Complete characterization of channel independent general DMT systems with cyclic prefix

The following fact is well known about discrete multitone transmission (DMT) systems: in the special case of orthogonal frequency division multiplexing (OFDM) when the input and output transforms are the IDFT and DFT matrices respectively, and the length of cyclic prefix is longer than the channel length. ISI free transmission is possible for almost all channel parameter values. In this paper, we ask whether more general DMT systems with cyclic prefix enjoy similar channel resistance? We show that among all possible FIR transmitting and receiving filters, of arbitrary order, channel resistant ISI free transmission requires (a) that the receive filter be matched to the transmit filters, and (b) that to within a scaling and delay, the transmit and receive filters it must have IDFT and DFT coefficients. Thus we prove that, should cyclic prefix be applied, then trivial variations of OFDM are the only channel resistant DMT system.