Block transmission over dispersive channels: transmit filter optimization and realization, and MMSE-DFE receiver performance

Optimal transmit filters for packet-based data transmission on dispersive Gaussian-noise linear time-invariant channels are derived by maximizing the mutual information, subject to a fixed input power budget. A quasi-stationary approximation to the optimal nonstationary input covariance process is derived and shown to exhibit negligible mutual information loss from the optimal case, for situations of most practical interest. Moreover, this quasi-stationary approximation results in efficiently computed lattice or pole-zero implementations of the transmit filter. By considering the popular finite-impulse-response minimum-mean-square-error decision-feedback equalizer (FIR MMSE-DFE) as a receiver structure, we show that transmitter optimization results in an appreciable improvement in the decision-point signal-to-noise ratio. Finally, we show that, as the output blocklength becomes infinite, the optimum finite-dimensional nonstationary input covariance process converges to a stationary process whose power spectrum obeys the well-known water-pouring distribution.