What is the relation between noise (AWGN) variance and number of antennas?

I'm working in two Matlab scripts trying to simulate a MIMO system using OFDM (downlink) and SC-FDE (uplink).

My question is: for different numbers of transmit and receive antennas, what is the relationship between the AWGN variance and the number of antennas? Does it depend if it is uplink or downlink?

I'm using matricial equations like: Y = HX + N , with matrix dimensions: Y(NR x length) , H(NR x NT) , X(NT x length) , N(NR x length)

Usually, the model is that every receiver antenna picks up noise of the same PSD, $N_0/2$. This means that the variance of noise samples in each quadrature branch is $N_0/2$. This noise is local to each antenna and is independent of the rest of the system.
There is no relationship if the noise if white. For the system $$\mathbf{y}=\mathbf{H}\mathbf{x}+\mathbf{n}$$ where $$\mathbf{n}$$ is $$K$$-dimensional, the covariance matrix is $$\sigma_n^2\mathbf{I}_{K\times K}$$, where $$\sigma_n^2$$ is the noise variance, and $$\mathbf{I}_{K\times K}$$ is the $$K\times K$$ identity matrix.