[Paper Review] Deep-LMS for gigabit transmission over unshielded twisted pair cables

Avi Zanko, Itsik Bergel+1 more|arXiv (Cornell University)|May 30, 2017

Power Line Communications and Noise21 references3 citations

TL;DR

This paper proposes Deep-LMS, a novel adaptive crosstalk cancellation algorithm for gigabit-over-DSL systems using unshielded twisted pair cables. Inspired by deep neural networks, it employs a sequential, layered adaptive preprocessing matrix to accelerate convergence of the conventional LMS algorithm, achieving significantly faster convergence—especially critical in the high-bandwidth, ill-conditioned G.fast environment—without sacrificing stability or precision.

ABSTRACT

In this paper we propose a rapidly converging LMS algorithm for crosstalk cancellation. The architecture is similar to deep neural networks, where multiple layers are adapted sequentially. The application motivating this approach is gigabit rate transmission over unshielded twisted pairs using a vectored system. The crosstalk cancellation algorithm uses an adaptive non-diagonal preprocessing matrix prior to a conventional LMS crosstalk canceler. The update of the preprocessing matrix is inspired by deep neural networks. However, since most the operations in the Deep-LMS algorithm are linear, we are capable of providing an exact convergence speed analysis. The role of the preprocessing matrix is to speed up the convergence of the conventional LMS crosstalk canceler and hence the convergence of the overall system. The Deep-LMS is important for crosstalk cancellation in the novel G.fast standard, where traditional LMS converges very slowly due to the ill-conditioned covariance matrix of the received signal at the extended bandwidth. Simulation results support our analysis and show significant reduction in convergence time compared to existing LMS variants.

Motivation & Objective

• Address the slow convergence of traditional LMS algorithms in high-bandwidth G.fast systems due to ill-conditioned signal covariance matrices.
• Overcome the limitations of fixed-step-size LMS and NLMS in vectoring-based DSL systems with extended bandwidth (up to 212 MHz).
• Develop a low-complexity, rapidly converging crosstalk cancellation algorithm suitable for real-time, high-data-rate upstream transmission over copper lines.
• Enable practical gigabit-per-second data rates over existing copper infrastructure by improving convergence speed in vectored DSL systems.
• Provide an exact convergence analysis for a nonlinear, layered adaptive algorithm grounded in linear operations, enabling theoretical performance guarantees.

Proposed method

• Propose a Deep-LMS architecture that applies a non-diagonal, adaptive preprocessing matrix before a conventional LMS crosstalk canceler, emulating deep network layering.
• Use a sequential, layer-by-layer update of the preprocessing matrix, where each layer adapts to reduce the effective condition number of the input signal covariance matrix.
• Design the update rule based on gradient descent principles, with step-sizes derived from the eigenstructure of the input correlation matrix to accelerate convergence.
• Maintain linearity in all operations to allow exact convergence speed analysis, unlike standard deep networks.
• Integrate the preprocessing matrix into the LMS framework such that the overall system minimizes the mean square error (MSE) at the receiver output.
• Ensure the algorithm remains computationally efficient by leveraging the fact that all operations are linear, enabling real-time implementation in high-throughput DSL systems.

Experimental results

Research questions

• RQ1 Can a layered, adaptive preprocessing matrix significantly accelerate the convergence of the conventional LMS crosstalk canceler in high-bandwidth DSL systems?
• RQ2 How does the Deep-LMS algorithm’s convergence speed compare to existing LMS variants (e.g., NLMS, diagonal step-size LMS) under the same ill-conditioned channel conditions?
• RQ3 What is the theoretical convergence rate of the Deep-LMS algorithm, and can it be analytically bounded given the linear structure of the algorithm?
• RQ4 Does the proposed algorithm maintain stability and accuracy while achieving faster convergence in the G.fast standard’s extended bandwidth (up to 212 MHz)?
• RQ5 Can the Deep-LMS framework be analyzed exactly despite its non-traditional, multi-layered structure, given that all operations remain linear?

Key findings

• The Deep-LMS algorithm achieves significantly faster convergence than conventional LMS and its variants, especially in the high-bandwidth, ill-conditioned G.fast environment.
• Theoretical analysis confirms that the convergence rate is governed by the eigenvalue spread of the input correlation matrix, with the preprocessing matrix effectively reducing this spread.
• Simulation results demonstrate that the Deep-LMS reduces convergence time by orders of magnitude compared to standard LMS, particularly in scenarios with high crosstalk and extended bandwidth.
• The algorithm maintains stability and accuracy due to the exact convergence analysis enabled by its linear structure, avoiding the instability issues common in nonlinear deep networks.
• The SINR at the receiver output is bounded below by a function of the MSE, and the algorithm ensures that the effective channel response approaches identity, minimizing interference.
• The optimal step-size matrix is shown to be proportional to the inverse of the eigenvalues of the correlation matrix, and the algorithm converges to the MMSE solution with minimal misadjustment.