A separation principle for optimum biorthogonal dmt without a high bit rate assumption

We consider the design of optimum biorthogonal, as opposed to orthonormal, discrete multitone (DMT) systems supporting a service whose quality of service (QoS) requirements are quantified by bit rate and symbol error rate specifications. Our goal is to minimize 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. We find an optimum bit loading scheme that distributes the bit rate transmitted across the various subchannels, and an optimum transceiver. Earlier papers, [2] and [4] showed the following: (i) Relaxing the orthonormality constraint yields no performance improvement. (ii) The optimum transceiver is unaffected by changing service characteristics, and depends only on the channel and interference conditions. (iii) The QoS requirements, only affect bitloading. These conclusions form a separation principle that has important implications to wireline applications like DSL. These papers, [2] and [4], however worked with an approximation that only works if each subchannel supports a very high data rate. In this paper we show that even if one relaxes this high bit rate assumption, (i-iii) still hold.