The nature of radio signals received off-air is that they are accompanied by undesired noise.

A key measure of the ability to decode a radio signal is its Signal to Noise ratio (S/N) at the demodulator (or referred to some common point).

We can speak of think of an external S/N figure as \(S/N_{ext}=10 log\frac{S_{ext}}{N_{ext}}\) in dB.

Receiver systems are not perfect, and one of the imperfections is that they contribute undesired noise.

So, the S/N becomes \(S/N=10 log\frac{S_{ext}}{N_{int}+N_{ext}}\).

A useful metric in system design is the extent to which the external S/N is degraded by the receiver system, I will call it Signal to Noise Degradation (SND).

\(SND=10 log\frac{\frac{S_{ext}}{N_{ext}}}{\frac{S_{ext}}{N_{int}+N_{ext}}}\)Simplifying this by dividing top and bottom by \(S_{ext}\) we get

\(SND=10 log\frac{N_{int}+N_{ext}}{N_{ext}}\).

So, SND gives us a metric that simply depends on the external noise and the receiver internal noise, a quantitative measure of the system in an application context.

You might think that receiver Noise Figure does just that, but it does not. Receiver Noise Figure assumes the external equivalent noise temperature is 290K, a laboratory metric.

## Caveats

The methods presented here apply to linear systems, they do not capture the effects of non-linear behavior such as IMD noise.

## Calculator tools

Though the calculation is not difficult, a convenient online calculator is at Signal to Noise ratio degradation by receiver internal noise.

ITU P.372 ambient noise might also be useful.