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Re: [Discuss-gnuradio] FSK performance as a function of Fd?

From: Brian Padalino
Subject: Re: [Discuss-gnuradio] FSK performance as a function of Fd?
Date: Sun, 16 Dec 2012 23:36:56 -0500

On Sun, Dec 16, 2012 at 9:39 PM, Michael Ossmann <address@hidden> wrote:
On Sun, Dec 16, 2012 at 11:27:47PM +0100, Joanna Rutkowska wrote:
> Thanks for the detailed answer! I did some more study and my
> understating is that what you wrote above applies to (theoretical)
> coherent demodulation. AFAIU nearly all practical receivers use
> non-coherent demodulation (because it's cheaper, and apparently, has
> about 1dB penalty only on sensitivity?). This non-coherent detection
> is apparently realized using two bandpass filters centered around the
> two frequencies.

I believe you are correct that sensitivity vs. deviation is strongly
dependent on the receiver implementation.  You may not be correct
assuming anything about the particular receiver implementation in the
Atmel part.

> So, my understanding goes, in any practical realization, it should be
> better (not worse at least) to use as large Fd as one can, because it
> makes the job of the two filters easier...
> But, it's apparently not like this. Here's the link to the Atmel paper
> I mentioned before (again, please take a look at Figure 9-2):
> www.atmel.com/Images/doc9174.pdf

Making a guess about the receiver implementation, I'd say you correctly
describe why the sensitivity improves as Fd increases toward 50 kHz.
I'd further guess that the reason sensitivity gets worse above 50 kHz
deviation is that the bandwidth of the signal exceeds the fixed IF
filter in the receiver.

The IF filter says it's around 400kHz wide at the 3dB points, so I doubt a 50kHz deviation is hitting those limits.  They also have frequency offset numbers which suggest they can handle significant frequency offset and still get their data through.

Looking at the graph and reading through the datasheet it seems there is a noise figure of around 10dB and 8.5dB SNR required to work well.  At the 120kHz deviation, we can get the input level at room temperature as such:

  -174 dBm/Hz + 10*log10(120e3*2) + 10dB + 8.5dB = -101.7dBm

Very close to the -102dBm they show in their graph.  Even at 30kHz deviation which is shown as -107dBm on the graph comes up with a very close -107.7dBm from the calculation.

What's actually interesting is for a value of 100kHz deviation shows on the graph a sensitivity of -105dBm whereas the calculation comes up with -102.5dBm.

If the receiver were actually implemented as a pair of bandpass filters as in Figure 9-1, then the above calculation wouldn't hold since the noise between the filters would be filtered out and not contribute to the SNR calculation.  If the two bandpass filters actually covered -f_dev to just below carrier and just above carrier to +f_dev they would effectively cover the entire -f_dev to f_dev bandwidth.  If the lower cutoff of each bandpass filter was actually pushed out (like in Figure 9-1), filtering out the noise and limiting the bandwidth of the system to be less than the occupied bandwidth of the transmission, that might explain what is happening.

It's really just an SNR in a given bandwidth problem.  Your two frequencies could be hundreds of MHz apart.  If the two bandpass filters are the same width, the effective bandwidth of the system is the same - is it not?

After writing all this, I am not sure I've convinced myself I am right or wrong but it's fun to think about.  Thanks!


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