Re: Calculating SNR of an incoming signal

[Alex Batts]

The effective noise bandwidth is part of the calculation. I'm using the radar range equation.

My purpose for including the bandwidth in my response was that any time I try to use a filter with a frequency greater than my sampling rate/2 I get an error returned. I agree that ideally I would use a band-pass filter with very narrow cutoffs to best capture the signal in its entirety, however, I can't because the frequency I'm trying to set my filter at is more than half my sampling rate, giving me an error. Maybe there is something askew with that error and it's something else, but it returns saying 0 < fa <= sampling_rate/2

On Thu, Jun 25, 2020 at 3:27 PM Marcus Müller <mueller@kit.edu> wrote:

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