Optimumisi-free DMT systems withconcave SNR tobit rate relations: when does othonornmality suffice?

We consider the design of optimum ISI-free, discrete multi- tone transmission (DMT) systems designed to achieve a quality of service (QoS) requirement quantified by bit rate and symbol error rate (SER) specifications. 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. In our earlier papers we considered conditions under which relaxation of an orthonormality requirement produced no improvements, and which produced an attractive modular optimizing solution. The conditions in question were on a function that for a given SER related the bit rate to the SNR required to achieve this SER and involved a convexity requirement not satisfied by power efficient modulation schemes such as FSK, orthogonal and biorthogonal modulation. For these schemes this function is in fact concave. In this paper we show that concavity also suffices for these attractive properties of optimality to hold.