Baseband vs Passband simulation in terms of noise impact

Question

From other posts I understood that it is normally no problem to simulate a communication system in the baseband though it is carrier modulated in reality. It just speeds up the simulation.

But what if I want to add noise to the signal and the noise shape is depending on the frequency? Of course I want to superpose my signal with the noise around my carrier frequency and not the baseband noise. I guess that simply adding noise and baseband signal would falsify the simulation...

Is there a solution so that I can still simulate in the in the baseband? Maybe to transfer the noise to baseband somehow?

Answer 1

In fact, bandpass noise (or any kind of noise process) can be modelled as a system $h(t)$. As so, there is a lowpass equivalent $h_l(t)$ such that

\begin{equation} h(t) = Re[h_l(t)\exp(j2\pi f_0t)] \end{equation}

So you can work with $h_l(t)$ in the baseband.