Congratulations to you, Dex and the rest of the team on this work, including
73% channel capacity in the midst of many constraints!
I had planned to ask if you thought that any atmospheric phase noise
information might be implicit in the team's data from this experiment, for
phase error spectral components anywhere near your information rate*. Your
reconstructed-carrier information seems to answer that question, given that
there are 4 inflection points in the phase trend from 00:00 to 07:00. I'm
guessing that the multiple inflections could be manifestations of amplitude
noise alone (given ~14dB SNR and < 7 degrees between inflections), such that
any atmospheric phase noise estimate more accurate than (for example) ten
degrees would need to be made over an interval of multiple hours; and that
information (of precision better than ten degrees for example) on phase
error spectral components near your information rate would therefore not be
available from this most recent data. Is the reasoning above incorrect?
Perhaps it's better to ask if channel capacity tests provide some unique
value to phase error measurement: do encoding and comparison to the Shannon
limit offer any potentially unique information regarding phase noise,
notwithstanding low amplitude-SNR?
Great experiments and results!
* (6.8E-3 bps for test 3 based on 24.6 bph?)
From: [email protected]
[mailto:[email protected]] On Behalf Of Paul Nicholson
Sent: Monday, January 5, 2015 1:25 PM
To: [email protected]
Subject: Re: VLF: Transatlantic messages at 8822Hz
By reversing the modulation of Dex's Jan 1st transmission, the carrier is
reconstructed. S/N and phase in in 1 hour
00:00 to 01:00 11.6 dB -122.1
01:00 to 02:00 13.1 dB -119.4
02:00 to 03:00 12.6 dB -131.9
03:00 to 04:00 14.3 dB -135.0
04:00 to 05:00 12.7 dB -111.0
05:00 to 06:00 15.2 dB -118.9
06:00 to 07:00 13.4 dB -111.7
Average of above: 13.27 dB
This agrees well with the S/N of 13.33 dB in 278uHz calculated from the
symbol error rate.
Note the steady phase which is what allows coherent BPSK to be used when the
signal is too weak to extract a reference phase.
The decoder merely has to try phases (in say 30 degree steps) until it gets
> information rate ... 80% of the channel capacity.
I made a mistake and forgot to allow for the 16 CRC bits (they belong to the
coding, not the information payload).
Actually the rate was 73% of capacity. I suppose we'll just have to do
In the same series of tests, I received a 9 character message from Markus
DF6NM with symbol error rate 0.395, Es/N0 = -14.4dB,
Eb/N0 = 0.0 dB at an effective code rate of 1/27.85. This
achieved 71% of channel capacity. In fact it was quite an
easy decode of the 10 second symbols (it did not require list
decoding) and with hindsight we could have used 8.5 symbols to obtain 83% of
capacity. This illustrates the challenge of selecting a symbol rate for any
given test. It is essential to have some reliable carrier S/N measurements
Another result: On 30th December a 4 character message from W4DEX was
decoded from the natural radio receiver at Sebring FL, distance 869 km.
Eb/N0 was +2.8 dB so it was nowhere near the channel capacity and we could
have used a much longer, faster message.
I am very grateful to Markus and Dex for making these tests happen and
turning what would have been just a computing exercise, into reality.
It seems there are three essentials for success at VLF:
Teamwork; A GPS; And the following advice -
"Get started and see what happens...
Turn your DREAM into REALITY!!"
...Mal Hamilton G3KEV, Feb 2010.