Hello,

We are trying to measure the angle of arrival of FM using USRP B210. We
have run into some problems with the measurements and hence we are writing
this email. It would be nice if we can get some inputs from you on how to
fix this issue. We have used two methods for computing the phase
difference. We have used the first one most of the time. However, we are
posting both the methods here for you to have a look.

I have attached method 1 (phase_difference_probe.grc for probing and
phase_difference_view.grc which provides a nice GUI to look at) and method
2 (complex_method.grc). Method 1 is based on the following "paper":

http://www.egr.msu.edu/classes/ece480/capstone/spring14/group02/docs/Application%20Note%20-%20Phase%20George%20Godby%20Team%202.pdf

We use these flow graphs and run them in another script which probes the
"top_block" to get 500 samples which are then averaged to produce one data
point.

We also attach a diagram (AoA_Figure.pdf) which shows a basic idea of how
the antennas and transmitter are setup and what the Angle of Arrival (AoA)
is, when it comes to our measurements.

We tried our code in two different situations. In our first test, our
transmitter was another B210 and we were in an open field. The frequency we
tried ranged from 200 MHz to 1.0 GHz and then 3 GHz and 4 GHz. Our Phase
difference and consequently our AoA measurement were not too far off, when
the antenna array was facing the transmitter (i.e. at an expected AoA of 0
degs). As we moved closer towards an AoA of +- 90 the accuracy of the
measurement fell off. But the consistency of the 500 samples was still
pretty good (we were getting a standard deviation under 0.10 radians).

For our second test, we tried to get the AoA from FM radio towers. We got
about 800-1000m away from a popular radio station tower and pointed the
antenna array at the tower (expecting an AoA of around 0 degs). But we got
measurements which were way off. We did this for a couple of different
spots but the measurements were all over the place (the standard deviation
for individual data points were pretty good but the measurement for the 0
deg position at one spot was different for another spot around the tower).
We did manege to get angle measurements at one point when we were about 800
meters from the tower. The expected angle was 0 but we got 60 - 70 degrees
as the measured angle. We also tried at other places, one was about 800 m
from the tower and the other about 1200m. But both these places were
problematic.

It would be nice to get your inputs on the flow graphs. What are your
thoughts about the flow graph? Do you see any glaring problems with the
flow graph or with the set up? If you have any more questions about the
setup then feel free to ask.

Most of the information about the setup that we are using are in the
attached grc files. Thanks a lot for all your time.

Sincerely,
Michael Duckett

USRP-users mailing list
USRP-users@lists.ettus.com
http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com

We are using two antennas on the same B210 and the distance between
them is 7cm (the distance between the two "TX/RX" ports). We
understand that this affects the measured phase difference and the
further calculation for the AOA. For future tests we may try to widen
the distance between the two antennas to half the wavelength (I think
that would be around 1.3 to 1.7 m for FM radio station frequencies).

This distance between the two antennas brings us to the first
question. Because the distance between the antennas was small compared
to half the wavelength of the frequency, the range of valid phase
differences was shrunk, too. Most of the time when we were measuring
we got phase differences which were out of range of the valid region.
In one spot close to the tower, we positioned our antenna array at the
0 degree orientation and  phase difference values which corresponded
to 60-70 degrees. In another spot with the same orientation, we got
phase difference values which were out of range. So when we rotated
the antenna array, it was difficult to compared the AOA because most
of the time that calculation wasn't possible. But we can see
noticeable changes in the phase difference when rotating the array.
But there doesn't seem to be an easily decipherable pattern to the error.

We haven't been monitoring the time domain signal levels. We can try
that next time, as well.

On Fri, Apr 8, 2016 at 2:19 PM, Derek Kozel <derek.kozel@ettus.com
mailto:derek.kozel@ettus.com> wrote:

 Hello Michael,

 In addition to Alexander's good thoughts, are you monitoring the
 time domain signal levels to ensure that the receive gain is set
 appropriately? I see a QT GUI Sink (you may consider using the QT
 Frequency Sink), but it would be worth while looking at a QT Time
 Sink as well to see if you are clipping.

 Regards,
 Derek


 On Fri, Apr 8, 2016 at 10:28 AM, Alexander Levedahl via USRP-users
 <usrp-users@lists.ettus.com <mailto:usrp-users@lists.ettus.com>>
 wrote:

     I do not have the ability to look at files right now so sorry
     if I am asking questions that are answered in the files.

     If you stand in one spot and rotate, is the error consistent? 
     I.e., if you are pointing the array right at it, it shows the
     AOA as 60-70.  If you change to pointing 30 degrees, does the
     AOA change to 90-100?
     Are the results consistent across restarting the B210? 
     Depending on the answer to these questions, it may simply be a
     calibration problem.  I.e., when you turn it on there needs to
     be a calibration step.

     Finally, how many antennas are you using 2 or are you using
     multiple B210s?  Is your antenna spaced appropriately for the
     operating frequency?


     On Fri, Apr 8, 2016 at 12:51 PM, Michael Duckett via
     USRP-users <usrp-users@lists.ettus.com
     <mailto:usrp-users@lists.ettus.com>> wrote:

         Hello,

         We are trying to measure the angle of arrival of FM using
         USRP B210. We have run into some problems with the
         measurements and hence we are writing this email. It would
         be nice if we can get some inputs from you on how to fix
         this issue. We have used two methods for computing the
         phase difference. We have used the first one most of the
         time. However, we are posting both the methods here for
         you to have a look.

         I have attached method 1 (phase_difference_probe.grc for
         probing and phase_difference_view.grc which provides a
         nice GUI to look at) and method 2 (complex_method.grc).
         Method 1 is based on the following "paper":


         http://www.egr.msu.edu/classes/ece480/capstone/spring14/group02/docs/Application%20Note%20-%20Phase%20George%20Godby%20Team%202.pdf


         We use these flow graphs and run them in another script
         which probes the "top_block" to get 500 samples which are
         then averaged to produce one data point.

         We also attach a diagram (AoA_Figure.pdf) which shows a
         basic idea of how the antennas and transmitter are setup
         and what the Angle of Arrival (AoA) is, when it comes to
         our measurements.

         We tried our code in two different situations. In our
         first test, our transmitter was another B210 and we were
         in an open field. The frequency we tried ranged from 200
         MHz to 1.0 GHz and then 3 GHz and 4 GHz. Our Phase
         difference and consequently our AoA measurement were not
         too far off, when the antenna array was facing the
         transmitter (i.e. at an expected AoA of 0 degs). As we
         moved closer towards an AoA of +- 90 the accuracy of the
         measurement fell off. But the consistency of the 500
         samples was still pretty good (we were getting a standard
         deviation under 0.10 radians).

         For our second test, we tried to get the AoA from FM radio
         towers. We got about 800-1000m away from a popular radio
         station tower and pointed the antenna array at the tower
         (expecting an AoA of around 0 degs). But we got
         measurements which were way off. We did this for a couple
         of different spots but the measurements were all over the
         place (the standard deviation for individual data points
         were pretty good but the measurement for the 0 deg
         position at one spot was different for another spot around
         the tower). We did manege to get angle measurements at one
         point when we were about 800 meters from the tower. The
         expected angle was 0 but we got 60 - 70 degrees as the
         measured angle. We also tried at other places, one was
         about 800 m from the tower and the other about 1200m. But
         both these places were problematic.

         It would be nice to get your inputs on the flow graphs.
         What are your thoughts about the flow graph? Do you see
         any glaring problems with the flow graph or with the set
         up? If you have any more questions about the setup then
         feel free to ask.

         Most of the information about the setup that we are using
         are in the attached grc files. Thanks a lot for all your time.

         Sincerely,
         Michael Duckett


         _______________________________________________
         USRP-users mailing list
         USRP-users@lists.ettus.com <mailto:USRP-users@lists.ettus.com>
         http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com



     _______________________________________________
     USRP-users mailing list
     USRP-users@lists.ettus.com <mailto:USRP-users@lists.ettus.com>
     http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com

USRP-users mailing list
USRP-users@lists.ettus.com
http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com

Hi Michael,

So, I'm currently having a look at your flow graphs; they look sound
to me; especially the complex method (Which pretty much is equivalent
to picking one frequency bin from the FFT, if you add a sharp bandpass
filter, so that you only see one frequency) looks efficient. In fact,
seeing both approaches in one place reminded me of OFDM radar, where
one actually takes advantage of the

offset to an angle?

will definitely be an interesting use case for both SDR in general, the
USRP B210, and GNU Radio; I don't remember fully, but I think the cel-kit
account on github has a gr-specest repo, where you can find a few examples
of parametric spectrum estimators; amongst these MUSIC, an algorithm
actually originating in the world of direction detection, applied to
frequency estimation. It should be pretty straightforward to adapt the
algorithm to spatial problems – basically, you'd replace the estimated
signal autocovariance matrix by a antenna cross-correlation matrix.

station tower is better. The Tower probably is an array so you will not be
in the main beam anyway. Find the tallest building in the area and ask if
you can do your tests on their roof. A clear and open line of sight to the
tower is your goal here.

receiver.  This can be easily tested by removing the antennas and verifying
that the signals drop by at least 10 dB.  The more it drops, the better
your measurement. I would try and get at least 20 dB of isolation for a
good AoA measurement.

Hi Michael,

After a quick look, it seems that the methodology is sound, but you may
have problems with the way you are testing. Here are a few things you can
do to improve your measurements and test the performance.

First, height is your friend. Don’t think that getting closer to the
station tower is better. The Tower probably is an array so you will not be
in the main beam anyway. Find the tallest building in the area and ask if
you can do your tests on their roof. A clear and open line of sight to the
tower is your goal here.

Second, what else can the signal be bouncing off of? Is there a tall water
tower nearby? Could you be seeing the effects of reflected signals? For
this, again, height is your friend. By moving to a tall building, you will
minimize the number and strength of possible reflective surfaces.

Third, is the signal really entering the antenna? Or is it coupling to the
receiver.  This can be easily tested by removing the antennas and verifying
that the signals drop by at least 10 dB.  The more it drops, the better
your measurement. I would try and get at least 20 dB of isolation for a
good AoA measurement.

Evan

From: USRP-users [mailto:usrp-users-bounces@lists.ettus.com] *On Behalf
Of *Marcus D. Leech via USRP-users
Sent: Friday, April 08, 2016 3:17 PM
To: usrp-users@lists.ettus.com
Subject: Re: [USRP-users] Fwd: Angle of Arrival Measurements

On 04/08/2016 04:21 PM, Marcus Müller via USRP-users wrote:

Hi Michael,

So, I'm currently having a look at your flow graphs; they look sound to
me; especially the complex method (Which pretty much is equivalent to
picking one frequency bin from the FFT, if you add a sharp bandpass filter,
so that you only see one frequency) looks efficient. In fact, seeing both
approaches in one place reminded me of OFDM radar, where one actually takes
advantage of the

I use the complex-conjugate method in astronomical interferometry, which
is related to AoA, at least in an incidental sense--the emergence
of fringes is due to change in phase due to change in arrival angle
relative to the baseline between the antenna.

I also just use it for measuring and/or looking-for phase-drift between
two sources that should be phase-coherent.

time/frequency structure of the signal, and, more elementarily, the fact
that a shift in time domain is a modulation with an offset frequency in
frequency domain. Maybe [1] is a bit of a fun read to you; for the angle of
arrival problem (which for your approaches is really but a time offset
problem), things boil down to:
If [image: $x$]and [image: $y$]are the same signal, but [image:
$y(t)=x(t-\tau)$]is delayed by [image: $\tau$], then their Fourier
transforms [image: $X$]and [image: $Y$]are also the same but for the
latter [image: $Y=e^{-j2\pi\tau f} X$]being the first modulated by a
complex sinusoid. Estimating that sinusoid's frequency gives you the timing
offset; you can get the "pure" tone by just dividing [image: $\frac YX$].
Looking at the discrete signal case, note that the frequency resolution you
can get depends on the DFT you're doing – i.e. longer observation/larger
DFT has a very positive effect on accuracy!

I'd really love to see multiple approaches at AoA being implemented, that
will definitely be an interesting use case for both SDR in general, the
USRP B210, and GNU Radio; I don't remember fully, but I think the cel-kit
account on github has a gr-specest repo, where you can find a few examples
of parametric spectrum estimators; amongst these MUSIC, an algorithm
actually originating in the world of direction detection, applied to
frequency estimation. It should be pretty straightforward to adapt the
algorithm to spatial problems – basically, you'd replace the estimated
signal autocovariance matrix by a antenna cross-correlation matrix.

Best regards,
Marcus

[1] Braun, Martin. Ofdm radar algorithms in mobile communication
networks. Diss. Karlsruhe, Karlsruher Institut für Technologie (KIT),
Diss., 2014, 2014.
http://d-nb.info/104838490X/34

On 08.04.2016 21:15, Michael Duckett via USRP-users wrote:

We are using two antennas on the same B210 and the distance between them
is 7cm (the distance between the two "TX/RX" ports). We understand that
this affects the measured phase difference and the further calculation for
the AOA. For future tests we may try to widen the distance between the two
antennas to half the wavelength (I think that would be around 1.3 to 1.7 m
for FM radio station frequencies).

This distance between the two antennas brings us to the first question.
Because the distance between the antennas was small compared to half the
wavelength of the frequency, the range of valid phase differences was
shrunk, too. Most of the time when we were measuring we got phase
differences which were out of range of the valid region. In one spot close
to the tower, we positioned our antenna array at the 0 degree orientation
and  phase difference values which corresponded to 60-70 degrees. In
another spot with the same orientation, we got phase difference values
which were out of range. So when we rotated the antenna array, it was
difficult to compared the AOA because most of the time that calculation
wasn't possible. But we can see noticeable changes in the phase difference
when rotating the array. But there doesn't seem to be an easily
decipherable pattern to the error.

We haven't been monitoring the time domain signal levels. We can try that
next time, as well.

On Fri, Apr 8, 2016 at 2:19 PM, Derek Kozel derek.kozel@ettus.com wrote:

Hello Michael,

In addition to Alexander's good thoughts, are you monitoring the time
domain signal levels to ensure that the receive gain is set appropriately?
I see a QT GUI Sink (you may consider using the QT Frequency Sink), but it
would be worth while looking at a QT Time Sink as well to see if you are
clipping.

Regards,

Derek

On Fri, Apr 8, 2016 at 10:28 AM, Alexander Levedahl via USRP-users <
usrp-users@lists.ettus.com> wrote:

I do not have the ability to look at files right now so sorry if I am
asking questions that are answered in the files.

If you stand in one spot and rotate, is the error consistent?  I.e., if
you are pointing the array right at it, it shows the AOA as 60-70.  If you
change to pointing 30 degrees, does the AOA change to 90-100?

Are the results consistent across restarting the B210?  Depending on the
answer to these questions, it may simply be a calibration problem.  I.e.,
when you turn it on there needs to be a calibration step.

Finally, how many antennas are you using 2 or are you using multiple
B210s?  Is your antenna spaced appropriately for the operating frequency?

On Fri, Apr 8, 2016 at 12:51 PM, Michael Duckett via USRP-users <
usrp-users@lists.ettus.com> wrote:

Hello,

We are trying to measure the angle of arrival of FM using USRP B210. We
have run into some problems with the measurements and hence we are writing
this email. It would be nice if we can get some inputs from you on how to
fix this issue. We have used two methods for computing the phase
difference. We have used the first one most of the time. However, we are
posting both the methods here for you to have a look.

I have attached method 1 (phase_difference_probe.grc for probing and
phase_difference_view.grc which provides a nice GUI to look at) and method
2 (complex_method.grc). Method 1 is based on the following "paper":

http://www.egr.msu.edu/classes/ece480/capstone/spring14/group02/docs/Application%20Note%20-%20Phase%20George%20Godby%20Team%202.pdf

We use these flow graphs and run them in another script which probes the
"top_block" to get 500 samples which are then averaged to produce one data
point.

We also attach a diagram (AoA_Figure.pdf) which shows a basic idea of how
the antennas and transmitter are setup and what the Angle of Arrival (AoA)
is, when it comes to our measurements.

We tried our code in two different situations. In our first test, our
transmitter was another B210 and we were in an open field. The frequency we
tried ranged from 200 MHz to 1.0 GHz and then 3 GHz and 4 GHz. Our Phase
difference and consequently our AoA measurement were not too far off, when
the antenna array was facing the transmitter (i.e. at an expected AoA of 0
degs). As we moved closer towards an AoA of +- 90 the accuracy of the
measurement fell off. But the consistency of the 500 samples was still
pretty good (we were getting a standard deviation under 0.10 radians).

For our second test, we tried to get the AoA from FM radio towers. We got
about 800-1000m away from a popular radio station tower and pointed the
antenna array at the tower (expecting an AoA of around 0 degs). But we got
measurements which were way off. We did this for a couple of different
spots but the measurements were all over the place (the standard deviation
for individual data points were pretty good but the measurement for the 0
deg position at one spot was different for another spot around the tower).
We did manege to get angle measurements at one point when we were about 800
meters from the tower. The expected angle was 0 but we got 60 - 70 degrees
as the measured angle. We also tried at other places, one was about 800 m
from the tower and the other about 1200m. But both these places were
problematic.

It would be nice to get your inputs on the flow graphs. What are your
thoughts about the flow graph? Do you see any glaring problems with the
flow graph or with the set up? If you have any more questions about the
setup then feel free to ask.

Most of the information about the setup that we are using are in the
attached grc files. Thanks a lot for all your time.

Sincerely,

Michael Duckett

USRP-users mailing list
USRP-users@lists.ettus.com
http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com

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USRP-users@lists.ettus.com
http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com

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USRP-users@lists.ettus.com

http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com

USRP-users mailing list

USRP-users@lists.ettus.com

http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com

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USRP-users@lists.ettus.com
http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com

Hello Usrp Users,

Yesterday we did a couple of more tests on top of a parking garage. In an attempt to improve our results, we extended the distance between the antennas and tried our tests on higher ground as suggested (about 100ft above the ground which is enough to be over the tree line in most of the region). We had clear line of sight of two antennas, one tower and one on top of a building. The first antenna was a translator stations and didn't have very good strength
of signal even though we were in the presumed 60 dbm region according to the fcc database. The second antenna was a college music station and it had very good strength. But neither antenna seems to give the expected results. The first antenna gave fairly erratic results. The range for each orientation was very wide and usually never centered around the expected result. The results for the second antenna were very tight in precision but not in accuracy. We would hold the antenna array in the 0 degrees orientation and get an angle of about -4 degrees and then rotate it to the 90 degree orientation and get around -8 degrees and then go back to the 0 degree orientation and get about -16 degrees.

So after seeing these results, we tried to transmit a frequency on another B210 and find the angle based on that. The setup for this is in the attached picture. Because our transmitted signal isn't very strong, in order to get any decent results, we had to keep the transmitter very close to the receiving antennas (within one wavelength of the antenna array). But this ruins the angle of arrival approximation, so a lot of our results for this were dubious. We did try the 0 degree orientation for which we should still expect 0 degrees. We got mixed results which seemed to depend on the height of the transmitter.

All in all the results were poor. We didn't get any out of range errors (since it's built into the calculation). But the measured phase differences for the angles didn't seem to scale with the increase in distance between the receiving antennas. The majority of our results for the second antenna were in the range -20 to 20 degrees no matter what the orientation was, which means that the phase difference was also in that respective range. Is it possible that the cables which connect the receiving antennas to the B210 are also acting as antennas? If so, would insulating the cables with some material help reduce that effect?

Sincerely,
Michael Duckett

On Wed, Apr 13, 2016 at 1:19 PM, Michael Duckett mathyomama@gmail.com wrote:

Thank you everybody for the help and suggestions.
Yesterday we ran a few more tests near another radio tower. We were able to extend the distance between the two antennas to about 90 cm using some SMA cables that we had (we are getting more to give us the full distance we want) and the frequency we were measuring was 104.9 MHz (wavelength is about 285 cm). Unfortunately, we didn't have a rig set up for our B210 and antennas, so we resorted to holding the B210 and antennas ourselves (will this affect the signal received?). For the 0 degrees orientation, we were getting phase offsets which were still out of range of the arcsin domain even for the larger distance between the antennas. As we changed the orientation, we noticed very small changes in the phase offset. The majority of phase offsets were hanging around the pi/-pi boundary.

We then tried a few runs without the wires and instead tilted the antennas outward so that the tips of the antennas were about 10 in. or 25.4 cm apart. This seemed to give us mixed results. My partner would hold the device in one location at the 0 degree orientation and find phase differences out of range of the arcsin domain and then move to another location (about a step away) and find measurements which were at least in the arcsin domain (the calculated angles ranged from 40 to 90 degrees, so they were way off still). So the results for that experiment were spotty.

what antenna type are you using?

We are using an omni-directional rubber ducky antenna.
Do you do any higher order tracking before or after converting the phase offset to an angle?

No, we are not. What do you mean by higher order tracking?
I'd really love to see multiple approaches at AoA being implemented, that will definitely be an interesting use case for both SDR in general, the USRP B210, and GNU Radio; I don't remember fully, but I think the cel-kit account on github has a gr-specest repo, where you can find a few examples of parametric spectrum estimators; amongst these MUSIC, an algorithm actually originating in the world of direction detection, applied to frequency estimation. It should be pretty straightforward to adapt the algorithm to spatial problems - basically, you'd replace the estimated signal autocovariance matrix by a antenna cross-correlation matrix.

The MUSIC algorithm seems like something we should definitely try out.
First, height is your friend. Don't think that getting closer to the station tower is better. The Tower probably is an array so you will not be in the main beam anyway. Find the tallest building in the area and ask if you can do your tests on their roof. A clear and open line of sight to the tower is your goal here.

I think we are going to look for a tall place today or tomorrow and try to get measurements from there.
Third, is the signal really entering the antenna? Or is it coupling to the receiver.  This can be easily tested by removing the antennas and verifying that the signals drop by at least 10 dB.  The more it drops, the better your measurement. I would try and get at least 20 dB of isolation for a good AoA measurement.

When we took the antennas off the SMA cables, there was a significant drop in dB across the whole bandwidth (at least 20 dB). So it seems like the signal was entering the antenna.

We are going to try to run more tests soon and hopefully with a structure which will hold together our B210, cables, and antennas. Thanks again for the support.

Sincerely,
Michael Duckett

On Tue, Apr 12, 2016 at 9:59 AM, Evan Merewether via USRP-users usrp-users@lists.ettus.com wrote:

Hi Michael,

After a quick look, it seems that the methodology is sound, but you may have problems with the way you are testing. Here are a few things you can do to improve your measurements and test the performance.

First, height is your friend. Don't think that getting closer to the station tower is better. The Tower probably is an array so you will not be in the main beam anyway. Find the tallest building in the area and ask if you can do your tests on their roof. A clear and open line of sight to the tower is your goal here.

Second, what else can the signal be bouncing off of? Is there a tall water tower nearby? Could you be seeing the effects of reflected signals? For this, again, height is your friend. By moving to a tall building, you will minimize the number and strength of possible reflective surfaces.

Third, is the signal really entering the antenna? Or is it coupling to the receiver.  This can be easily tested by removing the antennas and verifying that the signals drop by at least 10 dB.  The more it drops, the better your measurement. I would try and get at least 20 dB of isolation for a good AoA measurement.

Evan

FROM: USRP-users [mailto:usrp-users-bounces@lists.ettus.com] ON BEHALF OF Marcus D. Leech via USRP-users
SENT: Friday, April 08, 2016 3:17 PM
TO: usrp-users@lists.ettus.com
SUBJECT: Re: [USRP-users] Fwd: Angle of Arrival Measurements

On 04/08/2016 04:21 PM, Marcus Müller via USRP-users wrote:

Hi Michael,

So, I'm currently having a look at your flow graphs; they look sound to me; especially the complex method (Which pretty much is equivalent to picking one frequency bin from the FFT, if you add a sharp bandpass filter, so that you only see one frequency) looks efficient. In fact, seeing both approaches in one place reminded me of OFDM radar, where one actually takes advantage of the

I use the complex-conjugate method in astronomical interferometry, which is related to AoA, at least in an incidental sense--the emergence
of fringes is due to change in phase due to change in arrival angle relative to the baseline between the antenna.

I also just use it for measuring and/or looking-for phase-drift between two sources that should be phase-coherent.

time/frequency structure of the signal, and, more elementarily, the fact that a shift in time domain is a modulation with an offset frequency in frequency domain. Maybe [1] is a bit of a fun read to you; for the angle of arrival problem (which for your approaches is really but a time offset problem), things boil down to:
If and are the same signal, but is delayed by , then their Fourier transforms and are also the same but for the latter being the first modulated by a complex sinusoid. Estimating that sinusoid's frequency gives you the timing offset; you can get the "pure" tone by just dividing . Looking at the discrete signal case, note that the frequency resolution you can get depends on the DFT you're doing - i.e. longer observation/larger DFT has a very positive effect on accuracy!

I'd really love to see multiple approaches at AoA being implemented, that will definitely be an interesting use case for both SDR in general, the USRP B210, and GNU Radio; I don't remember fully, but I think the cel-kit account on github has a gr-specest repo, where you can find a few examples of parametric spectrum estimators; amongst these MUSIC, an algorithm actually originating in the world of direction detection, applied to frequency estimation. It should be pretty straightforward to adapt the algorithm to spatial problems - basically, you'd replace the estimated signal autocovariance matrix by a antenna cross-correlation matrix.

Best regards,
Marcus

[1] Braun, Martin. Ofdm radar algorithms in mobile communication networks. Diss. Karlsruhe, Karlsruher Institut für Technologie (KIT), Diss., 2014, 2014.
http://d-nb.info/104838490X/34

On 08.04.2016 21:15, Michael Duckett via USRP-users wrote:

We are using two antennas on the same B210 and the distance between them is 7cm (the distance between the two "TX/RX" ports). We understand that this affects the measured phase difference and the further calculation for the AOA. For future tests we may try to widen the distance between the two antennas to half the wavelength (I think that would be around 1.3 to 1.7 m for FM radio station frequencies).

This distance between the two antennas brings us to the first question. Because the distance between the antennas was small compared to half the wavelength of the frequency, the range of valid phase differences was shrunk, too. Most of the time when we were measuring we got phase differences which were out of range of the valid region. In one spot close to the tower, we positioned our antenna array at the 0 degree orientation and  phase difference values which corresponded to 60-70 degrees. In another spot with the same orientation, we got phase difference values which were out of range. So when we rotated the antenna array, it was difficult to compared the AOA because most of the time that calculation wasn't possible. But we can see noticeable changes in the phase difference when rotating the array. But there doesn't seem to be an easily decipherable pattern to the error.

We haven't been monitoring the time domain signal levels. We can try that next time, as well.

On Fri, Apr 8, 2016 at 2:19 PM, Derek Kozel derek.kozel@ettus.com wrote:

Hello Michael,

In addition to Alexander's good thoughts, are you monitoring the time domain signal levels to ensure that the receive gain is set appropriately? I see a QT GUI Sink (you may consider using the QT Frequency Sink), but it would be worth while looking at a QT Time Sink as well to see if you are clipping.

Regards,

Derek

On Fri, Apr 8, 2016 at 10:28 AM, Alexander Levedahl via USRP-users usrp-users@lists.ettus.com wrote:

I do not have the ability to look at files right now so sorry if I am asking questions that are answered in the files.

If you stand in one spot and rotate, is the error consistent?  I.e., if you are pointing the array right at it, it shows the AOA as 60-70.  If you change to pointing 30 degrees, does the AOA change to 90-100?

Are the results consistent across restarting the B210?  Depending on the answer to these questions, it may simply be a calibration problem.  I.e., when you turn it on there needs to be a calibration step.

Finally, how many antennas are you using 2 or are you using multiple B210s?  Is your antenna spaced appropriately for the operating frequency?

On Fri, Apr 8, 2016 at 12:51 PM, Michael Duckett via USRP-users usrp-users@lists.ettus.com wrote:

Hello,

We are trying to measure the angle of arrival of FM using USRP B210. We have run into some problems with the measurements and hence we are writing this email. It would be nice if we can get some inputs from you on how to fix this issue. We have used two methods for computing the phase difference. We have used the first one most of the time. However, we are posting both the methods here for you to have a look.

I have attached method 1 (phase_difference_probe.grc for probing and phase_difference_view.grc which provides a nice GUI to look at) and method 2 (complex_method.grc). Method 1 is based on the following "paper":

http://www.egr.msu.edu/classes/ece480/capstone/spring14/group02/docs/Application%20Note%20-%20Phase%20George%20Godby%20Team%202.pdf

We use these flow graphs and run them in another script which probes the "top_block" to get 500 samples which are then averaged to produce one data point.

We also attach a diagram (AoA_Figure.pdf) which shows a basic idea of how the antennas and transmitter are setup and what the Angle of Arrival (AoA) is, when it comes to our measurements.

We tried our code in two different situations. In our first test, our transmitter was another B210 and we were in an open field. The frequency we tried ranged from 200 MHz to 1.0 GHz and then 3 GHz and 4 GHz. Our Phase difference and consequently our AoA measurement were not too far off, when the antenna array was facing the transmitter (i.e. at an expected AoA of 0 degs). As we moved closer towards an AoA of +- 90 the accuracy of the measurement fell off. But the consistency of the 500 samples was still pretty good (we were getting a standard deviation under 0.10 radians).

For our second test, we tried to get the AoA from FM radio towers. We got about 800-1000m away from a popular radio station tower and pointed the antenna array at the tower (expecting an AoA of around 0 degs). But we got measurements which were way off. We did this for a couple of different spots but the measurements were all over the place (the standard deviation for individual data points were pretty good but the measurement for the 0 deg position at one spot was different for another spot around the tower). We did manege to get angle measurements at one point when we were about 800 meters from the tower. The expected angle was 0 but we got 60 - 70 degrees as the measured angle. We also tried at other places, one was about 800 m from the tower and the other about 1200m. But both these places were problematic.

It would be nice to get your inputs on the flow graphs. What are your thoughts about the flow graph? Do you see any glaring problems with the flow graph or with the set up? If you have any more questions about the setup then feel free to ask.

Most of the information about the setup that we are using are in the attached grc files. Thanks a lot for all your time.

Sincerely,

Michael Duckett

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