α-Fair Dynamic Spectrum Management for QRD-Based Precoding with User Encoding Ordering in Downstream G.fast Transmission

In next generation DSL networks such as G.fast, employing discrete multi-tone transmission in high frequencies up to 212 MHz, the crosstalk among lines reaches very high levels. To precompensate the crosstalk in downstream transmission, QRD-based precoding has been proposed as a near-optimal dynamic spectrum management (DSM) technique. However, the performance of QRD-based precoding is greatly affected by the user encoding ordering (UEO). Since current multi-tone UEO methods are rather heuristic in the way they approach fairness, we develop in this paper a set of novel DSM algorithms for joint power allocation and UEO that enforce a generalized α- fairness policy. Since finding the globally optimal UEO entails a combinatorial optimization problem with excessive computational complexity, an iterative algorithm is proposed that uses pertone exhaustive searches (PTES's) and provides near-optimal approximate solutions. To further reduce the computational complexity, two suboptimal methods are suggested to replace the expensive PTES's, leading to two additional α-fair DSM algorithms that are tractable for large scenarios against little performance loss. Simulations of a G.fast cable binder show that the α-fair DSM algorithms achieve an efficient trade-off between fairness and performance in contrast to current UEO methods.