Adding white noise to complex signal (complex envelope) Good day everyone.
So, I run in to trouble - How to add white noise to signal samples?
For now I'm working with MSK signal - quadrature modulator and quadrature demodulator + Viterbi processor.  My signal samples at TX and RX side represents Q and I signals of modulator(real and complex part of the signal). Model works nice in ideal situation, without any noise and other interference.
So, I'm working with complex envelope of the MSK signal with amplitude equal to one. Currently, I would like to test my demodulator with some noise.
It looks like, I just need to add (+) samples from my noise generator to samples of transmitted signal. But I'm not sure if this is correct way,

Should I sum both Q and I channels to one sample of noise signal or not?
And I'm pretty confused how to determine signal to noise ratio after this. I would like to measure bit error ratio at some SNR points. As I read in some books changing $\sigma$ parameter of white noise generator will play a role here, but still how to determine SNR in numbers after this?
If you want a complex white noise sample with variance $N_0$, then you should generate two independent noise samples each with variance $\frac{N_0}{2}$. The two samples that you generate make up the real and imaginary parts of the desired complex noise sample. The resulting complex value will have the desired variance $N_0$. You should then sum this with your complex baseband signal to get the effect that you want.