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LF: m-FSK: SNR vs bandwidth

To: [email protected]
Subject: LF: m-FSK: SNR vs bandwidth
From: [email protected]
Date: Wed, 2 Jan 2002 16:38:46 EST
Reply-to: [email protected]
Sender: <[email protected]>
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


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