How to Generate White Gaussian Noise with Known PSD in MATLAB
The specific PSD is basically white noise which was filtered with a filter which its Magnitude is the same as the PSD.

This is a result of the Wiener Khinchin Theorem.

So if you have the shape of the PSD do the following:


Create a filter which in the Frequency domain has the magnitude (More accurately the squared magnitude $ {\left| H \left( \omega \right) \right|}^{2} $) of the PSD you want (Namely, you don't care about the phase).
Create a White Noise.
Filter the white noise with the filter created in 1.


I would note that in the case of a White Noise the PSD is constant.
Hence in this case all you need is to generate white noise with normalized variance and then to multiply it by a constant (Changing its variance) to the value you're after.

Enjoy...