It looks clear that coherently stacking repeated messages
does work as expected, in fact works quite well at 6470 Hz
because we have seen that the day-to-day and night-to-night
phase variations are quite small.

So long as we normalise each reception by dividing by its
total RMS value before summing, we get some small additional
gain even when a reception is poor quality.

Repeating a message N times is theoretically not as effective
as sending the message once using N times as many symbols
to exploit a lower rate stronger coding.  In both case Eb
increases by the factor N while N0 remains constant, so both
methods have an overall factor N increase of Eb/N0. But the
single transmission with the stronger code has a better
chance of decoding at that Eb/N0.

However, if you're already using the strongest available code
and you have increased symbol duration to the point where
your message duration is just short of hitting a terminator,
then the only option is to repeat and stack.

To reliably exploit repeats, both tx and rx need to be either
glitch-free or have absolute phase (so that after a reset it
continues with the same phase).

Stefan wrote:

> Would it makes sense, when we try the longest VLF message ever
> (it must be 75 characters, i found an important message! :-) ),
> to run day and night transmissions?

Yes, I can adjust for a nominal 28.8 nighttime phase lag and
combine day and night.  But we don't get much contribution
from the nights though.  About four nights make up for one day.

75 chars will be interesting, 150 Gbyte of RAM for a K=25
decode, only 2 Gbyte for a K=19 decode, 8 Gbyte for K=21.

Average daytime S/N has been -60.8 dB in 2500 Hz. Plugging
that into the signal calculator gives


http://abelian.org/ebnaut/calc.php?sndb=-60.8&snbws=2500&snmps=&code=8K19&sp=60&crc=16&nc=4

for the TEST messages with 60 second symbols.  For 75 chars
within 8 hours we might use 8K19 and 7 second symbols


http://abelian.org/ebnaut/calc.php?sndb=-60.8&snbws=2500&snmps=&code=8K19&sp=7&crc=16&nc=75

or 3.5 second symbols with 16K21


http://abelian.org/ebnaut/calc.php?sndb=-60.8&snbws=2500&snmps=&code=16K21&sp=3.5&crc=16&nc=75

We need about 10dB stacking gain, so about 10 daytime repeats
but we might decode at 8 days.

Bielefeld has average S/N -58.6 dB and would have a good chance
of decoding in 5 or 6 day repeats.

> What about all the other stations out there, RX and/or TX?
> Are we alone now with our special stuff?

We are surely alone here!  Who would do this crazy stuff?
Counting electrons for a week in 35uHz bandwidth?  Here I find
a certain 'gemuetlichkeit' in spending the long winter evenings
teasing ludicrously weak signals out of the noise.

--
Paul Nicholson
--