# the best pre emphasis for MMSE equalizer

The system consists of multiple low-pass filter and noise, $$h_1$$, $$h_2$$, $$h_3$$, ..., $$n_1$$, $$n_2$$, $$n_3$$, ...

At the transmitter, the power of signal is fixed; and at the receiver, MMSE equalizer is used to minimize the MSE.

My question is that if we can pre-emphasis the signal in the transmitter to improve the overall performance. If the distribution of signal and noise is known, what is the optimal pre-emphasis system?