Lattice Reduction Aided Precoding Design in Downstream G.fast DSL Networks

• Published in: IEEE access Vol. 8; pp. 19208 - 19220
• Main Authors: Lanneer, Wouter, Nuzman, Carl, Lefevre, Yannick, Tsiaflakis, Paschalis, Coomans, Werner, Moonen, Marc
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Crosstalk; Design optimization; DSL; dynamic spectrum management; Gfast; Integers; lattice reduction; Lattices; Lower bounds; Matrices (mathematics); Maximization; non-linear pre- coding (NLP); Optimization; Precoding; Receivers; Reduction; Scalars; Signal to noise ratio
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2020.2967666

As a non-linear precoding alternative to Tomlinson-Harashima precoding (THP), in this paper, so-called lattice reduction aided precoding (LRP) is considered as a crosstalk precompensation technique for downstream transmission in G.fast DSL networks. First, a practically achievable bit-rate expression for LRP is proposed in function of the precoder and integer matrix. The problem then consists of a joint precoder and integer matrix design in order to maximize the weighted sum-rate (WSR) under per-line power constraints. For a fixed integer matrix, zero-forcing (ZF) precoder matrix design simplifies to gain scaling optimization with complex gain scalars, for which a successive lower bound maximization method is presented. Additionally, it is established that the achievable ZF-LRP sum-rate is upper bounded by the achievable ZF-THP sum-rate at high SNR. For computing the optimal precoder matrix, on the other hand, an efficient method is developed by leveraging on the equivalence between the WSR maximization and the weighted sum of mean squared error (MSE) minimization, leading to a locally-optimal MMSE-LRP solution. Simulations with a measured G.fast cable binder are provided to compare the proposed LRP schemes with THP schemes.