Experimental Demonstration of Geometrically-Shaped Constellations Tailored to the Nonlinear Fibre Channel

A geometrically-shaped 256-QAM constellation, tailored to the nonlinear optical fibre channel, is experimentally demonstrated. The proposed constellation outperforms both uniform and AWGN-tailored 256-QAM, as it is designed to optimise the trade-off between shaping gain, nonlinearity and transceiver impairments

Challenges in Modelling Optical Fibres for Spatial Division Multiplexing

We review recent studies of the nonlinear interference in spatial division multiplexing systems. Different solution methods of the multimode Schrödinger equation are compared, highlighting the accuracy of a stochastic solution method including distributed mode coupling

Modeling and mitigation of fiber nonlinearity in wideband optical signal transmission [Invited]

The adoption of open optical networks (OONs) requires the development of open and effective network planning tools, enabling the use of multi-vendor or white-box transport solutions. Such tools for studying and planning optical networks must be able to take into account the physical layer impairments, including fiber nonlinearity. The use of wideband wavelength division multiplexing in OONs, with channel frequencies extending across the short, conventional, and long bands and beyond, offers a pathway to increasing data rates through the installed fiber infrastructure. However, achievable information rates are limited by the resulting signal distortion due to fiber nonlinearity as signal bandwidths are increased, in particular, inter-channel stimulated Raman scattering (ISRS). In this paper, we describe the nonlinear effects observed in wideband transmission systems, and review recently developed analytical tools, based on the Gaussian noise (GN) model of nonlinear interference with the inclusion of ISRS. Using the ISRS GN model, we assess the impact of fiber nonlinearity on the achievable information rates in transmission systems with bandwidths of up to 12 THz. We demonstrate the use of the model in the optimization of launch power spectral profiles for a variety of dynamic gain equalizer arrangements in a 1000 km standard single-mode fiber link, using particle swarm optimization and the steepest descent algorithm. Such nonlinear models and optimization methods could be applied in OON planning tools, for example, in optical link emulators to estimate quality-of-transmission and data throughput, and in impairment-aware software-defined network control and management

The Benefits of Using the S-Band in Optical Fiber Communications and How to Get There

The throughput gains of extending the optical transmission bandwidth to the S+C+L-band are quantified using a Gaussian Noise model that accounts for inter-channel stimulated Raman scattering (ISRS). The impact of potential ISRS mitigation strategies, such as dynamic gain equalization and power optimization, are investigated

Experimental Demonstration of a Simplified SOA Nonlinearity Mitigation scheme

We experimentally demonstrated a digital learned-filter mitigation scheme for semiconductor optical amplifier-induced nonlinear distortion of single-polarisation 32 GBd 16QAM and 64QAM signals in a back-to-back configuration

Geometric Shaping of 2-D Constellations in the Presence of Laser Phase Noise

In this article, we propose a geometric shaping (GS) strategy to design 8, 16, 32, and 64 -ary modulation formats for the optical fibre channel impaired by both additive white Gaussian (AWGN) and phase noise. The constellations were optimised to maximise generalised mutual information (GMI) using a mismatched channel model. The presented formats demonstrate an enhanced signal-to-noise ratio (SNR) tolerance in high phase noise regimes when compared with their quadrature amplitude modulation (QAM) or AWGN-optimised counterparts. By putting the optimisation results in the context of the 400ZR implementation agreement, we show that GS alone can either relax the laser linewidth (LW) or carrier phase estimation (CPE) requirements of 400 Gbit/s transmission links and beyond. Following the GMI validation, the performance of the presented formats was examined in terms of post forward error correction (FEC) bit-error-rate (BER) for a soft decision (SD) extended Hamming code (128, 120), implemented as per the 400ZR implementation agreement. We demonstrate gains of up to 1.2 dB when compared to the 64 -ary AWGN shaped formats

Joint estimation of dynamic polarization and carrier phase with pilot-based adaptive equalizer in PDM-64 QAM transmission system

A pilot-based adaptive equalizer is investigated for high cardinality polarizationdivision-multiplexing quadrature amplitude modulation transmission systems. Pilot symbols are periodically inserted for joint estimation of the dynamic state of polarization (SOP) and carrier phase, in a least mean square (LMS) sense. Compared to decision-directed least mean square (DDLMS) equalization and radially-directed equalization, the proposed equalizer can achieve robust equalization and phase estimation, especially in low optical signal-to-noise ratio (OSNR) scenarios. In an experiment on 56 GBaud PDM-64 QAM transmission over 400 km standard single-mode fiber, we obtained at least 0.35 bit per symbol generalized mutual information (GMI) improvement compared with other training symbol-based equalization when tracking 600 krad/s dynamic SOP. With the joint estimation scheme, the equalization performance will not be compromised even if the SOP speed reaches 600 krad/s or the laser linewidth approaches 2 MHz. For the first time, it is demonstrated that the pilot-based equalizer can track dynamic SOP rotation and compensate for fiber linear impairments without any cycle slips under extreme conditions

The Partially-Coherent AWGN Channel: Transceiver Strategies for Low-Complexity Fibre Links

Carrier phase estimation (CPE) is one of the key requirements to perform intradyne coherent detection in optical communication systems. Residual errors in the phase estimation at the receiver, also known as residual phase noise (RPN), follow the so-called Tikhonov distribution. In the digital domain, a channel where the phase has already been estimated by the CPE is generally known as a partially-coherent additive white Gaussian noise (PCAWGN) channel. Herein, we present a joint strategy to modulate and demodulate a 2-dimensional (2D) signal in a PCAWGN channel. Using a low-complexity demapper, we geometrically shape (GS) 8- to 64- ary modulation formats for a PCAWGN channel. Through numerical simulations, we then assess the bit-wise achievable information rates (AIRs) and post forward error correction (FEC) bit error rates (BER) of the presented constellations with the: theoretical optimum model, Euclidean model and the low-complexity PCAWGN model. The resulting constellations are shown to be tolerant to a significant amount of RPN and are therefore applicable to coherent optical communication systems using high linewidth lasers (e.g., >500 kHz) and/or lower symbol rates. Moreover, we demonstrate that shaped PCAWGN constellations combined with a low-complexity demapper can either significantly relax laser linewidth (LW) or carrier phase estimation (CPE) requirements. Assuming a rate-9/10 LDPC scheme, we demonstrate post-FEC BER shaping gains of up to 2.59 dB and 2.19 dB versus uniform 64QAM and 64-ary constellations shaped for the purely AWGN channel, respectively

2048-QAM transmission at 15 GBd over 100 km using geometric constellation shaping

We experimentally investigated a pilot-aided digital signal processing (DSP) chain in combination with high-order geometric constellation shaping to increase the achievable information rates (AIRs) in standard intradyne coherent transmission systems. We show that the AIR of our system at 15 GBd was maximised using geometrically-shaped (GS) 2048 quadrature amplitude modulation (QAM), reaching 18.0 b/4D-symbol in back-to-back transmission and 16.9 b/4D-symbol after transmission through 100 km of a single-mode fibre after subtracting the pilot overhead (OH). This represents the highest-order GS format demonstrated to date, supporting the highest AIR of any standard intradyne system using conventional optics and 8-bit electronics. Detailed characterisation of the DSP, transceiver performance, and transmission modelling has also been carried out to provide insight into sources of impairments and directions for further improvement