Redundant filterbank precoders and equalizers Part I: Unification and optimal designs

Transmitter redundancy introduced using filterbank precoders generalizes ex isting modulations including OFDM, DMT, TDMA, and CDMA schemes encountered with single- and multiuser communications. Sufficient conditions are derive d to guarantee that with FIR filterbank precoders FIR channels are equalize d perfectly in the absence of noise by FIR zero-forcing equalizer filterban ks, irrespective of the channel zero locations. Multicarrier transmissions through frequency-selective channels can thus be recovered even when deep f ades are present. Jointly optimal transmitter-receiver filterbank designs a re also developed, based on maximum output SNR and minimum mean-square erro r criteria under zero-forcing and fixed transmitted power constraints. Anal ytical performance results are presented for the zero-forcing filterbanks a nd are compared with mean-square error and ideal designs using simulations.