Optimal FIR transmit filterbanks and non-linear DFE receivers are derived for block-based transmissions over frequency-selective channel.The joint optimization of precoders and equalizers is based on the maximum mutual information criteria subject to fixed transmission power constraint.We get a new result from which the precoder can be interpreted as converting the frequency fading channel into a set of independent flat fading subchannels

and the feedback filter is equivalent to a direct subchannel

thus the SNR of each subchannel is increased and the system has better overall BER performance while maintains all the advantages of Scaglione's optimization.Simulations illustrate the merits of our design.