Happy New Year,

I believe that Markus, DF6NM has made some salient points:

...... The question for our weak-signal work is not so much how to
decrease the error rate of a strong signal, but rather whether we can
actually lower the threshold bit-energy below the noise energy (kT, equal

to

noise-power per bandwidth).

For m-ary FSK, the task of the receiver is simply to select the channel
having the highest energy (or the highest in-phase voltage for coherent
detection). The problem is that with more channels, the statistical
probability of noise in one of the many unwanted channels being stronger

than

the signal channel becomes higher. To keep the error rate constant, you

have

to spend a little more TX power. For large m, this logarithmic loss in
SNR-efficiency per symbol finally eats up the logarithmic increase of the
number of bits per symbol.

Just have a look at one of the 7FSK screenshots with marginal signal: The
choice of selecting the "right one in a crowd of seven" is more difficult
than for a crowd of two.

I have not been closely following the 7FSK discussion due to other calls on
my time, but I have been generally sceptical that anything with more than
binary coding is the way to go for amateur LF DX two-way contacts.  So
rather belatedly, I have some remarks on basic issues, stimulated by the
comments from Markus:

My understanding is that binary phase shift keying (BPSK) has the lowest
detection threshold of any type of modulation and that ANY higher order
scheme (intended to give an increase in spectral "efficiency" in terms of
transmitted bits/second/Hz) accordingly has a penalty of less energy per bit
for a given transmitter power, so the claim of "efficiency" has an overhead
in needing higher RF signal to noise ratio at the receiver.  A "binary"
scheme is always a winner in terms of noise performance and of the various
binary schemes, "phase shift" keying is the best performer.  Differential
BPSK (DBPSK) may have practical benefits that justify a small degradation in
ultimate noise performance.  For a given demodulated bit error ratio (and
including using a visual display for operator assisted decoding), a higher
RF signal to noise ratio is needed by any higher order modulation scheme.
Amateurs have an eirp cap on radiated power, so there is a limit on how much
the DX receiving situation can be improved in terms of "solving the problem
by applying more transmitter power".   For a two-way contact there is also
the question of completing the QSO within the time of a propagation opening.
Thus a deduction can be made as to the slowest bit rate needed to achieve
the desired results.  There may as well be pre-set options for bit rate, to
facilitate local testing and for QSOs within a few hundred kilometres.

The message content needs to be succinct so there needs to be good use made
of prior agreed codes.  Good coding is also part of the overall scheme.

So in summary, I believe that extending LF DX achievements will be best
served by developing a BPSK or DBPSK scheme.

73, Bob ZL2CA