What's the expression of the noise for a RF signal? I am confused about how to give the expression of noise. Can someone tell me if my equations are correct?

If the received RF signal is expressed as: 



where



If I want to add a AWGN, can I give the expression of noise as the following?



If not, what is the correct equation of the noise? Also, in the MATLAB simulation, I often add noise to a baseband signal by using: sqrt(NoisePower) * randn(). What should I do in the case of bandpass signal? Thanks guys!
Yes, you can represent your bandpass noise as:

$ n(t) =n_I(t)\cos(2\pi f_c t)-n_Q(t)\sin(2\pi f_c t),$

where $n_I(t)$ and $n_Q(t)$ represent the inphase and quadrature components of the noise signal. In matlab you can generate this sequence as

n = sqrt(Npwr/2) *(randn(1,len)+j*randn(1,len))


The scaling factor is different than in the baseband case because both the inphase and quadrature components have unit power (before scaling), so when added together the total power is equal to 2 and therefore the $\sqrt{2}$ factor is needed in the scaling factor to get unit power.