[time-nuts] Re: uncertainty/SNR of IQ measurements

[Dana Whitlow]

Just to be clear, the shift has to be in phase, not time per se.  A 90 deg
phase
shifter based on a constant delay will not work well at other frequencies.
That's
why phasing-type SSB exciters got so messy in the audio phase
splitter department
(in the old days).
Nowadays with digital processing, the mathematical transformation required
can
be done accurately over rather wide bandwidths.

Dana


On Thu, Aug 26, 2021 at 7:05 PM Graham / KE9H <ke9h.graham at gmail.com> wrote:

> I think Dana's explanation is a much clearer way to think of what is going
> on in an I-Q receiver.
>
> Until you are really far down the signal chain, at the demodulator, where
> you might process the I and Q signals differently,
> there is no 'splitting' or division of the signal into I and Q.
> The signal in the I and Q channels is the same, just shifted in time /
> phase in one of the channels, relative to the other.
>
> --- Graham
>
> ==
>
> On Thu, Aug 26, 2021 at 4:43 PM Dana Whitlow <k8yumdoober at gmail.com>
> wrote:
>
> > Hi Jim,
> >
> > I think the best way is to view the signal as a phasor, with any
> > noise present adding a
> > random trajectory (a fuzzball) to the tip of the signal vector.
> > Conceptually speaking,
> > this eliminates needing to worry about the distribution of power between
> I
> > & Q, etc.
> > It lets you view the whole thing without regard for choice of axes,
> > coordinate system,
> > and all that.
> >
> > If the S/N is good, the fuzzball is small in size compared to the length
> of
> > the phasor,
> > and you can immediately see that neither the length nor the angle of the
> > sum vector
> > is much affected.
> >
> > But as the SNR is reduced, you eventually reach the point where some of
> the
> > noise
> > peaks almost reach down to the origin, and as the vector tip swings near
> > the origin
> > the phase angle changes very rapidly by nearly 180 deg, but the effect
> is a
> > temporary
> > glitch of zero area.
> >
> > But if the noise peak is a little bit bigger, the vector tip swings all
> the
> > way around the
> > origin, yielding an eventual effect of an added 360 deg (a whole extra
> > cycle) in phase
> > shift.  This tends to have a far more deleterious effect on a signal.  I
> > had a text given
> > to me by a friend in which the author used this kind of explanation to
> > explain, for
> > example, the "threshold effect" of noise in FM demodulation.  I just
> > looked, but could
> > not find the book, else I'd have given you the title and author
> > information.
> >
> > This mode of thought also leads towards an understanding of the "FM
> capture
> > effect",
> > which spec was always highlighted in datasheets of HiFi FM tuners.  But
> one
> > hears
> > little of it nowadays, I suspect because the advent of fast ICs has made
> it
> > so easy
> > to very- closely approach the "theoretical limit" that everybody is about
> > the same.
> > BTW, said "theoretical limit" is not fixed until one specifies other
> > parameters, and
> > at one time there was a standard test definition so that such a limit
> could
> > be defined
> > and measured against.
> >
> > In IQ demodulation I find the ATAN2 function a good deal more useful than
> > the old
> > arctan function, which needs a lot of help in order to work usefully.
> The
> > ATAN2
> > function takes two arguments (I & Q values) and automatically places the
> > angular
> > result in the correct quadrant and is not bothered by either of the
> > arguments being
> > zero.  The only place it gets in trouble is if *both* arguments are zero,
> > which is an
> > infinitely-tough nut to crack in any case.
> >
> > As with all the inverse trig functions, ATAN2 has a limited angular
> range,
> > from
> > -180 deg through zero to +180 deg, then snaps back to -180 deg again.
> > But it's not too difficult to "unwrap" the results so that a continuous
> > rotation of a
> > phasor leads to a nice smooth phase ramp with no discontinuities at all.
> > In many
> > cases this presentation makes the picture much clearer, although overly
> > high
> > noise peaks can create what some will call a false transition.  If you're
> > really
> > interested in the signal alone, yes you have a problem then.  But if you
> > consider
> > the "signal" to be the composite vector sum of some signal and added
> noise,
> > the unwrap process works correctly.
> >
> > Whew!
> >
> > Dana   K8YUM
> >
> >
> >
> > On Thu, Aug 26, 2021 at 3:52 PM Poul-Henning Kamp <phk at phk.freebsd.dk>
> > wrote:
> >
> > > --------
> > > Lux, Jim writes:
> > >
> > > >I'm looking for a simplified treatment of the uncertainty of I/Q
> > > >measurements.  Say you've got some input signal with a given SNR and
> you
> > > >run it into a I/Q demodulator - you get a series of I and Q
> measurements
> > > >(which might, later, be turned into mag and phase).
> > > >
> > > >[...]
> > > >
> > > >I'm looking for a sort of not super quantitative and analytical
> > > >treatment that I can point folks to.
> > >
> > > Good luck with that :-)
> > >
> > > Some of the noise processes will be along the "vector" and distributed
> > > between I & Q components depending on the phase, while other noise
> > > processes affect the components individually.
> > >
> > > To make matters worse, both kinds of noise processes may depend on the
> > > phase, usually because of cross-talk and/or insufficient isolation.
> > >
> > > Low-resolution ADC's are a particular nasty problem, because they add
> > > +/-1 count jitter independent of the phase, and that causes very
> > > large arctangent errors.
> > >
> > > Counterintuitive as it may sound, it is easier to process the bits from
> > > ADC's where the low two bits are pure noise, than ADC's where all bits
> > > are good...
> > >
> > > --
> > > Poul-Henning Kamp       | UNIX since Zilog Zeus 3.20
> > > phk at FreeBSD.ORG         | TCP/IP since RFC 956
> > > FreeBSD committer       | BSD since 4.3-tahoe
> > > Never attribute to malice what can adequately be explained by
> > incompetence.
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