[Paper Review] Correlated Eigenvalues Optical Communications

Wenqi Zhang, Tao Gui+6 more|arXiv (Cornell University)|Nov 25, 2017

Optical Network Technologies24 references3 citations

TL;DR

This paper proposes a noise modeling framework for nonlinear Fourier transform (NFT)-based optical communications, demonstrating that eigenvalue perturbations due to fiber transmission are correlated across channels and can be modeled as the accumulation of independent, segment-wise noise contributions. By exploiting this correlation, the authors show that system throughput can be maximized through optimized signal constellation design, validated experimentally over a 150 km fiber link using 2-soliton pulses and nonlinear spectral processing.

ABSTRACT

There is a fundamental limit on the capacity of fibre optical communication system (Shannon Limit). This limit can be potentially overcome via using Nonlinear Frequency Division Multiplexing. Dealing with noises in these systems is one of the most critical parts in implementing a practical system. In this paper, we discover and characterize the correlations among the NFT channels. It is demonstrated that the correlation is universal (i.e., independent of types of system noises) and can be exploited to maximize transmission throughput. We propose and experimentally confirm a noise model showing that end-to-end noise can be modeled as the accumulation of noise associated with each segment of optical communication which can be dealt with independently. Also, each point noise can be further decomposed into different components, some of which are more significant (and even dominating) than others. Hence, one can further approximate and simplify the noise model by focusing on the significant component.

Motivation & Objective

• To address the fundamental challenge of fiber nonlinearity limiting transmission capacity beyond the linear Shannon limit.
• To overcome the limitations of traditional linear signal processing in nonlinear optical fibers by leveraging the nonlinear Fourier transform (NFT).
• To model and exploit eigenvalue noise correlations in NFT-based optical communication systems for improved system performance.
• To develop an analytical framework that decomposes end-to-end noise into segment-wise, approximately independent perturbations for tractable modeling.
• To enable practical implementation of nonlinear frequency division multiplexing (NFDM) by characterizing and mitigating noise effects on eigenvalues.

Proposed method

• Uses the Darboux transformation method to recursively generate 2-soliton pulses with controlled spectral amplitudes and physical bandwidth at the transmitter.
• Employs a nonlinear Schrödinger equation (NLSE) model with distributed Raman amplification and negligible linear loss to simulate fiber propagation.
• Applies the Ablowitz-Ladik algorithm to compute nonlinear Fourier coefficients and the Newton-Raphson method for root searching in the spectral domain.
• Models eigenvalue noise as the accumulation of small, segment-wise perturbations from each fiber span, assuming weak correlation between segments.
• Uses a training symbol for timing synchronization and pilot tones to estimate and compensate laser phase noise and frequency offset at the receiver.
• Applies offline digital signal processing (DSP) to reconstruct and analyze eigenvalue perturbations from sampled I/Q signals using a 90° hybrid and balanced photodetectors.

Experimental results

Research questions

• RQ1 How do eigenvalue perturbations behave across multiple fiber spans in NFT-based optical communication systems?
• RQ2 To what extent are eigenvalue noises correlated, and can this correlation be exploited to improve system throughput?
• RQ3 Can end-to-end eigenvalue noise be modeled as the accumulation of independent, segment-wise noise contributions?
• RQ4 How does the proposed noise model compare to traditional additive white Gaussian noise (AWGN) assumptions in nonlinear spectral domain communications?
• RQ5 Can the noise model be extended to include transmitter and receiver noise sources in a unified framework?

Key findings

• Eigenvalue perturbations in NFT-based optical systems are correlated across channels and are universal across different types of system noise.
• The end-to-end noise in eigenvalues can be effectively modeled as the accumulation of independent, segment-wise noise contributions from each fiber span.
• The correlation between segment-wise noise components is weak enough to allow the assumption of statistical independence, simplifying the noise model.
• The proposed noise model enables the design of optimized signal constellations in the nonlinear spectral domain, leading to higher system throughput.
• Experimental results over a 150 km fiber loop with 2-soliton pulses confirm the validity of the noise model and the feasibility of exploiting eigenvalue correlations.
• The framework is extendable to include transmitter and receiver noise, with spectral amplitude perturbations also modeled as accumulated independent noise effects.