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View all threadsChanges in carrier phase due to Doppler
Hello USRP Users!
Can anyone give me some pointers?
Here is the problem.
Two radios: one radio (Tx1) is fixed, the other (Tx2) is mobile, say, it is moving towards Tx1.
Here is the signal transaction:
(1) Tx1 -> Tx2.
Tx2 receives packet from Tx1 and calculates phase, phase slope.
(2)Tx2 -> Tx1
Same, but on the other direction.
It seems if Tx2 is not moving, one can unwrap the phase of Tx2, received at Tx1, and calculate the distance between Tx1 and Tx2 relatively accurately.
But let's assume Tx2 is moving towards Tx1.
How do I go about finding the maximum velocity of Tx2 after which phase unwrapping at Tx1 does not result in credible result (result being the distance between the radios.)
I quote a paragraph from a patent mentioned below:
//---
The maximum relative velocity at which sequential Carrier Phase Range (CPR) measurements can be directly unwrapped can be described as the Nyquist velocity of the system. The Nyquist velocity can be described as one-half of the CPR measurement ambiguity (for example, one-half of a half-wavelength, or equivalently one-quarter wavelength when the measurement ambiguity is λ/2) per measurement sample interval. For example, in an embodiment having a radio operating at 5.8 GHz RF carrier frequency with a measurement rate of 366 Hz, the Nyquist velocity would be approximately 1.3 cm per 2.7 milliseconds, or about 480 cm/s. The Nyquist velocity is reduced if sequential measurements are “missed” or if the measurement rate is reduced. If the relative velocity of the two radios is greater than the Nyquist velocity, directly unwrapped CPR measurements will not yield an accurate CPR rate.
//---
My question is:
Measurement ambiguity being ... λ/2 -- Is it universally true?
Nyquist velocity being .... one-half of the CPR measurement ambiguity -- Is it universally true?
Or only in this particular set up?
Say, I use 920MHz radio, with a measurement rate of 100ms, would they be still true?
If someone has some knowledge about phase unwrapping, please give me some hints or some keywords that I can google with.
Thanks for reading!
US Patent # 20150346332
Hi Nik,
good questions!
some hints or some keywords that I can google with.
Well, I didn't google. I clicked on the patent you've linked to and got
out pen, paper and LaTeX:
So, it took me a few moments until I realized the method you're working
on is not just bistatic radar (which would be a funny thing to apply for
a patent on in 2015);
the important part here is that the TX1->TX2 frequency is /different/
from the TX2->TX1 frequency.
Idea seems to be that TX1 first sends a signal of known phase:
$s_1(t) = \cos\left(2\pi f_1 t + \phi_1\right)$,
and TX2 then estimates the phase (up to a $2n\pi,, n \in \mathbb N_0$
ambiguity) from the receive signal $r_1$:
$r_1(t) = s_1(t-\tau) = \cos\left(2\pi f_1 (t-\tau)+ \phi_1\right)$
as the arcustanges of the receive signal at a known time, after the
signal has propagated for a time $\tau$.
$\hat \varphi_1 = \phi_1 + 2\pi (f_1 \tau - n)$,
with $n$, the number of full wavelengths between TX1 and TX2 staying
unknown.
Very much the same applies for the reverse transmission, and we end up with:
$\hat \varphi_2 = \phi_2 + 2\pi (f_2 \tau - n)$.
Rearranging $\hat \varphi_2$ so that we get a description of $\tau$ yields
$\tau = \frac{\frac{\hat\varphi_2 - \phi_2}{2\pi}+n}{f_2}$,
which we'll insert into $\hat\varphi_1$:
$\hat\varphi_1 = \phi_1+ 2\pi
\left(\frac{f_1}{f_2}\left(\frac{\hat\varphi_2 - \phi_2}{2\pi}+n\right)
-n\right)$.
Isolating $n$ yields:
$n=\frac1{2\pi\left(\frac{f_1}{f_2}-1\right)},\left(\hat\varphi_1 -
\phi_1 - \frac{f_1}{f_2}\left(\hat\varphi_2 - \phi_2\right)\right)$;
of course, assuming I didn't make any mistakes rearranging this in my
head. It is just based on estimates!
Now, remember that our presumption (so that the system works at all) is
that we can accurately determine $f_1$ and $f_2$ (or, at least, their
ratio), which means that we can correct the Doppler in our $\hat\varphi$
estimates.
So, simply derive boundaries for when your $n$ will decrease or increase
by a whole 0.5, and you'll have your unambiguous range for
$\frac{f_1}{f_2}$; note that I was too lazy to do that and haven't tried
whether that leads to problems at certain points, or works continouosly
over all possible $\tau$.
So much for theory. Now for some practical aspects:
- The whole procedure presumes you know the phases of TX1 and TX2,
$\phi_1$ and $\phi_2$. In general, that's not the case, and unless
you're using one of the daughterboards which have the ability to
reset phase after tuning (SBX, UBX) and use timed commands, and have
a very good common timesource, this won't be the case. - Same goes for exact $f_1$ and $f_2$ – not only does a frequency
error contribute linearly to an error in $\tau$ estimates, but it
also drifts away $\phi$ by $\Delta f$; let's say you use a clock
source (not a common external clock) with a relative accuracy of 40
ppb and a carrier frequency (two well-working GPSDOs would be in
that region, I guess), at 920 MHz, you'd see 36.8 full oscillations
"drift" per second; in other words: at a measurement rate of 10 per
second (which you imply), you'd see up to 3.6 oscillations swing by
(or not) between measurements – so your $\phi$ "knowledge" would be
totally worthless. - If you're not using common time and frequency sources, hence, you'll
need to implement mutual continuous carrier tracking; of course, if
only considering the information that one side has, that would
eliminate the possibility to derive Doppler (as that would just get
"corrected" away), unless you know a lot about your movements ("this
thing is either still or accelerates very rapidly, or travels at a
constant speed of x") and can adapt to these special cases. By the
way, if you do that, you're information-wise inferior to TX1 doing
monostatic radar (but would get the much increased SNR of an active
transmitter at the target TX2 – but you could as well just implement
that with an amplifier and a circulator, or antenna -> (freq)
duplexer -> amplifier -> nonlinear element (self-intermodulation) ->
BPF that selects e.g $2f_1$ -> duplexer -> antenna. But with a lot
less SDR involved.
Best regards,
Marcus
On 15.08.2016 05:36, Nik B. via USRP-users wrote:
Hello USRP Users!
Can anyone give me some pointers?
Here is the problem.
Two radios: one radio (Tx1) is fixed, the other (Tx2) is mobile, say,
it is moving towards Tx1.
Here is the signal transaction:
(1) Tx1 -> Tx2.
Tx2 receives packet from Tx1 and calculates phase, phase slope.
(2)Tx2 -> Tx1
Same, but on the other direction.
It seems if Tx2 is not moving, one can unwrap the phase of Tx2,
received at Tx1, and calculate the distance between Tx1 and Tx2
relatively accurately.
But let's assume Tx2 is moving towards Tx1.
How do I go about finding the maximum velocity of Tx2 after which
phase unwrapping at Tx1 does not result in credible result (result
being the distance between the radios.)
I quote a paragraph from a patent mentioned below:
//---
The maximum relative velocity at which sequential Carrier Phase Range
(CPR) measurements can be directly unwrapped can be described as the
Nyquist velocity of the system. The Nyquist velocity can be described
as one-half of the CPR measurement ambiguity (for example, one-half of
a half-wavelength, or equivalently one-quarter wavelength when the
measurement ambiguity is λ/2) per measurement sample interval. For
example, in an embodiment having a radio operating at 5.8 GHz RF
carrier frequency with a measurement rate of 366 Hz, the Nyquist
velocity would be approximately 1.3 cm per 2.7 milliseconds, or about
480 cm/s. The Nyquist velocity is reduced if sequential measurements
are “missed” or if the measurement rate is reduced. If the relative
velocity of the two radios is greater than the Nyquist velocity,
directly unwrapped CPR measurements will not yield an accurate CPR rate.
//---
My question is:
Measurement ambiguity being ... λ/2 -- Is it universally true?
Nyquist velocity being .... one-half of the CPR measurement ambiguity
-- Is it universally true?
Or only in this particular set up?
Say, I use 920MHz radio, with a measurement rate of 100ms, would they
be still true?
If someone has some knowledge about phase unwrapping, please give me
some hints or some keywords that I can google with.
Thanks for reading!
US Patent # 20150346332
http://www.freepatentsonline.com/y2015/0346332.html
USRP-users mailing list
USRP-users@lists.ettus.com
http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com
Sorry, forgot to put things through TeX to get the images for /all/ the
formulas, so here once more:
-------- Forwarded Message --------
Subject: Re: [USRP-users] Changes in carrier phase due to Doppler
Date: Mon, 15 Aug 2016 12:00:20 +0200
From: Marcus Müller marcus.mueller@ettus.com
To: usrp-users@lists.ettus.com
Hi Nik,
good questions!
some hints or some keywords that I can google with.
Well, I didn't google. I clicked on the patent you've linked to and got
out pen, paper and LaTeX:
So, it took me a few moments until I realized the method you're working
on is not just bistatic radar (which would be a funny thing to apply for
a patent on in 2015);
the important part here is that the TX1->TX2 frequency is /different/
from the TX2->TX1 frequency.
Idea seems to be that TX1 first sends a signal of known phase:
$s_1(t) = \cos\left(2\pi f_1 t + \phi_1\right)$,
and TX2 then estimates the phase (up to a $2n\pi,, n \in \mathbb N_0$
ambiguity) from the receive signal $r_1$:
$r_1(t) = s_1(t-\tau) = \cos\left(2\pi f_1 (t-\tau)+ \phi_1\right)$
as the arcustanges of the receive signal at a known time, after the
signal has propagated for a time $\tau$.
$\hat \varphi_1 = \phi_1 + 2\pi (f_1 \tau - n)$,
with $n$, the number of full wavelengths between TX1 and TX2 staying
unknown.
Very much the same applies for the reverse transmission, and we end up with:
$\hat \varphi_2 = \phi_2 + 2\pi (f_2 \tau - n)$.
Rearranging $\hat \varphi_2$ so that we get a description of $\tau$ yields
$\tau = \frac{\frac{\hat\varphi_2 - \phi_2}{2\pi}+n}{f_2}$,
which we'll insert into $\hat\varphi_1$:
$\hat\varphi_1 = \phi_1+ 2\pi
\left(\frac{f_1}{f_2}\left(\frac{\hat\varphi_2 - \phi_2}{2\pi}+n\right)
-n\right)$.
Isolating $n$ yields:
$n=\frac1{2\pi\left(\frac{f_1}{f_2}-1\right)},\left(\hat\varphi_1 -
\phi_1 - \frac{f_1}{f_2}\left(\hat\varphi_2 - \phi_2\right)\right)$;
of course, assuming I didn't make any mistakes rearranging this in my
head. It is just based on estimates!
Now, remember that our presumption (so that the system works at all) is
that we can accurately determine $f_1$ and $f_2$ (or, at least, their
ratio), which means that we can correct the Doppler in our $\hat\varphi$
estimates.
So, simply derive boundaries for when your $n$ will decrease or increase
by a whole 0.5, and you'll have your unambiguous range for
$\frac{f_1}{f_2}$; note that I was too lazy to do that and haven't tried
whether that leads to problems at certain points, or works continouosly
over all possible $\tau$.
So much for theory. Now for some practical aspects:
- The whole procedure presumes you know the phases of TX1 and TX2,
$\phi_1$ and $\phi_2$. In general, that's not the case, and unless
you're using one of the daughterboards which have the ability to
reset phase after tuning (SBX, UBX) and use timed commands, and have
a very good common timesource, this won't be the case. - Same goes for exact $f_1$ and $f_2$ – not only does a frequency
error contribute linearly to an error in $\tau$ estimates, but it
also drifts away $\phi$ by $\Delta f$; let's say you use a clock
source (not a common external clock) with a relative accuracy of 40
ppb and a carrier frequency (two well-working GPSDOs would be in
that region, I guess), at 920 MHz, you'd see 36.8 full oscillations
"drift" per second; in other words: at a measurement rate of 10 per
second (which you imply), you'd see up to 3.6 oscillations swing by
(or not) between measurements – so your $\phi$ "knowledge" would be
totally worthless. - If you're not using common time and frequency sources, hence, you'll
need to implement mutual continuous carrier tracking; of course, if
only considering the information that one side has, that would
eliminate the possibility to derive Doppler (as that would just get
"corrected" away), unless you know a lot about your movements ("this
thing is either still or accelerates very rapidly, or travels at a
constant speed of x") and can adapt to these special cases. By the
way, if you do that, you're information-wise inferior to TX1 doing
monostatic radar (but would get the much increased SNR of an active
transmitter at the target TX2 – but you could as well just implement
that with an amplifier and a circulator, or antenna -> (freq)
duplexer -> amplifier -> nonlinear element (self-intermodulation) ->
BPF that selects e.g $2f_1$ -> duplexer -> antenna. But with a lot
less SDR involved.
Best regards,
Marcus
On 15.08.2016 05:36, Nik B. via USRP-users wrote:
Hello USRP Users!
Can anyone give me some pointers?
Here is the problem.
Two radios: one radio (Tx1) is fixed, the other (Tx2) is mobile, say,
it is moving towards Tx1.
Here is the signal transaction:
(1) Tx1 -> Tx2.
Tx2 receives packet from Tx1 and calculates phase, phase slope.
(2)Tx2 -> Tx1
Same, but on the other direction.
It seems if Tx2 is not moving, one can unwrap the phase of Tx2,
received at Tx1, and calculate the distance between Tx1 and Tx2
relatively accurately.
But let's assume Tx2 is moving towards Tx1.
How do I go about finding the maximum velocity of Tx2 after which
phase unwrapping at Tx1 does not result in credible result (result
being the distance between the radios.)
I quote a paragraph from a patent mentioned below:
//---
The maximum relative velocity at which sequential Carrier Phase Range
(CPR) measurements can be directly unwrapped can be described as the
Nyquist velocity of the system. The Nyquist velocity can be described
as one-half of the CPR measurement ambiguity (for example, one-half of
a half-wavelength, or equivalently one-quarter wavelength when the
measurement ambiguity is λ/2) per measurement sample interval. For
example, in an embodiment having a radio operating at 5.8 GHz RF
carrier frequency with a measurement rate of 366 Hz, the Nyquist
velocity would be approximately 1.3 cm per 2.7 milliseconds, or about
480 cm/s. The Nyquist velocity is reduced if sequential measurements
are “missed” or if the measurement rate is reduced. If the relative
velocity of the two radios is greater than the Nyquist velocity,
directly unwrapped CPR measurements will not yield an accurate CPR rate.
//---
My question is:
Measurement ambiguity being ... λ/2 -- Is it universally true?
Nyquist velocity being .... one-half of the CPR measurement ambiguity
-- Is it universally true?
Or only in this particular set up?
Say, I use 920MHz radio, with a measurement rate of 100ms, would they
be still true?
If someone has some knowledge about phase unwrapping, please give me
some hints or some keywords that I can google with.
Thanks for reading!
US Patent # 20150346332
http://www.freepatentsonline.com/y2015/0346332.html
USRP-users mailing list
USRP-users@lists.ettus.com
http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com
Hi Marcus,
Thank you for taking time to answer.
I guess I got a lot more (good thing in this case) than I asked for!
Time to start reading [😊]
N
差出人: USRP-users usrp-users-bounces@lists.ettus.com が Marcus Müller via USRP-users usrp-users@lists.ettus.com の代理で送信
送信日時: 2016年8月15日 20:41
宛先: usrp-users@lists.ettus.com
件名: [USRP-users] Fwd: Re: Changes in carrier phase due to Doppler
Sorry, forgot to put things through TeX to get the images for all the formulas, so here once more:
-------- Forwarded Message --------
Subject: Re: [USRP-users] Changes in carrier phase due to Doppler
Date: Mon, 15 Aug 2016 12:00:20 +0200
From: Marcus Müller marcus.mueller@ettus.commailto:marcus.mueller@ettus.com
To: usrp-users@lists.ettus.commailto:usrp-users@lists.ettus.com
Hi Nik,
good questions!
some hints or some keywords that I can google with.
Well, I didn't google. I clicked on the patent you've linked to and got out pen, paper and LaTeX:
So, it took me a few moments until I realized the method you're working on is not just bistatic radar (which would be a funny thing to apply for a patent on in 2015);
the important part here is that the TX1->TX2 frequency is different from the TX2->TX1 frequency.
Idea seems to be that TX1 first sends a signal of known phase:
[$s_1(t) = \cos\left(2\pi f_1 t + \phi_1\right)$],
and TX2 then estimates the phase (up to a [$2n\pi,, n \in \mathbb N_0$] ambiguity) from the receive signal [$r_1$] :
[$r_1(t) = s_1(t-\tau) = \cos\left(2\pi f_1 (t-\tau)+ \phi_1\right)$]
as the arcustanges of the receive signal at a known time, after the signal has propagated for a time [$\tau$] .
[$\hat \varphi_1 = \phi_1 + 2\pi (f_1 \tau - n)$],
with [$n$] , the number of full wavelengths between TX1 and TX2 staying unknown.
Very much the same applies for the reverse transmission, and we end up with:
[$\hat \varphi_2 = \phi_2 + 2\pi (f_2 \tau - n)$].
Rearranging [$\hat \varphi_2$] so that we get a description of [$\tau$] yields
[$\tau = \frac{\frac{\hat\varphi_2 - \phi_2}{2\pi}+n}{f_2}$],
which we'll insert into [$\hat\varphi_1$] :
[$\hat\varphi_1 = \phi_1+ 2\pi \left(\frac{f_1}{f_2}\left(\frac{\hat\varphi_2 - \phi_2}{2\pi}+n\right) -n\right)$].
Isolating [$n$] yields:
[$n=\frac1{2\pi\left(\frac{f_1}{f_2}-1\right)},\left(\hat\varphi_1 - \phi_1 - \frac{f_1}{f_2}\left(\hat\varphi_2 - \phi_2\right)\right)$];
of course, assuming I didn't make any mistakes rearranging this in my head. It is just based on estimates!
Now, remember that our presumption (so that the system works at all) is that we can accurately determine [$f_1$] and [$f_2$] (or, at least, their ratio), which means that we can correct the Doppler in our [$\hat\varphi$] estimates.
So, simply derive boundaries for when your [$n$] will decrease or increase by a whole 0.5, and you'll have your unambiguous range for [$\frac{f_1}{f_2}$] ; note that I was too lazy to do that and haven't tried whether that leads to problems at certain points, or works continouosly over all possible [$\tau$] .
So much for theory. Now for some practical aspects:
- The whole procedure presumes you know the phases of TX1 and TX2, [$\phi_1$] and [$\phi_2$] . In general, that's not the case, and unless you're using one of the daughterboards which have the ability to reset phase after tuning (SBX, UBX) and use timed commands, and have a very good common timesource, this won't be the case.
- Same goes for exact [$f_1$] and [$f_2$] – not only does a frequency error contribute linearly to an error in [$\tau$] estimates, but it also drifts away [$\phi$] by [$\Delta f$] ; let's say you use a clock source (not a common external clock) with a relative accuracy of 40 ppb and a carrier frequency (two well-working GPSDOs would be in that region, I guess), at 920 MHz, you'd see 36.8 full oscillations "drift" per second; in other words: at a measurement rate of 10 per second (which you imply), you'd see up to 3.6 oscillations swing by (or not) between measurements – so your [$\phi$] "knowledge" would be totally worthless.
- If you're not using common time and frequency sources, hence, you'll need to implement mutual continuous carrier tracking; of course, if only considering the information that one side has, that would eliminate the possibility to derive Doppler (as that would just get "corrected" away), unless you know a lot about your movements ("this thing is either still or accelerates very rapidly, or travels at a constant speed of x") and can adapt to these special cases. By the way, if you do that, you're information-wise inferior to TX1 doing monostatic radar (but would get the much increased SNR of an active transmitter at the target TX2 – but you could as well just implement that with an amplifier and a circulator, or antenna -> (freq) duplexer -> amplifier -> nonlinear element (self-intermodulation) -> BPF that selects e.g [$2f_1$] -> duplexer -> antenna. But with a lot less SDR involved.
Best regards,
Marcus
On 15.08.2016 05:36, Nik B. via USRP-users wrote:
Hello USRP Users!
Can anyone give me some pointers?
Here is the problem.
Two radios: one radio (Tx1) is fixed, the other (Tx2) is mobile, say, it is moving towards Tx1.
Here is the signal transaction:
(1) Tx1 -> Tx2.
Tx2 receives packet from Tx1 and calculates phase, phase slope.
(2)Tx2 -> Tx1
Same, but on the other direction.
It seems if Tx2 is not moving, one can unwrap the phase of Tx2, received at Tx1, and calculate the distance between Tx1 and Tx2 relatively accurately.
But let's assume Tx2 is moving towards Tx1.
How do I go about finding the maximum velocity of Tx2 after which phase unwrapping at Tx1 does not result in credible result (result being the distance between the radios.)
I quote a paragraph from a patent mentioned below:
//---
The maximum relative velocity at which sequential Carrier Phase Range (CPR) measurements can be directly unwrapped can be described as the Nyquist velocity of the system. The Nyquist velocity can be described as one-half of the CPR measurement ambiguity (for example, one-half of a half-wavelength, or equivalently one-quarter wavelength when the measurement ambiguity is λ/2) per measurement sample interval. For example, in an embodiment having a radio operating at 5.8 GHz RF carrier frequency with a measurement rate of 366 Hz, the Nyquist velocity would be approximately 1.3 cm per 2.7 milliseconds, or about 480 cm/s. The Nyquist velocity is reduced if sequential measurements are “missed” or if the measurement rate is reduced. If the relative velocity of the two radios is greater than the Nyquist velocity, directly unwrapped CPR measurements will not yield an accurate CPR rate.
//---
My question is:
Measurement ambiguity being ... λ/2 -- Is it universally true?
Nyquist velocity being .... one-half of the CPR measurement ambiguity -- Is it universally true?
Or only in this particular set up?
Say, I use 920MHz radio, with a measurement rate of 100ms, would they be still true?
If someone has some knowledge about phase unwrapping, please give me some hints or some keywords that I can google with.
Thanks for reading!
US Patent # 20150346332
http://www.freepatentsonline.com/y2015/0346332.html
USRP-users mailing list
USRP-users@lists.ettus.commailto:USRP-users@lists.ettus.com
http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com
