Redundant filterbank precoders and equalizers-part I: Unification and optimal designs

Transmitter redundancy introduced using fllterbank precoders generalizes existing modulations including OFDM, DMT, TDMA, and CDMA schemes encountered with single- and multiuser communications. Sufficient conditions are derived to guarantee that with FIR fllterbank precoders, FIR channels are equalized perfectly in the absence of noise by FIR zero-forcing equalizer fllterbanks, irrespective of the channel zero locations. Multicarrier transmissions through frequencyselective channels can thus be recovered, even when deep fades are present. Jointly optimal transmitter-receiver fllterbank designs are also developed based on maximum-output signal-to-noise ratio (SNR) and minimum mean-square error criteria under zero forcing and fixed transmitted power constraints. Analytical performance results are presented for the zero-forcing filterbanks and are compared with mean-square error and ideal designs using simulations.