Joint alpha-fairness based power allocation and user encoding ordering for zero-forcing nonlinear precoding in G.fast downstream transmission

In next generation digital subscriber line (DSL) systems, like G.fast that exploits high frequencies up to 212 MHz, the crosstalk levels among lines (i.e. users) get increasingly stronger. To precompensate the crosstalk in downstream transmission, nonlinear precoding (NLP) is proposed as a near-optimal dynamic spectrum management (DSM) technique. However, existing DSM algorithms for multi-tone NLP user encoding ordering (UEO) are rather heuristic in how they approach fairness and suffer from substantial suboptimality. In this paper, we develop a suit of novel DSM algorithms for joint power allocation and UEO that enforce a generalized alpha-fairness policy, called alpha-fair UEO. Since finding the globally optimal UEO is a combinatorial optimization problem with excessive computational complexity, first an algorithm is developed that uses iterative per-tone exhaustive searches and provides near-optimal approximate solutions. To further improve the computational complexity, next two efficient suboptimal methods are suggested to replace the expensive pertone exhaustive searches, leading to two other alpha-fair UEO algorithms which are tractable for large scenarios against only little performance loss. Simulations of a G.fast cable binder show that alpha-fair UEO achieves a trade-off between fairness and performance that outperforms the state-of-the-art UEO methods.