From: MarkusVester@aol.com
Message-ID: <169.68ea4ad.2964d7e6@aol.com>
Date: Wed, 2 Jan 2002 16:38:46 EST
Subject: LF: m-FSK: SNR vs bandwidth
To: rsgb_lf_group@blacksheep.org
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Dear Rik, dear LF group,

> Assuming a QRSS QSO takes 2 hours you can have the same QSO in abt.
> 38 minutes using DFCW and in abt 22 minutes using 7FSK, leaving the SNR
> unchanged.
> 7FSK is ... abt. 2.5dB superior to DFCW

Implicitly, you raise a very interesting point here: What if we used 1024 
freqs to encode 10 bits, would the SNR per symbol still be the same? If so, 
could we use infinitely less energy per bit, by spending (exponentially) more 
bandwidth?

Spending BW to improve SNR is often done, classical examples are wideband FM 
and digital audio. But all these techniques have in common a detection 
threshold. If the input SNR is below that minimum, demodulation breaks down 
completely. The question for our weak-signal work is not so much how to 
decrease the error rate of a strong signal, but rather whether we can 
actually lower the threshold bit-energy below the noise energy (kT, equal to 
noise-power per bandwidth).

For m-ary FSK, the task of the receiver is simply to select the channel 
having the highest energy (or the highest in-phase voltage for coherent 
detection). The problem is that with more channels, the statistical 
probability of noise in one of the many unwanted channels being stronger than 
the signal channel becomes higher. To keep the error rate constant, you have 
to spend a little more TX power. For large m, this logarithmic loss in 
SNR-efficiency per symbol finally eats up the logarithmic increase of the 
number of bits per symbol.

Just have a look at one of the 7FSK screenshots with marginal signal: The 
choice of selecting the "right one in a crowd of seven" is more difficult 
than for a crowd of two.

Regards
de Markus, DF6NM