Direct sequence spread spectrum modulation
Multiplying $r_t$ by the pseudo random spreading code does different things to $m_t$ and $i_t$: Because $m_t$ is correlated to the spreading code, it is despread while keeping its power, so the power spectral density will be higher in a small bandwidth (due to remaining modulation). On the other hand, $i_t$ is not correlated and is translated to wideband noise again.

This gives you the opportunity to filter with a bandpass and just use the band, where the signal to noise ratio is above unity.

The noise is not eliminated, but its overall power is reduced, because your bandpass rejects some of the noise (that is still wideband) and passes all of the signal (that is now narrowband).