LF: Signalling margins and Shannon

["Talbot Andrew" <ACTALBOT@dera.gov.uk>]

Has anyone looked at what Signal to Noise is realistically viewable on a spectrogram display ?   Assuming bandwidth equal to FFT bin size, my few tests suggest around 10dB but it would be nice to have a more authoritative  figure to calculate with.   Obviously depends on colour palette and number of colours on the display so after a couple of years of experience with Spectrogram and now Argo, what has anyone found ?

 

A back of envelope calculation on signalling capabilities using DFCW :

(Switch off now those not interested in communications theory and working out what Could be done <:-)

 

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For DFCW, signal bandwidth needs to be at least twice that of a dot interval in order to be able to distinctly see the on-off transitions.   Doubled again, since two frequencies are involved, but some overlap of sidebands is allowed as we can sttill se which of the frequencies is intended, so take a total signalling bandwidth of 3 times the dot interval as being the minimum needed.   This gives a signalling rate of   1 / 3 Bit / second per Hz   (0.33 B/s/Hz)

 

Shannon's law relates signalling rate to Signal to Noise by :

 

R = LOG(1 + S/N)     (LOG to the base 2 and S/N in numerical units, not dB)

 

so for R = 0.33, signalling should be possible (at an 'arbitrarily low' error rate)  in a S/N of 0.258  = -5.8dB (yes, negative S/N)

 

If 10dB S/N is needed for viewing then we are almost 16dB down on Shannon

And this does not even allow for further signal degradation due to multipath / fading,

 

The only scheme I have ever come across that reckons to get within less than 1 dB of Shannon makes use of the very latest Turbo coding schemes now possible with high speed DSP, coupled with continuous phase modulation (partially related to MSK)    It is / was a contender for third generation mobile phones to increase data rate there in the congested bandwidth available.   PSK and QAM modulation sits somewhere between.

 

Coding :

DFCW codes the alphabet into between 1 and 5 bit intervals per character plus a gap for inter letter spacing, which, with the two frequency level coding, equates to between 4 to 12 bits per character.   The letter frequency of plain language text coupled with the one bit for E, two for A,N and 4 for Q, Z etc means there is probably an average of around 5 - 6 bits per letter, which is not bad coding efficiency - simple Baudot manages 7.5 bits / character and PSK31 about 5.5 - 6.  The very best dictionary based coding schemes, transmitting codes to represent words or even whole phrases, can claim 1 bit or less per letter equivalence.

 

However, the coding efficiency only affects the time to send the overall message since it dictates the Total number of bits needed, not the S/N needed in which to send it;  that only dictates the rate.

 

Andy  G4JNT

 

 

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