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A Low-Complexity Detector for Memoryless Polarization-Multiplexed Fiber-Optical Channels

Christian Häger, Lotfollah Beygi, Erik Agrell, Pontus Johannisson, Magnus Karlsson, Alexandre Graell i Amat

TL;DR

The paper addresses nonlinear phase noise in polarization-multiplexed fiber channels by extending a low-complexity NLPN compensation detector from SP to PM-$M$-PSK. The authors propose amplitude-dependent phase rotations to transform NLPN-distorted decision boundaries into straight lines, enabling simple 2D detection while maintaining much of the ML performance. Analytical SER expressions for PM-Det1 and PM-Det2 are derived, and results show PM schemes outperform SP at the same data rate in the linear regime, with PM-Det2 offering notable gains in NL regimes. The work highlights practical detector designs suitable for memoryless channels and dispersion-managed links, while noting the memoryless model’s limitations at high symbol rates.

Abstract

A low-complexity detector is introduced for polarization-multiplexed M-ary phase shift keying modulation in a fiber-optical channel impaired by nonlinear phase noise, generalizing a previous result by Lau and Kahn for single-polarization signals. The proposed detector uses phase compensation based on both received signal amplitudes in conjunction with simple straight-line rather than four-dimensional maximum-likelihood decision boundaries.

A Low-Complexity Detector for Memoryless Polarization-Multiplexed Fiber-Optical Channels

TL;DR

The paper addresses nonlinear phase noise in polarization-multiplexed fiber channels by extending a low-complexity NLPN compensation detector from SP to PM--PSK. The authors propose amplitude-dependent phase rotations to transform NLPN-distorted decision boundaries into straight lines, enabling simple 2D detection while maintaining much of the ML performance. Analytical SER expressions for PM-Det1 and PM-Det2 are derived, and results show PM schemes outperform SP at the same data rate in the linear regime, with PM-Det2 offering notable gains in NL regimes. The work highlights practical detector designs suitable for memoryless channels and dispersion-managed links, while noting the memoryless model’s limitations at high symbol rates.

Abstract

A low-complexity detector is introduced for polarization-multiplexed M-ary phase shift keying modulation in a fiber-optical channel impaired by nonlinear phase noise, generalizing a previous result by Lau and Kahn for single-polarization signals. The proposed detector uses phase compensation based on both received signal amplitudes in conjunction with simple straight-line rather than four-dimensional maximum-likelihood decision boundaries.

Paper Structure

This paper contains 6 sections, 3 theorems, 10 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model and Preliminaries
  3. The ML Receiver for SP-$M$-PSK
  4. Receivers for PM-$M$-PSK
  5. Performance Analysis
  6. Conclusion

Key Result

Lemma 1

Let $f_{X}(x)$ be the (periodic) pdf of a random angle $X$. Furthermore, let the pdf be symmetric around $x_\text{max} \in (-\pi, \pi]$, the value where $f_{X}(x)$ has its maximum. If the pdf decreases monotonically from $x_\text{max}$ to $x_\text{max} \pm \pi$, then $x_\text{max} = -\arg\Psi_{X}(

Figures (3)

  • Figure 1: Receiver for PM-$M$-PSK with (a) separate detection (PM-Det1) and (b) joint calculation of the amplitude-dependent phase rotations (PM-Det2).
  • Figure 2: Scatter plots in the x polarization for (a) no compensation, (b) compensation according to Fig. 1(a), and (c) according to Fig. 1(b). Decision boundaries in (b) and (c) are straight lines. In (a), the boundaries are spiral shaped and depend on the received amplitude in the y polarization.
  • Figure 3: The SER of SP and PM systems with 4-PSK versus the transmitted power per polarization $P_\text{t}$.

Theorems & Definitions (3)

  • Lemma 1
  • Theorem 1
  • Theorem 2