Nonlinear Transmission Regime Research Articles

Statistical properties of nonlinear distortion of a polarization-multiplexed OFDM signal in long-haul fiber links.

We investigate nonlinear transmission regimes of a polarization-multiplexed 16-quadrature amplitude modulation (PDM-16-QAM) orthogonal frequency-division multiplexed (OFDM) signal in a long-haul optical link. We study the dependence between the strength of nonlinear distortion and statistical properties of a PDM-OFDM signal. We also consider the constellation shaping-based solutions that allow to significantly reduce the bit error rate (up to three to 12 times at the cost of 5%-20% signal redundancy) and propose a method to analytically optimize the symbol distribution for higher-order modulation formats using only the initial signal.

Replacing the Soft-Decision FEC Limit Paradigm in the Design of Optical Communication Systems

The FEC limit paradigm is the prevalent practice for designing optical communication systems to attain a certain bit error rate (BER) without forward error correction (FEC). This practice assumes that there is an FEC code that will reduce the BER after decoding to the desired level. In this paper, we challenge this practice and show that the concept of a channel-independent FEC limit is invalid for soft-decision bit-wise decoding. It is shown that for low code rates and high-order modulation formats, the use of the soft-decision FEC limit paradigm can underestimate the spectral efficiencies by up to 20%. A better predictor for the BER after decoding is the generalized mutual information, which is shown to give consistent post-FEC BER predictions across different channel conditions and modulation formats. Extensive optical full-field simulations and experiments are carried out in both the linear and nonlinear transmission regimes to confirm the theoretical analysis.

Routing, modulation, spectrum and launch power assignment to maximize the traffic throughput of a nonlinear optical mesh network

We investigate the optimization of routing, modulation format adaptation, spectral and launch power assignment as a means of improving the utilization of limited network resources and increasing the network throughput. We consider a transparent optical network operating in the nonlinear transmission regime and using the latest software adapted coherent optical techniques. We separate the problem into one of routing, modulation adaption and channel assignment, followed by channel spectral assignment, and launch power allocation. It is shown, for three test networks, that the launch power allocation and channel spectral assignment can improve the transmission SNR margin over the fixed modulation, fixed power, fully loaded link worst case by approximately 3---4 dB. This increase in SNR margin can be utilized through modulation format adaption to increase the overall network throughput. This paper highlights that increased gains in network throughput can be achieved in nonlinear impaired networks when individual transmitter spectral assignment and launch power are optimized to minimize the nonlinear interference.

System Performance Prediction With the Gaussian Noise Model in 100G PDM-QPSK Coherent Optical Networks

We demonstrate that the transmission BER, OSNR penalty, and system margin can be accurately predicted for multiple fiber types using the back-to-back response together with the Gaussian Noise model of nonlinear penalties. We first experimentally quantify the 1600 km link performance of SMF, MDF, and LAF fiber types in a coherent, WDM PDM-QPSK system at both 28 and 32 GBaud employing all-EDFA amplification and nearly identical span lengths to isolate fiber performance effects. We quantify the BER, OSNR transmission penalty, and link margin versus per-channel launch power in both linear and nonlinear transmission regimes. We demonstrate that the total system performance can be directly and accurately predicted using the fiber parameters α, D, and γ, the number spans and noise figures, and back-to-back performance of the transmitter-receiver pair. We also show that the system margins scale as (α |D|/γ2)1/3 as predicted by the Gaussian Noise model of nonlinear penalties in uncompensated systems.

Nonlinear spectral management: Linearization of the lossless fiber channel

Using the integrable nonlinear Schrödinger equation (NLSE) as a channel model, we describe the application of nonlinear spectral management for effective mitigation of all nonlinear distortions induced by the fiber Kerr effect. Our approach is a modification and substantial development of the so-called "eigenvalue communication" idea first presented in A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993). The key feature of the nonlinear Fourier transform (inverse scattering transform) method is that for the NLSE, any input signal can be decomposed into the so-called scattering data (nonlinear spectrum), which evolve in a trivial manner, similar to the evolution of Fourier components in linear equations. We consider here a practically important weakly nonlinear transmission regime and propose a general method of the effective encoding/modulation of the nonlinear spectrum: The machinery of our approach is based on the recursive Fourier-type integration of the input profile and, thus, can be considered for electronic or all-optical implementations. We also present a novel concept of nonlinear spectral pre-compensation, or in other terms, an effective nonlinear spectral pre-equalization. The proposed general technique is then illustrated through particular analytical results available for the transmission of a segment of the orthogonal frequency division multiplexing (OFDM) formatted pattern, and through WDM input based on Gaussian pulses. Finally, the robustness of the method against the amplifier spontaneous emission is demonstrated, and the general numerical complexity of the nonlinear spectrum usage is discussed.

Experimental demonstration of a format-flexible single-carrier coherent receiver using data-aided digital signal processing

We experimentally demonstrate the use of data-aided digital signal processing for format-flexible coherent reception of different 28-GBd PDM and 4D modulated signals in WDM transmission experiments over up to 7680 km SSMF by using the same resource-efficient digital signal processing algorithms for the equalization of all formats. Stable and regular performance in the nonlinear transmission regime is confirmed.

Digital coherent superposition for performance improvement of spatially multiplexed coherent optical OFDM superchannels

We demonstrate the use of digital coherent superposition to improve the performance of space-division-multiplexed (SDM) 676-Gb/s OFDM-16QAM superchannels, achieving ~4 dB improvement in OSNR by using two SDM copies and 1075-km (14 x 76.8 km) transmission over a seven-core-fiber with an effective aggregate spectral efficiency of 23.7 b/s/Hz. We further show that the performance improvement from the coherent superposition is retained in the nonlinear transmission regime through coordinated scrambling of signal constellations at the transmitter and appropriate unscrambling at the receiver, by using a series of simple scrambling functions.

Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime

Coherent superposition of light waves has long been used in various fields of science, and recent advances in digital coherent detection and space-division multiplexing have enabled the coherent superposition of information-carrying optical signals to achieve better communication fidelity on amplified-spontaneous-noise limited communication links. However, fiber nonlinearity introduces highly correlated distortions on identical signals and diminishes the benefit of coherent superposition in nonlinear transmission regime. Here we experimentally demonstrate that through coordinated scrambling of signal constellations at the transmitter, together with appropriate unscrambling at the receiver, the full benefit of coherent superposition is retained in the nonlinear transmission regime of a space-diversity fiber link based on an innovatively engineered multi-core fiber. This scrambled coherent superposition may provide the flexibility of trading communication capacity for performance in future optical fiber networks, and may open new possibilities in high-performance and secure optical communications.

Nonperiodic quasi-stable nonlinear optical carrier pulses with sliding chirp-free points for transmission at 40 Gbit/s rate

We present a novel nonlinear transmission regime at 40Gbit/s using nonperiodic carrier pulses with 50% duty cycle and sliding (with propagation) chirp-free points. Quasi-stable transmission of such carrier pulses is supported by a large normal span average dispersion and misbalanced optical amplification. The possibility of applying this new nonlinear carrier pulse to WDM transmission systems is illustrated with two examples.