V.34 Fax Training in a High Noise Environment
Suppose for the moment that you've been given the task of constructing
a V.34 fax demodulator from various pre-built demodulation routines you
happen to have laying around. Further suppose that instead of a clean
signal, you're expected to deal with a rather nasty/noisy signal, and
that you don't get to pick the 'easy' settings (such as four point
train) that might make it simpler to produce. Where do you start?
(If it were me, I would simply buy one from the guys over at
VoCAL. Fax demodulation is hard,
and it'll take a long time to do better than they do.)
This is more difficult than it sounds, because the half duplex mode
used by V.34 fax has very fast setup times. V.34 is also a very
complex, very advanced modulation scheme. Fortunately, the part
discussed below is one of the simpler aspects.
There are usually four adaptive components you will need to deal with:
- AGC - this is typically standalone, obvious to understand, and
easy to jam.
- Baud Timing Recovery - this is also standalone, and usually
consists of a set of narrow filters with an active PLL to detect
- Equalizer - the output of the equalizer depends on the AGC and
- Phase Loop - this rotates the output of the equalizer prior
to equalizer update.
Since the phase loop adjusts the equalizer output which is used to
update the equalizer, these two active components are dependent on
each other. They are also configured in a feedback configuration,
and need to be carefully managed to prevent instability.
The AGC and baud timing should be brought up first, as they have
no dependencies and can often be jammed to reasonable values very
early in the startup sequence.
And now, a rough guide through the various phases. Some of these
may or may not work well for you depending on your situation.
1) - Detect the S sequences at the start of the training period. Use
these to preset your agc and baud timing recovery as best you can.
Start running baud timing recovery and agc. Note that if it's not
possible to get good enough timing recovery or agc convergence at
this point, you may need to delay the start of the next step below
until a few symbols of PP have passed.
2) - At the start of PP, preset your equalizer and start feeding data into
it. PP is a periodic signal with 48 symbols, 12 points arranged in a
circle. Your equalizer should be preset, probably with a single real
tap, such that the output (combined with your previously jammed agc)
is statistically near the amplitude of perfect PP points.
3) - After your equalizer is full, start the equalizer and collect its
output in a buffer. Make sure you don't start the equalizer until after
the entire delay buffer is full of valid PP symbols. At this time you
should also jam the equalizer phase loop to zero.
4) - Collect the output of the equalizer for 48 symbols. This is a
full set of the periodic PP signal. After you have all 48 symbols,
cross correlate the equalizer output with the reference PP signal to
get both exact timing and the equalizer phase loop offset. Jam the
phase loop and equalizer update with this information.
5) - Start up the equalizer update, training on PP. You have six full
frames of PP to train on; the first one you used to fill up your
equalizer. The second one you used to derive fairly exact timing
for the phase loop and your training data. The remainder of PP
will be used to train the equalizer and optionally the phase loop.
Note that your phase loop should still be jammed at this point.
A note on equalizer training: the noisier your signal, the slower
you need to train. You should be training as fast as you can without
going unstable, but keep in mind that as the noise floor rises it
becomes much easier for the equalizer to diverge and much harder to
get a good train.
An additional note is that it may be worthwhile to only train the
center quarter of your equalizer during PP. Typically, most of the
large equalizer taps lie near the center, within a small range.
V.34 requires a large equalizer (40+ taps) for the densely packed
high-rate constellations, but for quick brute force training (on
a 12 point circle no less) you may be able to get substantially
faster convergence using only a quarter of your taps.
It may also be possible to improve the initial equalizer convergence
by using a more computationally expensive training approach, such
as an RLS or affine algorithm. A second order affine update is
often trivial to implement and can decrease convergence time if used
carefully. Typically these approaches are not required, as careful
design can give acceptable convergence with a simple LMS style
6) - The remainder of PP should be used for equalizer training.
Because we're expecting a very noisy signal, it's important that
the phase loop pll be disabled at this point. It's hard enough
for the equalizer to train already; adding the extra variation of
an unlocked phase loop into the system will make things
7) - After PP comes the four or 16 point square constellations.
If you've been using a partial equalizer update, you should
probably begin using a full update around this point.
The four point constellation is about as close to trivial to
train as can be had; the remainder of this discussion will
be regarding training on 16 point constellations, which is
substantially more difficult in a high noise environment.
By the time you are finished with PP, you should have enough
of a train that you can at least make out a rough square (or
perhaps even the individual points) in the 16 point
Note - one of the problems with the 16 point constellation is that
the points are so much closer together that the threshold
for oscillation between an active phase loop and the equalizer
update is much lower than for a four point constellation.
It should be safe to start/unjam the phase loop at this point,
but only if the update is set to be -very- slow. You want to
use this time to try to acquire the second order drift term,
but if the pll moves around too quickly it can very easily
damage the delicate state of the equalizer. Keep in mind
that the equalizer will be doing its best to compensate
for phase loop drift by retraining its coefficients.
An issue that can arise with both the phase loop and equalizer
updates being enabled is a type of 'local minimum' situation.
For a 16 point constellation with zero phase drift, there is
naturally a global minimum on a proper train. There is also
a local minimum consisting of a high rotation rate combined
with a circular pattern that has a high density in the center
that decreases outward. The high density area in the center
is created by the inner four points of the 16 point constellation.
The 4 point constellation does not have this local minimum,
as there are no center points. Technically, the 4 point
constellation is very similar to the PP signal, as all points
lie on a circle.
One way to eliminate this local minimum is simply to ignore
training attempts on the center four points. The training
rate is reduced by a corresponding amount (around 25%), but
this may be tolerable if the noise and phase loop drift are
sufficiently high. Other more extreme measures might be to
only train on half of the constellation, for example the
upper and lower two lines of four points each.
Once you have fairly good convergence on the constellation,
it's safe to bring up the gain on the phase loop to guarantee
that it has locked properly.
Typically the equalizer training constant and the phase loop
gain decreases from this point forward, to whatever value
is typical of steady state. For low noise environments,
you want the equalizer training constant to be relatively
high so as to maximize convergence with what little error
you may have. For high noise environments, you need to have
a relatively small training constant to allow the noise to
be statistically smoothed out of the equalizer coefficients.
Unfortunately, the smaller training constant means a longer
convergence time, on top of the already long convergence
time due to the large amount of noise present.
The above only addresses the initial training phase, which
is relatively long compared to the resynchronization training
which occurs during data phase. In a lot of ways,
resynchronization is easier, as the active components are known
to be well trained and only need to acquire the proper timing
and initial values.
Something to keep in mind during resynchronization is that
every single symbol matters. If you want a good resync that's
reliable, you have to get every symbol as close as you can,
especially on transitions between various phases of the startup
signals. You have 12 symbols of S-bar, 288 symbols of PP, and
120 symbols of B1 to work with, then you're in data mode.
That's very little time for a modulation that may be pushing
to within 3 db of Shannon. This kind of exacting, every-symbol-matters
detail is less important on the initial train sequence, which
can be several seconds long.
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