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LF: Eb/N0 values for amateur modes

To: [email protected]
Subject: LF: Eb/N0 values for amateur modes
From: Pieter-Tjerk de Boer <[email protected]>
Date: Thu, 8 Jan 2015 23:07:55 +0100
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A couple of days ago, Markus posted Eb/N0 numbers for WSPR and OPERA,
for comparison to the BPSK VLF tests (see below).
Some may be interested in a table with Eb/N0 values for some more amateur
modes, which I composed some weeks ago for an article in the Dutch amateur
radio magazine 'Electron':

                           Needed SNR    Net datarate   Needed
          Mode             in 2500 Hz     in bits/s      Eb/N0         Comments
        SSB voice             +10 dB          20        +31 dB         very 
rough estimate
  CW (ZRO-test, by ear)       -18 dB           0.54     +16 dB         based on 
avg.pwr; peak 3 dB higher
  CW (QRSS-3, waterfall)      -26 dB           0.13     +14 dB         same
CW (RSCW software, 12 wpm)    -12 dB           4        +13 dB         same
        OPERA-2               -23 dB           0.23     +14 dB         peak 
pwr. 3 dB higher; 2 dB lower if counting CRC-bits as information
          RTTY                 -5 dB          32        +14 dB
          PSK31               -10 dB          31         +9 dB
          WSPR                -29 dB           0.45      +5 dB         not 
counting energy in sync bits; otherwise 3 dB higher
        WSPR-15               -38 dB           0.056     +5 dB         same
     JT65 (for EME)           -24 dB           1.54      +5 dB         same
  Coherent BPSK on VLF        -57 dB           0.0058    -1 dB
     Theoretical limit                                   -1.59 dB

(The table is formatted for display using a fixed-width font.)

I have to emphasize that the SNR and Eb/N0 values should be taken with a
grain of salt, especially for the modes that do not use heavy FEC, since
those don't have a no sharp threshold.
The SNR values quoted come from a variety of sources on the web, and the
BPSK/VLF line is based on Markus and Paul's experiments from last May
(obviously, since I created the table before the recent experiments by Dex
and Paul).

73, Pieter-Tjerk, PA3FWM

On Sun, Jan 04, 2015 at 04:11:22PM +0100, Markus Vester wrote:

> [....]
> 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) 

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