Phantastic, many thanks for the summary
Markus.
"Brute force" in a very elegant context !
Cheers,
Wolf .
Am 04.01.2015 16:11, schrieb Markus Vester:
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/
--
