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Big congratulations again to Paul and Dex!
What Paul described in unpretentious and
matter-of-fact words should really be regarded as a major achievement. It has
been a well-deserved fruit of several months of effort, and there were a number
of difficulties to be overcome. As I was lucky to be included in the preceding
email exchange, I had the chance to witness milestones and setbacks during the
process.
Most members of the LF group will appreciate the
challenges to Dex on the sub-9kHz transmit side, dealing with large coils and
high voltage, realizing accurate GPS-derived frequencies and sub-second bit
timing, and last not least being able to leave the signal on air reliably for
many hours.
The information processing side handled solely by
Paul surely presented an even higher hurdle: In the first place, he searched and
found a small handful of "good" FEC codes. The search involved extensive
simulations on powerful multicore computers hired from the Amazon cloud. Then
the soft Viterby decoding of a potential receive signal is also computer
intensive, especially for longer messages. There need to be numerous trials
while optimising reference phase evolution, bit timing, and antenna
weights.
Perhaps the most challenging part was guessing
appropriate parameters before a transmission, ie. how many characters should be
sent in which amount of time. Although some experience had been gained from
carrier measurements during previous nights, ionospheric and atmospheric
variations make it hard to predict SNR accurately enough if you want to exploit
the channel capacity to the last couple of dBs. In the third round on new year's
night, Dex and Paul dared to take a bet, and won. Allow me to cite from their
final email exchange on Dec 31st:
Dex:
Want to test the limits?
Paul:
Yes please.
Let's go for broke.
8
seconds is close to the limit, which is what I'd like to see.
The ultimate goal of this work has been to take decoding sensitivity
close to the theroretical limit. An universal metric for this is Eb/N0, the
ratio of the received signal energy per payload bit (Eb in Joules) and the noise
spectral power density (N0 in Watt/Hertz, equivalent to "noise energy" in
Joules). The Shannon limit for long messages spread to infinite bandwidth is
Eb/N0 = ln(2) = -1.59 dB,
which (similar to the speed of light)
cannot be surpassed by any possible encoding scheme. Paul's and Dex' experiments
showed that his codes can come within about a dB of this limit in a real
long-distance propagation experiment.
To put that into perspective, let's derive Eb/N0 figures for two popular
digital modes:
WSPR-15 transmits 50 information bits in 15 minutes, ie one bit in 18
seconds. The decoding threshold is -38 dB in 2.5 kHz, or -4 dBHz. This gives
Eb/N0 = 10 log(18) - 4 dB = +8.5 dB,
ie. about 10 dB above the
Shannon limit. Note that although different speed variants (eg WSPR-2) need
different power, the minimum energy per bit has to remain the same.
Opera-32 carries 28 information bits in 32.6 minutes, ie. one bit in 70
seconds. The threshold is about -39.5 dB in 2.5 kHz, (-5.5 dBHz), referenced to
the average power of the 50% dutycycle on-off keying. This gives
Eb/N0
= 10 log(70) - 5.5 dB = +13 dB
or about 14.5 dB above Shannon. Note however
that for LF / VLF transmissions, the limit will often be antenna voltage and
peak power rather than average power, which can result in a further 3 dB
disadvantage for Opera against frequency- or phase-modulated
techniques.
The opds correlation decoder can go about 9 dB lower than Opera. But of
course it can only find the best match from an a-priori defined list of
callsigns, and doesn't attempt to decode any message.
However we must recognize that the amateur modes spend a significant part
of their energy to provide a reference for synchronisation, so not all of the
Eb/N0 difference is due to less efficient encoding. The "nude" FEC-PSK mode
doesn't contain any such overhead. So it can only work when the link has a
stable phase (like on VLF), and the decoder has been given accurate information
on carrier frequency and symbol timing.
All the best,
Markus (DF6NM)
Sent: Sunday, January 04, 2015 1:13 PM
Subject: VLF: Transatlantic messages at 8822Hz
W4DEX achieved another 'first' recently by sending a series
of
messages across the Atlantic at 8822 Hz which were successfully
copied
at Todmorden UK, range 6194km.
Transmissions used coherent BPSK
signalling with ERP of around
150uW. The modulation encoded the
messages using a rate
1/16 terminated convolutional code with constraint
length 25,
cascaded with an outer error detection code.
The first
message was received at 2014-12-30 03:00, a 4
character message 'EM95'.
Eb/N0 was -0.8dB using 9 second
symbols.
A second test the following
night managed 12 characters 'PAUL
HNY DEX' using 14 second symbols giving
Eb/N0 of +1.0dB.
Conditions were good and we could have used shorter
symbols
and a longer message.
The third test and best result so far
was a 25 character message
'8822HZ 2015 JAN 1 TA TEST' sent from 2015-01-01
00:00 using
8 second symbols. This was received with Eb/N0 =
-0.1dB.
In the 0.125 Hz bandwidth of a code symbol, the S/N was
-13.2dB.
That corresponds to -56dB S/N in a 2.5kHz audio bandwidth
after
sferic blanking. Before the blanker the S/N would be
around
-76dB.
The source encoding uses 6 bits per character to produce
a
payload of 150 bits. An outer code adds a 16 bit CRC and
the
convolutional encoder expands the message to 3040 signal bits.
The
effective code rate is therefore 150/3040 = 1/20.27.
Of the 3040 signal
bits, 1153 were demodulated incorrectly
but the FEC was able to fix them all
to reveal the message.
Received signal was around 0.12 fT and it was
necessary to
combine H-field and E-field receiver outputs to obtain
a
sufficient S/N to decode.
The decoder is a soft Viterbi list
decoder. The signals are too
weak to reveal a reference phase by the
usual method of summing
the squared complex symbol amplitudes. Instead
the decoder has
to do a brute force trial and error search.
The
information rate in the 3rd test was 24.6 bits per hour
which is 80% of the
channel capacity.
--
Paul Nicholson
http://abelian.org/
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