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

Wouter Lanneer,Yannick Lefevre,Paschalis Tsiaflakis,Marc Moonen,Werner Coomans,Carl Nuzman

doi:10.1109/access.2020.2967666

Wouter Lanneer, Yannick Lefevre + Show 4 more

Open Access

https://doi.org/10.1109/access.2020.2967666

Copy DOI

Abstract

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.

Highlights

Ultra-broadband digital subscriber line (DSL) networks like G.fast [2] aim at providing gigabit data speeds over very short copper lines by signaling in high frequencies
It is established that the achievable ZF-lattice reduction aided precoding (LRP) sum-rate is always upper bounded by the achievable ZF-Tomlinson-Harashima precoding (THP) sum-rate at high SNR values, leading to a sum-rate gap between both precoding schemes
A practically achievable bit-rate expression has been proposed for LRP, in order to cast the design problem as a weighted sum-rate (WSR) maximization in function of a precoder matrix and an integer matrix

Summary

INTRODUCTION

Ultra-broadband digital subscriber line (DSL) networks like G.fast [2] aim at providing gigabit (i.e. fiber-like) data speeds over very short copper lines (below 100 m) by signaling in high frequencies (up to 212 MHz). Like THP, LRP uses (non-linear) modulo operations to transmit equivalent lower power signals, it features a complete forward data path (like in LP schemes) This reduces the implementation complexity increase of the NLP scheme and results in a relaxed circuit timing problem compared to THP, especially for scenarios with a large number of users. The LRP design problem is formulated as the joint optimization of the precoder matrix and integer matrix in order to maximize the weighted sum-rate (WSR) under per-line power constraints.. This may increases the power of u (and of x) To deal with this issue, the multiplication is followed by a scalar (componentwise) non-linear modulo operation to bound the value of the transmit signal, as used in THP [16], [17], and the addition of a so-called dither vector v [v1, . In case of the latter, the perturbation term [Td]n at the receiver of user n corresponds to a sum of multiple integers with different scalings {τm} which cannot be completely removed by a single mod-τ n operation

ACHIEVABLE BIT-RATE EXPRESSION

GAIN SCALING OPTIMIZATION

CONCLUSION