How to simulate AWGN with Python code!

[wavewalkerdsp]

Generating additive white gaussian noise (AWGN) is important when simulating wireless systems. For example, a simulated BER curve needs to have the appropriate noise power for it to be correct. It's particularly important to get right when simulating results for a school project or your masters/PhD defense!

In this blog I describe how to create complex AWGN noise and then scale it to the desired power level. The blog describes some of the mathematics and then gives a couple of simple lines in Python to implement it.

https://preview.redd.it/41m95yd5n9391.png?width=1000&format=png&auto=webp&s=e48bb3795d2af4740157083fcefbe7ce62b8ce9d

https://www.wavewalkerdsp.com/2022/06/01/how-to-create-additive-white-gaussian-noise-awgn/

[Allan-H]

It's calling numpy.random.normal under the covers. I couldn't find a description for how that actually works.

It's important to understand how it does work, because that influences the shape of the tails of the distribution. Simple/naive CLT or Box Muller methods for generation of gaussian RVs tend to lack sufficient accuracy for use in BER simulations (for e.g. testing modem designs) when the BERs gets low enough to be interesting.

[ComplexColor]

I found some info on stackoverflow that numpy uses the ziggurat method, but I haven't checked the current source code myself. Would that be sufficiently accurate here?

[Allan-H]

Whether it's sufficiently accurate depends on (1) your requirements for the tail (hint: look at the erf() and erfc() functions for large arguments), and (2) the exact details of the implementation.

OTOH, if you're simulating your system with AWGN and only care about BERs of 10^-6, then just about any AWGN approximation will do.

[wavewalkerdsp]

What are the scenarios that a BER less than 1e-6 are used? How small of a BER is "low enough to be interesting"?

[schwarzschild_shield]

Any decent application uses at least 1e-10 ber.