I have to make a correction to what I have posted above. The output signal from the coherent detection block is not still processed in electrical domain, so the amount of noise magnitude is not added to the symbols, as opposed to what I said about the shift being made and so on. However just to make sure Damian’s suggestion is right (which it most probably is), I would appreciate to know the distribution of the noise added to the signal in theory. I have attached the distribution of the magnitude of the PIN noise that I have plotted using Matlab. Thanks!