In the classic treatises on PLL, they consider phase detectors as purely 
phase detectors, i.e. devices which output the phase of the signal 
regardless of the instant magnitude of the signal. I wonder if there 
could be possible to improve the SNR of the PLL by considering the 
magnitude also. Do you know a book or article which talks about that?

VLV

I haven't seen anything about using the magnitude, but it has long bothered me
that PLLs seem to be most often used in places where the real goal is frequency
lock, not phase lock.  In other words, we are attempting to lock two signals by
comparing their integrals.  Granted, if two signals are phase-locked then they
are also frequency-locked, but it seems like there would be some advantage to
using a "frequency-locked-loop" when frequency-lock is the actual goal.

I don't know off-hand how a "frequency-locked-loop" would be implemented.

Greg

Vladimir Vassilevsky wrote:
> 
> In the classic treatises on PLL, they consider phase detectors as purely 
> phase detectors, i.e. devices which output the phase of the signal 
> regardless of the instant magnitude of the signal. I wonder if there 
> could be possible to improve the SNR of the PLL by considering the 
> magnitude also. Do you know a book or article which talks about that?

I have seen discussion in the context of carrier phase recovery from 
PSK, where the primary concern is that the loop gain changes with 
changing carrier strength.  But that's not what you meant.

If you treated the PLL as a Kalman filter wherein you wanted to make the 
optimal update each time, then you could certainly look at the magnitude 
of the signal for an indication of how much you should trust it's phase 
-- but I think that the amount you'd decide to trust its phase would 
then depend heavily on the expected channel characteristics.  E.g. 
normally if you saw a huge signal you'd think "good! high SNR!".  But in 
a channel that has impulse noise this situation would be much more 
likely to be a result of noise, not signal, and you may want to reject 
these outliers outright.

I think this would be something that would depend so heavily on the 
expected channel characteristics that you couldn't make many global 
deductions.  I suppose you could cover a broad range of RF applications 
by assuming Gaussian noise with the occasional 'event', or just Gaussian 
noise -- but I'm not sure that even that would be valid as equipment 
aged, etc.

-- 
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

On 5/12/2010 3:31 PM, Vladimir Vassilevsky wrote:
>
> In the classic treatises on PLL, they consider phase detectors as purely
> phase detectors, i.e. devices which output the phase of the signal
> regardless of the instant magnitude of the signal. I wonder if there
> could be possible to improve the SNR of the PLL by considering the
> magnitude also. Do you know a book or article which talks about that?
>
> VLV

Unless there's information in the magnitude that tells you something 
about the phase, I don't know how it would help if you're really trying 
to lock to the phase of the input signal.

Magnitude and phase are generally orthogonal, so ignoring magnitude 
shouldn't have any effect on performance if the information that drives 
the PLL is in the phase.   If that's not true, i.e., if there is some 
information in the magnitude that can affect the loop performance, then 
whatever the nature of that information might be would drive the changes 
to the phase detector.

It's not unusual to have a PLL phase detector that must be able to 
handle changing signal magnitudes.  QAM demodulators pretty much have to 
do this.

-- 
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

On 5/12/2010 6:52 PM, Greg Berchin wrote:
> I haven't seen anything about using the magnitude, but it has long bothered me
> that PLLs seem to be most often used in places where the real goal is frequency
> lock, not phase lock.  In other words, we are attempting to lock two signals by
> comparing their integrals.  Granted, if two signals are phase-locked then they
> are also frequency-locked, but it seems like there would be some advantage to
> using a "frequency-locked-loop" when frequency-lock is the actual goal.
>
> I don't know off-hand how a "frequency-locked-loop" would be implemented.

Some so-called phase-locked loops are actually frequency locked. The 
classic XOR detector develops a duty cycle that reflects the difference 
between the reference frequency and the LO's natural frequency. The duty 
cycle, in turn, is a measure of the phase error.

Jerry
-- 
"I view the progress of science as ... the slow erosion of the tendency
  to dichotomize." --Barbara Smuts, U. Mich.
�����������������������������������������������������������������������

Greg Berchin wrote:

> I haven't seen anything about using the magnitude, but it has long bothered me
> that PLLs seem to be most often used in places where the real goal is frequency
> lock, not phase lock.  In other words, we are attempting to lock two signals by
> comparing their integrals.  Granted, if two signals are phase-locked then they
> are also frequency-locked, but it seems like there would be some advantage to
> using a "frequency-locked-loop" when frequency-lock is the actual goal.
> 
> I don't know off-hand how a "frequency-locked-loop" would be implemented.

Frequency locked loops are actually used quite often; you only have to 
lock the derivative of phase rather then phase. This decreases the order 
of the system by one. The dynamics is simpler then that of PLL. However, 
frequency is relative whereas phase is absolute; so there is 3dB loss in 
loop SNR. At low SNRs, there will be nasty threshold behavior. There are 
also mixed mode loops with phase and frequency feedbacks.

VLV

On May 12, 11:31=A0pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> In the classic treatises on PLL, they consider phase detectors as purely
> phase detectors, i.e. devices which output the phase of the signal
> regardless of the instant magnitude of the signal. I wonder if there
> could be possible to improve the SNR of the PLL by considering the
> magnitude also. Do you know a book or article which talks about that?
>
> VLV

Virtually all coherent, adaptive underwater comms employ these types
of trickery which is perhaps an indicator of the difficulty of the
situation. In particular, often times you have a fractional channel, a
DFE, and a PLL all trying to jointly lock the phase down, then in DSSS
systems you'd look at the output of the despreader and use that to
guide the operation. All permutations are allowed and people have come
up with all sorts of configurations changing PLL constants, adaptation
updated, and the lot by feeding back a measure of SNR.

Anyway, to answer your question: Yes, people have done that, mostly
though it's still the stuff of research.

-Momo

Tim Wescott wrote:

> Vladimir Vassilevsky wrote:
> 
>>
>> In the classic treatises on PLL, they consider phase detectors as 
>> purely phase detectors, i.e. devices which output the phase of the 
>> signal regardless of the instant magnitude of the signal. I wonder if 
>> there could be possible to improve the SNR of the PLL by considering 
>> the magnitude also. Do you know a book or article which talks about that?
> 
> 
> I have seen discussion in the context of carrier phase recovery from 
> PSK, where the primary concern is that the loop gain changes with 
> changing carrier strength.  But that's not what you meant.
> If you treated the PLL as a Kalman filter wherein you wanted to make the 
> optimal update each time, then you could certainly look at the magnitude 
> of the signal for an indication of how much you should trust it's phase 
> -- but I think that the amount you'd decide to trust its phase would 
> then depend heavily on the expected channel characteristics.  E.g. 
> normally if you saw a huge signal you'd think "good! high SNR!".  But in 
> a channel that has impulse noise this situation would be much more 
> likely to be a result of noise, not signal, and you may want to reject 
> these outliers outright.

I've seen articles where they tracked QAM carrier while asigning the 
different "weights" to the phase measurements depending on the distance 
from the center of the constellation.

> I think this would be something that would depend so heavily on the 
> expected channel characteristics that you couldn't make many global 
> deductions.  I suppose you could cover a broad range of RF applications 
> by assuming Gaussian noise with the occasional 'event', or just Gaussian 
> noise -- but I'm not sure that even that would be valid as equipment 
> aged, etc.

The PLL with AWGN at high SNR is easy to analyse; however there is not 
much to gain as the SNR is good already. I wonder if something could be 
gained at marginally low SNRs, such as 3dB or below.

VLV

Eric Jacobsen wrote:

> On 5/12/2010 3:31 PM, Vladimir Vassilevsky wrote:
> 
>>
>> In the classic treatises on PLL, they consider phase detectors as purely
>> phase detectors, i.e. devices which output the phase of the signal
>> regardless of the instant magnitude of the signal. I wonder if there
>> could be possible to improve the SNR of the PLL by considering the
>> magnitude also. Do you know a book or article which talks about that?
>>

> Unless there's information in the magnitude that tells you something 
> about the phase, I don't know how it would help if you're really trying 
> to lock to the phase of the input signal.
> 
> Magnitude and phase are generally orthogonal, so ignoring magnitude 
> shouldn't have any effect on performance if the information that drives 
> the PLL is in the phase.   If that's not true, i.e., if there is some 
> information in the magnitude that can affect the loop performance, then 
> whatever the nature of that information might be would drive the changes 
> to the phase detector.

OK, I've ran the numbers. At the SNR ~ 1, the gain in the loop jitter 
due to processing of the amplitude as well as phase could be ~2dB.
The problem is related to the capacity of the channel, and the result is 
what could be expected.

It is interesting to see that if the noise is Gaussian, then the huge 
values of the signal are more likely to be correct. The expected RMS 
error is decreasing with magnitude to some asymptotic value.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

>I've seen articles where they tracked QAM carrier while asigning the 
>different "weights" to the phase measurements depending on the distance 
>from the center of the constellation.

For PSK in AWGN condition into account the amplitude will not change
anything. But not for flat fading channels, you can use the amplitude
(before AGC) for the weight of the phase error.

On Wed, 12 May 2010 20:25:06 -0400, Jerry Avins <jya@ieee.org> wrote:

>Some so-called phase-locked loops are actually frequency locked. The 
>classic XOR detector develops a duty cycle that reflects the difference 
>between the reference frequency and the LO's natural frequency. The duty 
>cycle, in turn, is a measure of the phase error.

I'm having a little trouble getting my head around this.  If the XOR detector
duty cycle represents frequency difference, then wouldn't the *integral* of the
duty cycle represent the phase error?  And what would the integral of a duty
cycle look like?

Greg

On Wed, 12 May 2010 19:35:16 -0500, Vladimir Vassilevsky <nospam@nowhere.com>
wrote:

>Frequency locked loops are actually used quite often; you only have to 
>lock the derivative of phase rather then phase. This decreases the order 
>of the system by one. The dynamics is simpler then that of PLL. However, 
>frequency is relative whereas phase is absolute; so there is 3dB loss in 
>loop SNR. At low SNRs, there will be nasty threshold behavior. There are 
>also mixed mode loops with phase and frequency feedbacks.

Thanks, Vladimir.  I've never used a "FLL", and never even seen one mentioned in
the literature.  But I admit, I'm a little out of my element here.

Greg

On May 12, 6:31=A0pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> In the classic treatises on PLL, they consider phase detectors as purely
> phase detectors, i.e. devices which output the phase of the signal
> regardless of the instant magnitude of the signal. I wonder if there
> could be possible to improve the SNR of the PLL by considering the
> magnitude also. Do you know a book or article which talks about that?
>
> VLV

Just a thought: don't some phase detectors that are often used have
some degree of this built-in? One example I'm thinking of is a Costas
loop where you might use I*Q as the phase error. If you scale the
amplitude of the received signal, that scale factor (squared) is
applied directly to the phase error. Of course, you might be able to
squeeze out some more information based on intelligently considering
the amplitude (i.e. by using some memory of the recent signal level
instead of just on a sample-by-sample basis), but as you already know,
many phase detectors already have some bit of amplitude sensitivity.

Jason

On May 13, 8:30=A0am, Greg Berchin <gberc...@comicast.net.invalid>
wrote:
> On Wed, 12 May 2010 19:35:16 -0500, Vladimir Vassilevsky <nos...@nowhere.=
com>
> wrote:
>
> >Frequency locked loops are actually used quite often; you only have to
> >lock the derivative of phase rather then phase. This decreases the order
> >of the system by one. The dynamics is simpler then that of PLL. However,
> >frequency is relative whereas phase is absolute; so there is 3dB loss in
> >loop SNR. At low SNRs, there will be nasty threshold behavior. There are
> >also mixed mode loops with phase and frequency feedbacks.
>
> Thanks, Vladimir. =A0I've never used a "FLL", and never even seen one men=
tioned in
> the literature. =A0But I admit, I'm a little out of my element here.
>
> Greg

One place where FLLs might be used is in a GPS receiver. In order to
make precise Doppler shift and carrier phase measurements used for
navigation, a PLL with a small noise bandwidth is desirable. However,
such a scheme has poor acquisition characteristics in the presence of
unknown frequency offset. During signal acquisition, you can use an
FLL (or a wider-bandwidth PLL) for fast acquisition, then transition
over to a tracking mode with a low-noise PLL.

Jason

Jason wrote:

> On May 12, 6:31 pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> 
>>In the classic treatises on PLL, they consider phase detectors as purely
>>phase detectors, i.e. devices which output the phase of the signal
>>regardless of the instant magnitude of the signal. I wonder if there
>>could be possible to improve the SNR of the PLL by considering the
>>magnitude also. Do you know a book or article which talks about that?
>>
> Just a thought: don't some phase detectors that are often used have
> some degree of this built-in? One example I'm thinking of is a Costas
> loop where you might use I*Q as the phase error.  If you scale the
> amplitude of the received signal, that scale factor (squared) is
> applied directly to the phase error. Of course, you might be able to
> squeeze out some more information based on intelligently considering
> the amplitude (i.e. by using some memory of the recent signal level
> instead of just on a sample-by-sample basis), but as you already know,
> many phase detectors already have some bit of amplitude sensitivity.

It is not obvious to me that the built-in sensitivity to the amplitude 
is anywhere near optimal; it could be detrimental in some cases. Another 
interesting question is the PLL behaviour during the acquisition.
There is clear correlation between the magnitude and the phase errors; 
the consideration of the amplitude improves the loop by 1..2dB.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On 5/13/2010 8:28 AM, Greg Berchin wrote:
> On Wed, 12 May 2010 20:25:06 -0400, Jerry Avins<jya@ieee.org>  wrote:
>
>> Some so-called phase-locked loops are actually frequency locked. The
>> classic XOR detector develops a duty cycle that reflects the difference
>> between the reference frequency and the LO's natural frequency. The duty
>> cycle, in turn, is a measure of the phase error.
>
> I'm having a little trouble getting my head around this.  If the XOR detector
> duty cycle represents frequency difference, then wouldn't the *integral* of the
> duty cycle represent the phase error?  And what would the integral of a duty
> cycle look like?

It was late and I put it poorly. (Anyhow, *I* knew what I meant.)

If the LO's free-running frequency is the same as the reference, it 
doesn't need to be pulled to achieve lock. The XOR's duty cycle will be 
50%. As the reference moves*, the duty cycle (and hence the average DC) 
will shift in order to generate the necessary control voltage for the 
VCO. The frequencies are locked, but their phase offset is proportional 
to how hard the LO has to be pulled. I.e., the frequency is locked, but 
the phase is not. Locking phase requires an extra integrator.

Jerry
__________________________
* In the '50s, before AFC was universal in FM receivers, a listener 
complained to a station manager that his station drifted. He told her, 
"Nowadays, you can get a receiver that drifts with the station" and 
referred her to my shop.
-- 
"I view the progress of science as ... the slow erosion of the tendency
  to dichotomize." --Barbara Smuts, U. Mich.
�����������������������������������������������������������������������

On 5/12/2010 9:37 PM, Vladimir Vassilevsky wrote:
>
>
> Eric Jacobsen wrote:
>
>> On 5/12/2010 3:31 PM, Vladimir Vassilevsky wrote:
>>
>>>
>>> In the classic treatises on PLL, they consider phase detectors as purely
>>> phase detectors, i.e. devices which output the phase of the signal
>>> regardless of the instant magnitude of the signal. I wonder if there
>>> could be possible to improve the SNR of the PLL by considering the
>>> magnitude also. Do you know a book or article which talks about that?
>>>
>
>> Unless there's information in the magnitude that tells you something
>> about the phase, I don't know how it would help if you're really
>> trying to lock to the phase of the input signal.
>>
>> Magnitude and phase are generally orthogonal, so ignoring magnitude
>> shouldn't have any effect on performance if the information that
>> drives the PLL is in the phase. If that's not true, i.e., if there is
>> some information in the magnitude that can affect the loop
>> performance, then whatever the nature of that information might be
>> would drive the changes to the phase detector.
>
> OK, I've ran the numbers. At the SNR ~ 1, the gain in the loop jitter
> due to processing of the amplitude as well as phase could be ~2dB.
> The problem is related to the capacity of the channel, and the result is
> what could be expected.
>
> It is interesting to see that if the noise is Gaussian, then the huge
> values of the signal are more likely to be correct. The expected RMS
> error is decreasing with magnitude to some asymptotic value.
>
>
> Vladimir Vassilevsky
> DSP and Mixed Signal Design Consultant
> http://www.abvolt.com

I think I see what's happening.  It is often easy to exclude undesirable 
detector samples by setting the output to zero.  There are generally not 
ill effects from excluding occassional input samples unless one starts 
to approach a limit in jitter tolerance.  So it may be effective to just 
ignore inputs that are below some magnitude theshold.  Often this is 
nearly as good as some optimized algorithm.

-- 
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

On May 13, 10:31=A0am, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> In the classic treatises on PLL, they consider phase detectors as purely
> phase detectors, i.e. devices which output the phase of the signal
> regardless of the instant magnitude of the signal. I wonder if there
> could be possible to improve the SNR of the PLL by considering the
> magnitude also. Do you know a book or article which talks about that?
>
> VLV

It will help but only if you have "special" problems with for example
FM ie co-cahannel or Multipath interference.

However, you don't interfere with the amplitude going into a PLL since
this will de-stabilise it and change the tracking properties. You use
a separate loop called an Amplitude-Locked Loop instead of a hard
limiter first. In this way when the amplitude of the FM goes to zero
at any time the ALL responds quickly and servo's out (as much as it
can) such changes without amplifying the noise (which a limiter does -
a limiter does no filtering of course).

Look here.
http://www.ampsysltd.co.uk/

Hardy

On May 13, 6:51=A0pm, Eric Jacobsen <eric.jacob...@ieee.org> wrote:
> On 5/12/2010 9:37 PM, Vladimir Vassilevsky wrote:
>
>
>
>
>
> > Eric Jacobsen wrote:
>
> >> On 5/12/2010 3:31 PM, Vladimir Vassilevsky wrote:
>
> >>> In the classic treatises on PLL, they consider phase detectors as pur=
ely
> >>> phase detectors, i.e. devices which output the phase of the signal
> >>> regardless of the instant magnitude of the signal. I wonder if there
> >>> could be possible to improve the SNR of the PLL by considering the
> >>> magnitude also. Do you know a book or article which talks about that?
>
> >> Unless there's information in the magnitude that tells you something
> >> about the phase, I don't know how it would help if you're really
> >> trying to lock to the phase of the input signal.
>
> >> Magnitude and phase are generally orthogonal, so ignoring magnitude
> >> shouldn't have any effect on performance if the information that
> >> drives the PLL is in the phase. If that's not true, i.e., if there is
> >> some information in the magnitude that can affect the loop
> >> performance, then whatever the nature of that information might be
> >> would drive the changes to the phase detector.
>
> > OK, I've ran the numbers. At the SNR ~ 1, the gain in the loop jitter
> > due to processing of the amplitude as well as phase could be ~2dB.
> > The problem is related to the capacity of the channel, and the result i=
s
> > what could be expected.
>
> > It is interesting to see that if the noise is Gaussian, then the huge
> > values of the signal are more likely to be correct. The expected RMS
> > error is decreasing with magnitude to some asymptotic value.
>
> > Vladimir Vassilevsky
> > DSP and Mixed Signal Design Consultant
> >http://www.abvolt.com
>
> I think I see what's happening. =A0It is often easy to exclude undesirabl=
e
> detector samples by setting the output to zero. =A0There are generally no=
t
> ill effects from excluding occassional input samples unless one starts
> to approach a limit in jitter tolerance. =A0So it may be effective to jus=
t
> ignore inputs that are below some magnitude theshold. =A0Often this is
> nearly as good as some optimized algorithm.
>
> --
> Eric Jacobsen
> Minister of Algorithms
> Abineau Communicationshttp://www.abineau.com

Yes, this is also often done especially in the convergence-contention
algorithms I described earlier. You *bootstrap* your algorithm by some
uncool method that you just know to work. This also underscores a
broader ideological difference in how you go about doing things;
thorough analysis vs. empirical verification. Folks in comp.dsp always
make me feel bad about how shallow I seem to be in comparison. It's
just that the people I work with live an die by empirical data and
don't want you to dig deep in designing anything. The proof is in the
pudding they say! Thoroughness is traded for being more varied.

-Momo

On May 14, 12:28=A0am, Greg Berchin <gberc...@comicast.net.invalid>
wrote:
> On Wed, 12 May 2010 20:25:06 -0400, Jerry Avins <j...@ieee.org> wrote:
> >Some so-called phase-locked loops are actually frequency locked. The
> >classic XOR detector develops a duty cycle that reflects the difference
> >between the reference frequency and the LO's natural frequency. The duty
> >cycle, in turn, is a measure of the phase error.
>
> I'm having a little trouble getting my head around this. =A0If the XOR de=
tector
> duty cycle represents frequency difference, then wouldn't the *integral* =
of the
> duty cycle represent the phase error? =A0And what would the integral of a=
 duty
> cycle look like?
>
> Greg

A phase-locked loop as a phase-locked loop! You get out rate of change
of phase of course.
If you change the inner dynamics you still get the same output but it
will track better or worse.
Can't see what the argument is about.


Hardy

On May 12, 6:31=A0pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> In the classic treatises on PLL, they consider phase detectors as purely
> phase detectors, i.e. devices which output the phase of the signal
> regardless of the instant magnitude of the signal. I wonder if there
> could be possible to improve the SNR of the PLL by considering the
> magnitude also. Do you know a book or article which talks about that?
>
> VLV

I have seen a related discussion in the context of using PLLs for
threshold extension FM demodulation.  What I recall is if the phase
detector is preceeded by a hard limiter, then the PLL FM detector
worked no better then a convention limiter discriminator, i.e. there
is no threshold extension.  On the other hand, if the phase detector
is fed the signal without limiting, then the PLL can provide threshold
extension.  The qualitative exlplination was that at low SNR the
limiter allows the noise to supress the desired signal.  At higher SNR
of course, it makes little difference.  I'm sorry I can't give you a
more qalitative answer but I suggest you investigate threshold
extension.

Mark

You can simply use an analog mixer as phase detector to extract both phase
and magnitude information. The mixer approach appears on textbook only and
is rarely used because it is undesirable to have the loop response
depending on magnitude of the PD output. Modern PLL always use digital PFD
to extract the phase difference and PFD is simply two D flip-flop in
principle. 

By the way, TYPE I PLL is frequency locked only which is considered
obsolete and rarely used nowadays. TYPE II PLL with charge pump can achieve
phase lock.


cfy30

>>I've seen articles where they tracked QAM carrier while asigning the 
>>different "weights" to the phase measurements depending on the distance 
>>from the center of the constellation.
>
>For PSK in AWGN condition into account the amplitude will not change
>anything. But not for flat fading channels, you can use the amplitude
>(before AGC) for the weight of the phase error.
>