The Multitone Channel

Multitone quadrature amplitude modulation (QAM) is an interesting candidate for data transmission over linear channels with frequency dependent transfer functions. In this paper, the maximum bit rate of multitone QAM over a general linear channel is found. First, the overall bit rate for an AWGN channel with a two-level transfer function is maximized, using a multitone QAM system. The power distribution between the tones and the number of bits/symbol per tone is optimized for a given symbol error rate. Extending these results to the general channel, it is shown that the optimum power division for multitone signals is similar to the water-pouring solution of information theory. Furthermore, multitone QAM performance is about 9 dB worse than the channel capacity, independent of the channel characteristics. The multitone results throughout are compared to those of an equivalent single-tone linearly equalized system. The comparison shows that the multitone system is useful for some channels, e.g., those with deep nulls in the transfer function. The maximum bit rate over a twisted-pair channel which is performance dominated by near-end crosstalk (NEXT) is also found.