# Adding Noise to a normalized signal

I saw this adding noise to a signal but I still have some questions.

I have normalized IQ data of a signal. Lets suppose that I know what the current SNR is (say 8dBm). How can I add noise to the I and Q components of my signal so that it has a new SNR (of course one with a worse SNR then what I am starting off with)?

My problem is 2 fold, the first one is, how can I add a precise amount of noise to an already noisy signal? I want to control what the new SNR will be, so I need to be careful how much noise I add.

The second is, technically, I have normalized I and Q data. How do I add noise to the I and Q components? Or, do I just need to recreate the signal with I and Q, add the noise, and then break it back up into I and Q components?

Thank you all for your help :)

UPDATE**** Attempt # 2: After thinking about this overnight, I do not believe that looking at the peaks does anything useful. SNR is a measure of a signal power to signal noise, so I think I need to look at the power of these signals. With that in mind, here is my thought: We start with:

S = clean signal power

N = noise power

Ps = observer S + n power (I can measure this)

SNR = signal to noise ratio in watts

S/N = SNR, with this being a known SNR in watts.

S = SNR*N, re-writing the equation

Ps = S + N

Ps = SNR*N+N = N(1+SNR)

N = Ps/(1+SNR), so now we can know the noise power

S = SNR*N, and we can find the signal power

If the above is correct, then when we go to add a new noise, we can measure the power of this noise signal before adding it, call it N2.

(S)/(N+N2) = newSNR

Does that look correct?

Thank you all for your help.