Adding Poisson noise to a time series signal I'm working on a radiation detection problem. I have simulated some measurement count data and want to add an amount of Poisson background noise to achieve a certain SNR. Radiation count measurement (due to the background radiation) is given by the Poisson random variable. 

After searching the web, I'm not seeing any clear indication of how to go about it doing this. Is there a similar method as in the case of AWGN? (https://www.mathworks.com/help/comm/ref/awgn.html).
If your data $\mathbf{x}$ has variance $\text{var}(\mathbf{x})$ and you want to add Poisson noise to it with signal to noise ratio of $\text{SNR}$ dB, then you can just generate Poisson random numbers with appropriate variance. The variance of the noise $\mathbf{n}$ you need is $\text{var}(\mathbf{n})=\frac{\text{var}(\mathbf{x})}{10^{\text{SNR}/10}}$. So now you just need to use your Poisson random number generator and then add the noise to get the noisy data: $\mathbf{x}+\mathbf{n}$