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From: Paul Nicholson <vlf0403@abelian.org>
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Date: Wed, 21 Feb 2018 10:37:44 +0000
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Subject: Re: VLF: DK7FC > W1VD 8.27 kHz EbN0 success!
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Jay W1VD wrote:

 > a successful decode of Stefan's message was made on last night's
 > transmission. s/n in 39 uHz 10.5 dB and Eb/N0 2.54 dB. It was
 > pretty convincing as the decode popped up in the 0,0,0,0 phase
 > trial and only improved thereafter.

I ran the path through LWPC, 8270Hz anisotropy comes out at 10dB.

For, say, 20uW ERP at Heidelberg LPWC predicts about 4nV.M E-field
at W1VD.

The nighttime noise on a quiet night can be around 2nV/m in
this bandwidth, so 10.5 dB S/N is within reach given a few
dB of luck.

I ran simulations with ebnaut decoder at this code setting.
With just noise on the decoder input, after 108 trials with full
phase search and 4e6 list length I had two false detections of
the 'T' message,

  rank 510624 Eb/N0 -6.4 dB
  rank 380976 Eb/N0 -5.5 dB

With a weak input signal (a carrier or some other message)
at about the -5dB Eb/N0 level, false decodes are more likely
and tend to be stronger.  After 260 trials I got 7 false decodes
of a 'T' messages - the strongest was

  rank 230167  Eb/N0 +1.9 dB

In the same run, I got 52 correct decodes of the -5dB Eb/N0 test
message - a 20% success rate.

Jay wrote:

 > It was pretty convincing as the decode popped up in the 0,0,0,0
 > phase trial

That's a good sign.  It means the average S/N was sufficient to
extract a useful reference phase.

So I think that a result with Eb/N0 +2.5 dB and rank 31465 is
very likely to be valid but was lucky.  The list rank is typical
for that Eb/N0 when using a large CRC with short message.

With the estimated signal strength and not relying on luck it
would take 3-axis reception and probably a few days of stacking
to have a reasonable chance of a decode as good as this.

Hopefully there will be a decode with stacking the 2-char message.
Even if it doesn't decode, we should see some repeatable phase
when testing the correlation.

I make the path 6096.4 km.

No decode from Forest at 6818 km, the best nights for correlation
at Forest were

  12/13 Eb/N0 -4.5 dB phase 51.7
  18/19 Eb/N0 -6.3 dB phase 81.3

The extra 700km of land path to Forest is making a difference here.

Congratulations to Jay and Stefan for achieving this long awaited
milestone.  At VLF it is always worth trying the almost impossible!
Hopefully further experiments will strengthen this result.

--
Paul Nicholson
--