Optimum ISI-Free DMT Systems with Integer Bitloading and Arbitrary Data Rates: When Does Orthonormality Suffice?

We consider the design of optimum ISI-free, discrete multitone transmission (DMT) systems designed to achieve a quality of service (QoS) requirement quantified by bit rate and symbol error rate specifications. The optimality is in the sense of minimizing the transmitted power given the QoS specifications subject to the knowledge of the channel and colored interference at the receiver input of the DMT system. Earlier papers, obtained their optimum DMT design based on approximations that included high bit rates and/or real (as opposed to integer) bit loading schemes, and showed that orthonormal transforms suffice for optimality. In this paper we relax both the high bit rate and the integer bitloading approximation, and provide sufficient conditions on the underlying modulation schemes for which orthonormal DMT remains optimum