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From: Paul Nicholson <vlf0403@abelian.org>
Message-ID: <952fc558-5e93-f229-2749-855bc73b1cbc@abelian.org>
Date: Fri, 5 Jan 2018 13:55:23 +0000
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Subject: Re: VLF: Finally back on the 58 km band...
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Jim AA5BW wrote:

 > A technical question: I notice ~ 9dB lower Eb/N0 than the
 > 1-character December 28th result (in Todmorden and Bielefeld);
 > is this essentially from an approximately 12x increase in
 > character rate?  Or does the symbol period independently also
 > affect Eb/N0 in this case?

N0 is the noise density, completely independent of the transmission.

It boils down to Eb, the signal energy per info bit.

Eb is proportional to the overall message duration, and
inversely proportional to the information content.

So the symbol period (or signal bandwidth), coding scheme and
modulation method, only come into it to the extent that they
affect the total time it takes to transmit the information.

The 1 char message (16K21A CRC 11, 60 second symbols) has
duration 35520 seconds and info 1 * 5.7 = 5.7 bits.

The 12 char message (16K21A CRC 6, 30 second symnols) has
duration 47040 seconds, info content 12 * 5.7 = 68.4 bits.

So we would expect Eb/N0 to differ by the factor
47040/35520 * 5.7/68.4 = 0.11 = -9.6 dB.

Stefan wrote:

 > f = 5170.1000 Hz
 > Start time: 29.Dec.2017  15:00:00 UTC
 > Symbol period: 30 s
 > Characters: 12
 > CRC bits: 20
 > Coding 16K21A
 > Duration: 14:56 [hh:mm]

Todmorden (881.2 km)
--------------------

  29/30 Eb/N0 +2.8 dB, S/N -26.2 dB/1Hz, phase 46.1 *Decoded*
  30/31 Eb/N0 +4.1 dB, S/N -24.9 dB/1Hz, phase 44.2 *Decoded*
  31/01 Eb/N0 +1.8 dB, S/N -27.1 dB/1Hz, phase 43.2 *Decoded*
  01/02 Eb/N0 +1.5 dB, S/N -27.5 dB/1Hz, phase 57.6 *Decoded*
  02/03 Eb/N0 -1.6 dB, S/N -30.6 dB/1Hz, phase 60.6;
  03/04 Eb/N0 -1.6 dB, S/N -30.6 dB/1Hz, phase 50.3;
  04/05 Eb/N0  0.0 dB, S/N -29.0 dB/1Hz, phase 61.3;

Bielefeld (303.8 km DL4YHF)
---------------------------

  29/30 Eb/N0 +8.6 dB, S/N -20.4 dB/1Hz, phase -53.5 *Decoded*
  30/31 Eb/N0 +8.3 dB, S/N -20.6 dB/1Hz, phase -52.1 *Decoded*
  31/01 Eb/N0 +8.1 dB, S/N -20.8 dB/1Hz, phase -56.3 *Decoded*
  01/02 Eb/N0 +8.4 dB, S/N -20.6 dB/1Hz, phase -47.9 *Decoded*
  02/03 Eb/N0 +4.0 dB, S/N -24.9 dB/1Hz, phase -38.1 *Decoded*
  03/04 Eb/N0 +5.6 dB, S/N -23.4 dB/1Hz, phase -46.1 *Decoded*
  04/05 Eb/N0 +8.8 dB, S/N -20.1 dB/1Hz, phase -47.0 *Decoded*

Warsaw (919.3 km SQ5BPF)
------------------------

  29/30 Eb/N0  -5.4 dB, S/N -34.4 dB/1Hz, phase -20.3;
  30/31 Eb/N0 -17.2 dB, S/N -46.2 dB/1Hz;
  31/01 Eb/N0  -7.8 dB, S/N -36.8 dB/1Hz, phase -44.2;
  01/02 Eb/N0  -6.1 dB, S/N -35.1 dB/1Hz, phase -36.1;
  02/03 Eb/N0  -8.2 dB, S/N -37.1 dB/1Hz, phase   2.9;
  03/04 Eb/N0 -10.2 dB, S/N -39.2 dB/1Hz, phase -33.1;
  04/05 Eb/N0  -8.1 dB, S/N -37.1 dB/1Hz, phase  -3.8;

  Seven stacked: Eb/N0 -0.8 dB;

Cumiana (504.6 km IK1QFK)
-------------------------

  29/30 Eb/N0 -5.4 dB, S/N -34.3 dB/1Hz, phase  176.7;
  30/31 Eb/N0 -1.3 dB, S/N -30.3 dB/1Hz, phase -176.2;
  31/01 Eb/N0 -4.9 dB, S/N -33.9 dB/1Hz, phase  177.4;
  01/02 No data from rx site, ADSL fault;
  02/03 No data from rx site, ADSL fault;
  03/04 No data from rx site, ADSL fault;
  04/05 Eb/N0 -1.6 dB, S/N -30.6 dB/1Hz, phase  174.5;

  Four stacked: Eb/N0 2.9 dB *Decoded*

--
Paul Nicholson
--