MIMO System Model in Matlab
In a wireless system, most of the noise is added by the receiver itself. The received signal is very weak (-100 dB or less is typical), and its power is comparable to the thermal noise of the receiver's amplifiers. That is the reason why noise is modeled as being added to the signal present in the antenna.

The noise still affects the estimated signal, of course; if the received vector is $r$, a naive ZF receiver would calculate

\begin{align} \hat{y} &amp;= H^{-1}r \\ &amp;= H^{-1}[Hy+n] \\ &amp;= y + Hn. \end{align}

Since the noise $Hn$ is correlated, this receiver has terrible performance.