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

[Graham / KE9H]

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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