Minimum redundancy for ISI free FIR filterbank transceivers

There has been great interest in the design of filterbank transceivers. Usually, with proper time domain equalization, the channel is modeled as an FIR filter. It is known that for FIR channels, the introduction of certain redundancy allows the receiver to cancel intersymbol interference (ISI) completely, and channel equalization is performed implicitly using FIR transceivers. This scheme allows us to trade bandwidth for ISI cancellation. In this paper, we derive the minimum redundancy required for the existence of FIR transceivers for a given channel. We see that the minimum redundancy is directly related to the zeros of the channel and to the Smith form of an appropriately defined channel matrix.