A new precoding for ISI cancellation using multirate filterbanks

In this paper, we propose a new precoding scheme for intersymbol interference (ISI) cancellation using multirate filterbanks. The ISI channel may not have inverses, such as frequency-selective fading channels. We present a necessary and sufficient condition on an FIR ISI transfer function in terms of its zero set such that a linear FIR ideal equalizer exists. The condition is easy to check and satisfy. Designs of pre/postcodings are also presented. A numerical example is presented to illustrate the theory.