Re: Calculating SNR of an incoming signal

[Marcus Müller]

Hi Alex,

On 25/06/2020 21.00, Alex Batts wrote:
> I'm sampling an incoming signal, but only around 2 MSps.

and that's fine! that's the *equivalent* baseband, it has all the same 
information as the RF signal.

> I need the signal power to noise power ratio at the receiver as part of 
> my range calculation. 

Yes, but you'd always want to do that "signal to noise" only in the 
bandwidth that actually contains your tone; the rest will just contain 
more noise, interferers... to make your measurement worse.

> So I would need to be able to distinguish between 
> the power of the tone vs the power of the surrounding noise and use 
> those two numerical values in an equation to calculate the range. 

You need to define "surrounding"! Your signal doesn't get worse by 
applying a filter that only selects your tone and as little else as 
possible. So you should do that – it makes your SNR better. Hence, your 
Signal power estimate gets more reliable (which you definitely want).

(that also highlights why I have a bit of doubt on your measurement 
methodology – if your SNR depends on receiver bandwidth, then how much 
does it actually tell you about the range, unless you specify the 
bandwidth alongside with it?)

Think about it: we typically assume noise to be white, i.e. to have 
identical power spectral density all over the spectrum, e.g. -170 dBm/Hz.

Now, if your receiver bandwidth is set to 2 MHz (because that's what 
your SDR is probably configured to filter out if you ask for 2 MS/s), 
then you get twice as much noise power than if you set the sampling rate 
to 1 MS/s.

It's the same thing that I always let students figure out by themselves 
the first time they use the lab spectrum analyzer:
Feed a 2 GHz -60 dBm tone into the spectrum analyzer.
Set the resolution bandwidth of the spectrum analyzer to 1 MHz, and tell 
me what the SNR is. Now set the resolution bandwidth to 300 kHz and tell 
me again.
You get as much "N" in your SNR as you let through your system. In the 
case of the spectrum analyzer, every point on the display is the power 
in 1 MHz (or 300 kHz) of filter. In the case of your Qt plot, it's the 
power in a FFT bin. There's (f_sample)/(FFT length) bandwidth to each 
bin; so your graphical analysis hinges on the setting of sample rate and 
FFT length (also, on window choice and labeling, and software 
convention). Proportionally!

It's really hard to define "SNR" for 0-bandwidth, i.e. a single tone 
(having a single tone, actually, gets tricky physically, but there's a 
lot of people who could tell you more about oscillators than I could).

If you'd be fair, the only choice for the noise filter bandwidth would 
be 0 Hz, because if you chose any wider, you always get more noise. But 
in 0 Hz, there's actually 0 noise power! So, that doesn't work.

Instead, you need to define SNR exactly on the bandwidth your detection 
system will have to use. That's a design parameter you haven't mentioned 
so far!

> This 
> is why I referenced the green and red lines on the qt gui freq. display, 
> this would seem to give me signal strength in dB.

Hopefully, above explained how much these lines depend on your 
configuration and aren't "SNR".

Cheers,
Marcus

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