Simulation of wireless communication system
This is done to change the noise power, keeping signal power same, thus effective changing the SNR. If you keep the signal to unit power and modify the variance of noise in accordance with $\frac{1}{\sqrt{SNR}}$. You would effectively get the desired SNR for the  received signal. In Monte Carlo simulations this is done many times for a fixed SNR to get the average bit error rate for that SNR point. Usually there would be a loop over SNR as well to simulate for different SNR points.

You could acheive the same thing by keeping the noise to be unit varainace and multiple by $\sqrt{SNR}$ to the signal part.

We use the linear scale because that is how the SNR actually impacts reception. The receiver signal model is linear in signal and noise.

Sample code:


  $$y = signal + \frac{randn(1,1)}{\sqrt{SNR}}$$
  
  Or
  
  $$y = \sqrt{SNR}*signal + randn(1,1)$$


Both have signal to noise ratio as SNR