Optimal transmit spectra for communication in the presence of crosstalk and imperfect echo cancellation

In many communication systems, including Digital Subscriber Lines, performance is severely limited by crosstalk interference. Previous work has presented a general framework for designing optimal transmit spectra for crosstalk avoidance. The technique uses the channel, noise, and interference characteristics to setup and solve an optimization problem which maximizes the capacity of neighboring lines, while maintaining spectral compatibility with other services. This joint signaling and optimal power distribution technique yields significant performance gains over conventional fixed spectra in terms of bit-rates and performance margins. In general, the spectra that result from this scheme have both an echo cancelled and frequency division multiplexed region. To ease the analysis, this technique assumed that the echo canceller has perfect echo rejection capability, which in practice is not true. In this paper, we propose an extension to these techniques, in which we factor the performance of practical echo cancellers into the optimization procedure. When echo rejection is not perfect, as is generally the case, our technique shows significant performance gains over previous techniques. As the performance of the echo canceller increases, our technique converges to the same solution.