Thread Subject: how to simulate correlated gaussian white noise of different channel

Hello everyone：

I am simulating multi-channel data acquistion process.
Normally, the noise of each channel is considered as
uncorrelated gaussian white noise. However, in reality, the
channels are usually correlated,because of the imperfect
design. In this case, the noise are no long uncorrelated
gaussian white noise.

So, My questions are:
what is the distribution of noise from these correlated
channels?
How to simulate the noise distribution when each channel is
correlated?

Thanks a lot!