[Paper Review] Maximum transmission reach for optical signals in elastic optical networks employing band division multiplexing

Esteban Paz, Gabriel Saavedra|arXiv (Cornell University)|Nov 4, 2020

Optical Network Technologies20 citations

TL;DR

This paper proposes a method to determine the maximum transmission reach for optical signals in elastic optical networks using band division multiplexing (BDM), accounting for linear and nonlinear impairments such as amplified spontaneous emission (ASE) noise and inter-channel stimulated Raman scattering (ISRS). Using a closed-form Gaussian noise model, it computes signal-to-noise ratio (SNR) per band across E, S, C, and L bands, deriving maximum reach for modulation formats (BPSK to 256QAM) at BER thresholds of 4.7×10⁻³, 10⁻⁶, and 10⁻⁹, with L band achieving the longest reach due to lowest ASE and optimal nonlinear trade-offs.

ABSTRACT

Multi-band transmission systems have emerged as a potential answer to the limited capacity of silica based optical fiber. It is based on utilizing the complete low-loss region of optical fibers. Additionally, elastic optical networks (EON) were proposed to efficiently manage limited resources in optical networks. The selection of route, modulation format and spectrum is the main problem that requires solving to operate an EON. Understanding how linear and nonlinear impairments accumulate during propagation in an optical fibre link in essential to solve this problem. Here we preset a study on the maximum reach optical signals can propagate in a multi-band environment for a variety of modulation formats with commonly used threshold values in EON.

Motivation & Objective

• To determine the maximum transmission reach of optical signals in multi-band elastic optical networks (EONs) using band division multiplexing (BDM).
• To analyze the impact of linear and nonlinear impairments—particularly ASE noise and inter-channel stimulated Raman scattering (ISRS)—on signal reach across E, S, C, and L bands.
• To compute the optimal launch power and SNR per band to support quality-of-service requirements defined by standard bit error rate (BER) thresholds.
• To provide a quantitative basis for the Routing, Modulation Level, and Spectrum Assignment (RMLSA) problem in EONs by delivering reach estimates for common modulation formats.

Proposed method

• Uses a closed-form approximation of the Gaussian noise model to compute nonlinear interference (NLI) coefficients, accounting for ISRS, self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM).
• Models ASE noise power using the formula PASE,ch = 2nsp hν(G−1), where G = αL is the amplifier gain, and α and L are fiber attenuation and span length.
• Calculates per-band SNR using SNRch = Pch / (PASE,ch + ηPch P³ch), where ηPch is the NLI coefficient dependent on signal power and wavelength.
• Assesses cumulative noise over multiple spans using incoherent addition: SNRch = Pch / (N·PASE,ch + N·ηch·P³ch), with N as the number of spans.
• Optimizes launch power per band to maximize SNR, identifying the optimal launch power for each transmission band.
• Maps SNR to BER using standard modulation format curves (BPSK, QPSK, 16QAM, 64QAM, 256QAM) to determine maximum reach at specified BER thresholds.

Experimental results

Research questions

• RQ1 What is the maximum transmission reach for BPSK, QPSK, 16QAM, 64QAM, and 256QAM signals in E, S, C, and L bands under multi-band transmission with ISRS?
• RQ2 How do ASE noise and nonlinear interference (NLI) from ISRS affect SNR and thus reach in different transmission bands?
• RQ3 What is the optimal launch power per band that maximizes SNR and thus transmission reach in a BDM-based EON?
• RQ4 How does the maximum reach vary across bands for different BER thresholds (4.7×10⁻³, 10⁻⁶, 10⁻⁹)?
• RQ5 What are the SNR thresholds required for each modulation format to meet standard BER requirements in a multi-band elastic optical network?

Key findings

• The L band achieves the highest maximum transmission reach (144 spans at 4.7×10⁻³ BER threshold) due to the lowest ASE noise and favorable nonlinear trade-offs.
• For a BER threshold of 10⁻⁹, 256QAM reaches 27 spans in the L band, while the E band supports only 5 spans, indicating strong band-dependent reach limitations.
• At a 4.7×10⁻³ BER threshold, 256QAM in the L band achieves a maximum reach of 144 spans, requiring an SNR threshold of 25.5 dB.
• The S band supports 130 spans for BPSK at 4.7×10⁻³ BER, while the E band supports only 31 spans, highlighting the performance gap between bands.
• For 10⁻⁶ BER, 64QAM reaches 5 spans in the L band and 4 spans in the C band, with no reach for 256QAM in E and S bands.
• The E band exhibits the lowest SNR and shortest reach across all modulation formats due to high ASE and nonlinear impairments, making it the least suitable for long-haul transmission.