Thanks for this Pieter!
There are a couple more modes that have
been used on LF, and of which I'd be interested to see quantitative SNR
threshold data:
Maybe someone in the group can help?
Markus (DF6NM)
Sent: Thursday, January 08, 2015 11:07
PM
Subject: LF: Eb/N0 values for amateur
modes
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 (ZROtest, by ear) 18
dB
0.54 +16
dB based on avg.pwr; peak 3 dB
higher CW (QRSS3, waterfall) 26
dB
0.13 +14
dB same CW (RSCW software, 12
wpm) 12
dB
4 +13
dB
same
OPERA2
23 dB
0.23 +14
dB peak pwr. 3 dB higher; 2 dB
lower if counting CRCbits 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
WSPR15
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 fixedwidth
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,
PieterTjerk, 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 longdistance propagation experiment. > > To
put that into perspective, let's derive Eb/N0 figures for two popular >
digital modes: > > WSPR15 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 WSPR2) need different power, the minimum
energy per bit has to > remain the same. > > Opera32
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 onoff 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
phasemodulated 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 apriori 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" FECPSK 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) >
