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A Block Least Mean Square Method for Fiber Longitudinal Power Profile Monitoring

Paolo Serena, Chiara Lasagni, Alberto Bononi, Fabien Boitier, Joana Girard-Jollet

Abstract

We propose a block least mean square (LMS) algorithm to monitor the longitudinal power profile of a fiber-optic link through receiver-based digital data from a coherent detector. Compared to the benchmark least squares (LS) method, the proposed algorithm does not require large matrix inversions or batch processing, thus allowing the received data to be processed in blocks of minimum size by an overlap-save algorithm, reducing complexity and latency. We propose an efficient implementation of the method with a stochastic gradient update leveraging a key computation in the frequency domain, offering computational savings over state-of-the-art monitoring techniques. We test the proposal in different scenarios by means of numerical simulations.

A Block Least Mean Square Method for Fiber Longitudinal Power Profile Monitoring

Abstract

We propose a block least mean square (LMS) algorithm to monitor the longitudinal power profile of a fiber-optic link through receiver-based digital data from a coherent detector. Compared to the benchmark least squares (LS) method, the proposed algorithm does not require large matrix inversions or batch processing, thus allowing the received data to be processed in blocks of minimum size by an overlap-save algorithm, reducing complexity and latency. We propose an efficient implementation of the method with a stochastic gradient update leveraging a key computation in the frequency domain, offering computational savings over state-of-the-art monitoring techniques. We test the proposal in different scenarios by means of numerical simulations.
Paper Structure (10 sections, 25 equations, 10 figures)

This paper contains 10 sections, 25 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Analog twin
  4. Digital twin
  5. Block LMS based on overlap-save
  6. Block diagram
  7. Polyphase implementation
  8. Numerical results
  9. Conclusions
  10. Overlap-save Algorithm

Figures (10)

  • Figure 1: (a): system identification problem setup. The objective is to find the adaptive taps $w_{l}$ of the digital twin that minimize the error $e$ between its output $y$ and the desired output $d$ in the presence of noise. (b): LMS concept based on a stochastic gradient update using the most recent observables. (c): Least squares method where all observables (red dots) are used to fit the desired function, here a plane.
  • Figure 2: LMS block diagram for monitoring the longitudinal power profile (represented by the filled taps) at coordinates $z_{l}$. The dark circle with a light ring represents FFT, while inverted colors indicate IFFT. An equalized replica of the data, $\mathbf{d}_{k}^{(\text{eq})}$, is a concomitant outcome of the monitoring procedure.
  • Figure 3: (a) One branch of the block diagram shown in Fig. \ref{['fig:LMS-block-diagram']}. (b) Polyphase implementation of the branch. The two structures are equivalent with similar complexity; however the polyphase one works at a halved sampling rate.
  • Figure 4: Top: A multianomaly case with six loss anomalies of $0.25$ dB every $15$ km. Bottom: net loss profile in the presence of backward Raman pumping. No additive noise.
  • Figure 5: RMSE vs. the number of symbols processed by the LMS algorithm at different normalized LMS step sizes $\bar{\mu}$. Three-span link with anomaly of $1$ dB after $125$ km. Taps initialized with the nominal fiber loss.
  • ...and 5 more figures