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From: "Talbot Andrew" <ACTALBOT@dera.gov.uk>
To: rsgb_lf_group@blacksheep.org
Subject: LF: Slow CW vs. BPSK etc.
Date: Thu, 1 Jun 2000 11:49:49 +0100
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>There's a lot of discussion going on at the moment on the US "LowFER"
>mailing list about the relative merits of slow CW versus BPSK (in this
case
>relating to the COHERENT/AFRICA software by Bill de Carle, VE2IQ). The
>general consensus of opinion seems to be that if you are going to use
>"machine" modes, BPSK has considerable superiority over any form of
slow CW
>for the kind of very weak signals often encountered on the LF bands.
>Estimates of the effective improvement range from 6dB to 23dB depending
on
>what factors are taken into account!

(Slow) CW vs BPSK etc..

To compare theoretically, firstly we need to make the assumption that
data rates are similar for the two modes.  CW employs a reasonably
efficient variable length coding scheme where character length depends
on letter frequency of occurence.  We need to compare like with like,
and in PSK31 something similar is used.  Both schemes (CW and varicode)
offer about 6 bits per character coding efficiency, not allowing for
inter letter framing pulses.

For a given data rate, there is at least a 6dB advantage to be had in
going from an on / off keyed waveform to a BPSK one.  This is because
the amplitude differnece for the 1 and 0 states is doubled.  For on /off
keying (OOK) it is from 0 to (say) 1 Volt.  For an equivalent BPSK
signal, since the amplitude is plus / minus for 180 degree keying the
total amplitude change is 2 Volts, ie. 6dB better in noise using this
very simple back of an envelope calculation.  

There is further adavantage to be had by using PSK as well.  For OOK a
non coherent detector is usually employed - ie human ears for CW or eyes
for QRSS etc.  Lets we have a perfect operator with golden ears (or
eyes) and   assume these are perfect power detectors for now, in other
words they cannot respond to voltage or phase so are definitely
non-coherent. Various statistical calculations can be made to define at
what level the signal is detectable above noise, but in practice a S/N
value of 10dB is usually the best we can get away with - this is in the
theoretical minimum bandwidth of the signal at roughly half the
signalling rate and does not take into account bandwidth limiting for
spectral reasons.

BPSK, however, is received coherently.  ie voltage is integrated over
the symbol period rather than power, which immediately calls up a square
root term to the detection statistics compared with power.   Again
statistical rules can be applied and Signal to Noise vs. error rate
curves can be generated for minimum bandwidth.  The results usually end
up with a S/N of 6 - 8dB being sufficient for 'reasonable' error rate.
By reasonable, we mean something that will communicate useful
information with errors that the brain can correct for,  - and lets not
get into a discussion of error correction coding.   While coherent
decoding could be applied to OOK signals, what is the point ?  If we go
to the effort of building a coherent detector, then we might as well
make the most of it and use BPSK which is as easy to generate as CW.
(You can even use a changeover realy in the antenna feed as a desperate
last resort)

So we now have something like 6db advantage from peak power alone, and
around another 3dB for coherent vs incoherent detection resulting in 9dB
advantage for PSK over On Off Keying.   I don't know if Coherent offers
the variable length coding to get the average data rate down, if it
doesn't then the advantage is marginally less but this is easily offset
by the heavy error correction that it does have as an option.  

This is a very simple calculation and  communications theory experts
will probably drill all sorts of holes in it, but I bet many of their
arguments will cancel out.   We do actually observe  8 - 10dB S/N
advantage in coherent PSK modes versus incoherent ones such as CW.
Broadly similar arguments apply to SSB vs. AM and no one disputes the
advantage there.

A completely different set of rules apply when noise is non Gaussian
(non white) such as bursts and for ionospheric propagation modes with
multipath, and mean that non coherent modes such as multilevel FSK do
have certain other advantages to offer.

The Shannon theoretical limit for communications in a noisy channel is
(Signaling Rate / Bandwidth, Bn) = LOG2(1 + S/N).    In other words, for
Signalling rate  equal to Bandwidth which is the easy to understand
case,  Signal to Noise equals Unity  =  0dB !!  
Consider CW, the best ears are probably equivalent to 50 Hz bandwidth
and the best operator can probably cope with 24WPM (= 20 Hz) in very
noisy conditions.  S / BW = 0.4 so according to Shannons limit, it ought
to be possible to receive this in a S/N ratio of  2^(0.4) - 1 = 0.32 =
-5dB  (yes, negative S/N !)  In the 200 Hz bandwidth filter usually
employed this becomes -11db S/N

Uncoded PSK itself will nowhere achieve the Shannon limit either, but
with very efficient Turbo error correction coding schemes now appearing,
it is possible to get within 0.7db of it.

PSK31 has a lot to offer on LF, but unfortunately due to the almost
universal use of switching high efficiency power amplifiers and dearth
of tranceivers, is hardly used.   While PSK can be transmitted over non
linear class C/D/E amplifiers, it generates disgusting sidelobes that
beat even key clicks for their annoyance value!

In the Data column in RadCom, in the fundamentals section which will
appear each issue, I am slowly developing an easy intuitive guide to
data communications.  So far three have appeared - any feedback would be
appreciated.

Which reminds me, the deadline for August's issue is only 15 days away !
Must get on with it.

Andy  G4JNT


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