ones use FPGA's to compute the four stokes
parameters and integrate data.

Usually the antenna feed back section separates
RHCP and LHCP and feed two independent
receivers that end up in a polarimetric correlator
which outputs are the first 3 (or the full 4)
stokes parameters.
Circular polarization is largely preferable over V and H
as gain asymmetries and gain drifts will affect
both the V and H components the same way.
The polarized radiation is only a small fraction of the
energy received, only about 1%, so using V and H one
can have far more instrumental errors than with CP,
I would say that V and H are not suitable. (one need
much better than 0.04dB
asymmetries to measure anything sensible using V and H
polarized antenna)

Luis Cupido
ct1dmk.

p.s.(I'm involved in the design of the fist full digital back-end
for radio-astronomy polarimetry for a 200MHz bandwidth system
(it has 4 input channels at 200Ms/s and does in real time
200Mcomputarions of the 4 stokes parameters per second and
integrate down to 1 stoke_param set per milisecond)

[Marcus D. Leech]

Luis Cupido wrote:
> Paul,
>
> On the contrary, stokes parameters is in fact
> what comes out of the polarimeter back-ends on
> radioastronomy.
>
>

Yes, I agree with you. The stokes parameters are important, and it
seems to me that I have everything
I need to compute them.

> Old times analog versions use mixers, delays sums and subtractions
> to compute the various stokes parameters.
>
> Modern ones use FPGA's to compute the four stokes
> parameters and integrate data.
>

For more modest bandwidths, you don't need an FPGA, I think.

> Usually the antenna feed back section separates
> RHCP and LHCP and feed two independent
> receivers that end up in a polarimetric correlator
> which outputs are the first 3 (or the full 4)
> stokes parameters.
> Circular polarization is largely preferable over V and H
> as gain asymmetries and gain drifts will affect
> both the V and H components the same way.
> The polarized radiation is only a small fraction of the
> energy received, only about 1%, so using V and H one
> can have far more instrumental errors than with CP,
> I would say that V and H are not suitable. (one need
> much better than 0.04dB
> asymmetries to measure anything sensible using V and H
> polarized antenna)
>
>

So, I have two orthogonal feed probes at 90deg to each other. Can I not
convert the incoming signal
to circular simply by phase-shifting one of them by 90deg compared to
the other, before further
processing?

> Luis Cupido
> ct1dmk.
>
> p.s.(I'm involved in the design of the fist full digital back-end
> for radio-astronomy polarimetry for a 200MHz bandwidth system
> (it has 4 input channels at 200Ms/s and does in real time
> 200Mcomputarions of the 4 stokes parameters per second and
> integrate down to 1 stoke_param set per milisecond)
>
>
>

I'd like to see more details of this!

[oxl...@att.net]

Luis

My comment was on the usefulness of the parameters, not the ability to measure or calculate them. After further review, it appears that they might be useful to determine the degree of polarization in addition to the values of the diferent polarizations that could be present.

 

Regarding the choice of V/H vs R/L as the detecting method, they both contain the same information. However, as you point out, one may be preferable considering gain deviations in the instrument. It should also be noted that the instruments likely have slightly different phase as well as absolute delay differences with either scheme. Considering the causes of differences in delay or phase such as filter caracteristics, wiring lengths, probe placement in the received waveguide, etc., many parameters would need to be controlled and fully understood to do the processing in software.

 

To overcome the differences, techniques such as using multiple antennas has been proposed. For example Krause discusses the work of Suzuki and Tauchiya on pages 4-19 & 20 in his book Radio Astronomy. Suzuki & Tauchiya used three antennas to collect the following powers:

 

Linear V & H

Linear Offset 45 degrees

Circular R & L using Helical Beam antennas

 

They state that "The aperatures of all the antennas , of course, must be equal. There is some redundancy in the above measurements. For a partially polarized wave four independent measurements are necessary, and for a completely polarized wave three are needed. Although some redundancy ma be useful, the number of independent measurements can be reduced for example, "

 

The four suggested are:

 

Right Circular

Left Circular

Linear Horizontal

Linear Horizontal offset 45 degrees.

 

From these, the four normalized Stokes parameters are calculated by his formulae shown in  4-100.

 

The difficulty appears to be the situation where there is a mix of polarizations that is likely dominated by random polarization in the signals observed. This is the normal case in RA observations due to the thermal component present.

 

Therefore, what do you propose doing with only two measurements?

 

Paul

 

-------------- Original message from Luis Cupido <cup...@mail.ua.pt>: --------------

> > : --------------
> >
> >
> > >
> > > Polarization is analyzed with the Stokes parameters:
> > >
> > > http://en.wikipedia.org/wiki/Stokes_parameters
> > >
> > > Matt
> > >
> > > On Fri, Aug 15, 2008 at 8:39 PM, Marcus D. Leech
> > > wrote:
> > > >
> > > > Since we'll be working with a dual-polarization feed system, I
> > decided
> > > > that it was time to upgrade the RA receiver code
> > > > to handle this.
> > > >
> > > > What I ended up doing was to compute the complex cross-power
> > between H
> > > > and V like so:
> > > >
> > > > power = avg(H(I)*V(I) + H(Q)*V(Q))
> > > >
> > > > This has the effect (like in a well-balanced correlation
> > interferometer)
> > > > of tending towards zero when there's no coherent input
> > > > between the polarizations. I think this is correct.
> > > >
> > > > Comments?
> > > >
> > > > --
> > > > Marcus Leech
> > > > Principal Investigator, Shirleys Bay Radio Astronomy Consortium
> > > > http://www.sbrac.org
> > > >
> > > >
> > > > >
> > > >
> > >
> > > > >
> >
>

[Luis Cupido]

Hi Marcus,

> For more modest bandwidths, you don't need an FPGA, I think.

Yes, as much as your math processing power allows.

I fear however that your bandwidth*efficiency product
will be rather small as the computations for the stokes
parameters require quite a bit of multiplications and additions
prior to integration.

I presume you refer to a 100% efficiency system
that is where all samples are used and the acquisition runs
full time. (no discarded data).
Hence the bandwidth depend on how much time you need to
compute the stokes parameter and integrate.
I'm curious to know how much you can do...

> So, I have two orthogonal feed probes at 90deg to each other.
> Can I not
> convert the incoming signal
> to circular simply by phase-shifting one of them by 90deg compared to
> the other, before further
> processing?

Sure you can,
I'll say better... You must !!!
It is simply feed the V and H to a 90deg hybrid coupler
they you have RHCP and LHCP.

Luis Cupido.
ct1dmk.

P.S. When the webpage has the interesting details
I'll let you know. In the mean time I'll look for the
paper that has the polarimeter-correlator and send you.

[Luis Cupido]

Forgot to say that you may have a huge bandwidth
if your ADC allows and compute stokes at a slower
pace, having thus a small information efficiency
and will require a larger integration time for
the same results.
(equals to less bandwidth and more samples integrated)

Well... the same as in any other radiometric measurement.

The equation is always the same....
so the key is the bandwidth*efficiency product
if one decides to go below 100% eff.

> I presume you refer to a 100% efficiency system
> that is where all samples are used and the acquisition runs
> full time. (no discarded data).

[Luis Cupido]

Paul,

The best choice of antenna polarization scheme will be
conditioned by analyzing the impact of the
most significant instrument imperfections.

Either gain or phase mismatch, common drift
differential drift or polarization
cross talk etc.

With todays technology you can have a reasonably well matched
pair of receiver chains (LNA + converter + FI etc)
never the less considering that our target is the ability to measure
an unpolarized signal with a linearly polarized component of
1% or less, the gain imbalance makes it prohibitive
to run linear frontends and receivers unless we can assure
differential imbalance changes of much less than 0.043dB for 1%

There are all the other factors to consider but I think the one
above intimidates any RF designer hi ;-)
Hence RHCP and LHCP would be the premium chioce.

Luis Cupido.
ct1dmk.

[oxl...@att.net]

Marcus & Luis

The placement of the probes in the waveguide is also important to establish the phase relationship between the V & H components. Sometimes, feedhorn designers use an offset to obtain the 90 degree shift, thus simplifying the conbiner.

 

You should also be able to do the 90 degree shift in software by delaying one of the sample streams by an equivalent of 90 degrees. If you have a nyquist sample rate, 90 degrees would be equivalent to a slip of 1 sample (1 out of the 4 samples needed for Nyquist sampling of a full sine wave at the maximum frequency). It should be noted that this method is precisely accurate only at the exact Nyquist frequency. It might be better to delay by 2 samples which would center the delay on 1/2 of the sampled bandwidth.

Paul

-------------- Original message from Luis Cupido <cup...@mail.ua.pt>: --------------

[Marcus D. Leech]

Luis Cupido wrote:
> Hi Marcus,
>
> > For more modest bandwidths, you don't need an FPGA, I think.
>
> Yes, as much as your math processing power allows.
>
> I fear however that your bandwidth*efficiency product
> will be rather small as the computations for the stokes
> parameters require quite a bit of multiplications and additions
> prior to integration.
>

Right now, my back-end is processing two complex (I & Q) streams at 8
megasamples/sec per stream. It's doing 100%
efficient (no dropped samples) radiometry on both H and V, and doing
an FFT-based spectral computation with discarded
frames at about 20% efficiency.

This is on a Pentium-D 925 processor, running at 3.0Ghz, with 2GB of
memory. Even though it's a dual-CPU system,
the entire radio stack runs inside a single thread, and thus on a
single CPU. Future versions of Gnu Radio (which is what
my stuff is based on) will provide for running parallel signal
processing paths in different threads, thus allowing you to spread
computations across multiple CPUs. I look forward greatly to this :-)

Cheers

[David Ocame]

As do I!~ :)

Marcus D. Leech wrote:
> look forward greatly to this :-)

> --
> http://www.qsl.net/n1yvv
> ***********************************
> ****I'm not dead, yet!************
> ***********************************
>
> Dave Ocame, WS1ETI
> Awards Chair
> The SETILeague, Inc
> www.setileague.org
>
> Stony Creek Observatory
> FN31og
> -72.834 longitude
> 41.272 latitude
> Member: The SETILeague, Inc. and,
> The Society for Amateur Radio Astronomy (SARA) and,
> The Planetary Society
>

[Marcus D. Leech]

David Ocame wrote:
> As do I!~ :)
>
>
>
Indeed :-)

By the way, I'll be checking in a version of the code that turns-on
8-bit sampling, which means that on your (nearly identical to mine)
system, you should be able to do 16Msamples/sec on your single
channel. You have to crank the gain up about 15dB, but this
appears to work splendidly!

[David Ocame]

Way cool!

Marcus D. Leech wrote:
>
> By the way, I'll be checking in a version of the code that turns-on
> 8-bit sampling, which means that on your (nearly identical to mine)
>

Nearly identical. Except for the part where your working on a dish that
is ~ 1 bazillion times larger than mine. :)

> system, you should be able to do 16Msamples/sec on your single
> channel. You have to crank the gain up about 15dB, but this appears to work splendidly!

Can't wait to give it a whirl.

[Marcus D. Leech]

David Ocame wrote:
> Way cool!
>
> Marcus D. Leech wrote:
>
>> By the way, I'll be checking in a version of the code that turns-on
>> 8-bit sampling, which means that on your (nearly identical to mine)
>>
>>
> Nearly identical. Except for the part where your working on a dish that
> is ~ 1 bazillion times larger than mine. :)
>
>

An inconsiderable detail my man, hardly worthy of comment :-)

[Luis Cupido]

Fine on the first approach.
making the 90deg shift on the waveguide
then using a 0 deg combiner or a 180 deg combiner.
Although as we want both RHCP and LHCP
simultaneously it may result in more complexity
then a simgle 90deg hybrid coupler.

Alternatively one may do a polarizer section in
the waveguide and use the H and V probes that
will be delivering RHCP and LHCP singnals.

Your second comment as a method to obtain RHCP or LHCP
in the digital domain is fine, but fails in our
purpose of having a RHCP and LHCP in the hardware
of the receiver which is our main goal.
(like that one receiver will have H and the other
will have V, that is exactely what we are trying to
avoid in the first place)

The purpose is not to receive RHCP or LHCP
the idea is to have the RF and IF stages operating
on RHCP and LHCP, in software we will be
doing far more by having the full polarizarion info
by calculating the stokes parameters.

Luis Cupido
ct1dmk.

[Marcus D. Leech]

Luis Cupido wrote:
> Fine on the first approach.
> making the 90deg shift on the waveguide
> then using a 0 deg combiner or a 180 deg combiner.
> Although as we want both RHCP and LHCP
> simultaneously it may result in more complexity
> then a simgle 90deg hybrid coupler.
>
> Alternatively one may do a polarizer section in
> the waveguide and use the H and V probes that
> will be delivering RHCP and LHCP singnals.
>
>
> Your second comment as a method to obtain RHCP or LHCP
> in the digital domain is fine, but fails in our
> purpose of having a RHCP and LHCP in the hardware
> of the receiver which is our main goal.
> (like that one receiver will have H and the other
> will have V, that is exactely what we are trying to
> avoid in the first place)
>
> The purpose is not to receive RHCP or LHCP
> the idea is to have the RF and IF stages operating
> on RHCP and LHCP, in software we will be
> doing far more by having the full polarizarion info
> by calculating the stokes parameters.
>
>

Right, OK. You want the *analog* bits (all the way out to the antennae)
to be sensitive to either circular polarization, because
by doing so, you gain sensitivity, and have more raw information
available to compute the stokes parameters. I think I have it
now.

So, I could modify my feed to make the H and V probes "see" LHCP and
RHCP, yes?

[Marcus D. Leech]

David Ocame wrote:
>
> Can't wait to give it a whirl.
>
>

I'll check it into the trunk in the next few days.

I also made another optimization (thought of it over dinner!) that
removes two stages of post-detection filtering, and thus
frees up computrons for other processing (like stokes parameters, for
example). So I just eliminated hundreds of multiply-adds
per sample by removing two of the post-detector FIR filters. So now,
the (previously final and now only) filter operates at
the input bandwidth rate, but acts as a very long (in terms of raw
sample rate) integrator. I then follow this with a simple
"keep_one_in_n" decimator which reduces the output rate to
1sample/sec, from the up-to 8Megasamples per second on input.

Cheers

[oxl...@att.net]

Luis

One additional thought from my experience. What you referred to as polarization crosstalk is usually called cross pole discrimination (XPD). Typical XPD values for a solid dish is about 30 dB on the bore site center of the main lobe. It degrades as you go off of bore site. To obtain higher levels of XPD techniques such as Grid antennas or polarization screens on the face of the antennas will improve the XPD. For example, some of the satellite based antennas use a grid in front of two antennas one with the grid aligned vertically and one horizontal to improve the XPD. In addition, any reflection or refraction in the path will degrade the XPD. In addition, the XPD can be degraded by imperfections in the waveguide that may cause additional modes to propogate. These imperfections can also rotate or distort the orthagonal relationship between the fields. Faraday rotation also occurs in the earth's atmosphere that is caused by the magnetic field of the earth.

 

Given all of the above, I expect that the antenna system may limit the sensitivity of any Stokes measurements.

 

Paul

[Luis Cupido]

Marcus,

Not really, no.

The point is only to get rid of the devastating effect of
gain imbalance and differential drift since the waves are
only a few % polarized and that small fraction
is essentially linear, working it in V and H you
will never know if you are measuring the polarization in the sky
or the system differential drifts.
(since to measure 1% polarization you need imbalance changes
far below 0.04dB I'll bet that you will be measuring
nothing else but your setup drifts).

You can try to visualize the effect of system imbalances
on CP and LIN while measuring a wave with a few % linear polarization.
Or if it fails to catch your brain, you may crack the stokes matrix
by multiplying the relevant elements by an error quantity and see
where those errors affect less the Q and V parameters.
You will find that for a LIN wave if the system uses RHCP and
LHCP the Q and U parameters are much less affected than if
receiver is V and H ...

> So, I could modify my feed to make the H and V probes "see" LHCP and
> RHCP, yes?

Correct, you should have the two receive chains to work
on RHCP and LHCP, and then have the set of equations that
compute IQUV from a RHCP and LHCP signals.

Luis Cupido.

P.S. I may be out of email for a few days.
tks.

[Luis Cupido]

Yeap, fine.

XPD yes... bad memory and bad English
I'm sorry.
You're right that is the term.

And yes the antenna sets one limit for polarization
discrimination.
The other limit is, in the case of RA, set by the
long integration time where the RX system changes affect
the polarization values measured.

No point to have a supper-duper antena if the RX
system doesn't descriminate that well over the
integration time required.

And no point also the other way around.

;-)

Luis Cupido
ct1dmk.

[kl7uw]

Not getting into the heavy math but hams have solved this in two
approaches:
1) The method I am reading most (above) is using a circular horn with
two orthogonal probes to retrieve orthogonal polarization and combing
this in a quadrature hybrid to retrieve simultaneous RH and LH CP
signals.
2) Effecting the phase shift in a cutoff septum feedhorn using two
probes to retrieve RH and LH directly.

This latter approach has the advantage of less insertion loss before
the LNA's. The septum may be metallic or dielectric. Either achieves
the needed phase shift.

MY 4.9m dish will be using a rectangular horn with a metallic stepped
septum for use on 1296-eme and 1420-RA.

73 Ed Cole
Argus Station BP40IQ
ham station KL7UW

> >      > > > > > >http://www.sbrac.org- Hide quoted text -
>
> - Show quoted text -

[oxl...@att.net]

Luis

I assume that the system you are selling has the simple way to reduce gain variations by normalizing the data over the integration period. This would reduce the impact of differences in gain to only be those that occur during the integration.

 

Please explain in plain english why you feel that circular polarization is less impacted by gain variations. It is not intuitively obvious.

Paul

 

[oxl...@att.net]

Luis & Marcus

If you depend only on the R/L Circular as your only input, you then become dependent on how accurately you can derive the R/L values. For example, if you create the R/L from linear probes that is a common technique, any error is embedded into the signals. For example, if the quadrature combiner has any error in phase, that error will be present in all measurements. In addition, since the quadrature combiner is a frequency sensitive device, the exact phase quadrature is only present on one frequency, not the whole bandwidth being monitored.

 

I suspect that is why Krause suggests multiple antennas to gain redundancy. He suggests using helical antennas for the R & L and linear arrays for the V & H.

 

It seems to me to be easier to get rid of gain variations over the integration period than phase errors.

Paul

-------------- Original message from Luis Cupido <cup...@mail.ua.pt>: --------------


>