Showing papers by "Norbert Hanik published in 2016"

On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear Fiber Channel

Abstract: Different aspects of probabilistic shaping for a multispan optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input probability mass functions (PMFs) for a range of signal-to-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR. It is shown that if a small penalty of at most 0.1 dB SNR to the full shaping gain is acceptable, just two shaped PMFs are required per quadrature amplitude modulation (QAM) over a large SNR range. For a multispan wavelength division multiplexing optical fiber system with 64QAM input, it is shown that just one PMF is required to achieve large gains over uniform input for distances from 1400 to 3000 km. Using recently developed theoretical models that extend the Gaussian noise (GN) model and full-field split-step simulations, we illustrate the ramifications of probabilistic shaping on the effective SNR after fiber propagation. Our results show that, for a fixed average optical launch power, a shaping gain is obtained for the noise contributions from fiber amplifiers and modulation-independent nonlinear interference (NLI), whereas shaping simultaneously causes a penalty as it leads to an increased NLI. However, this nonlinear shaping loss is found to have a relatively minor impact, and optimizing the shaped PMF with a modulation-dependent GN model confirms that the PMF found for AWGN is also a good choice for a multi-span fiber system.

Sensitivity Gains by Mismatched Probabilistic Shaping for Optical Communication Systems

Abstract: Probabilistic shaping of quadrature amplitude modulation (QAM) is used to enhance the sensitivity of an optical communication system. Sensitivity gains of 0.43 and 0.8 dB are demonstrated in back-to-back experiments by the shaping of 16QAM and 64QAM, respectively. Furthermore, numerical simulations are used to prove the robustness of probabilistic shaping to a mismatch between the constellation used and the signal-to-noise ratio (SNR) of the channel. It is found that, accepting a 0.1-dB SNR penalty, only four shaping distributions are required to support these gains for 64QAM.

Impact of 4D Channel Distribution on the Achievable Rates in Coherent Optical Communication Experiments

Abstract: We experimentally investigate mutual information and generalized mutual information for coherent optical transmission systems. The impact of the assumed channel distribution on the achievable rate is investigated for distributions in up to four dimensions. Single channel and wavelength-division multiplexing (WDM) transmission over transmission links with and without inline dispersion compensation are studied. We show that for conventional WDM systems without inline dispersion compensation, a circularly symmetric complex Gaussian distribution is a good approximation of the channel. For other channels, such as with inline dispersion compensation, this is no longer true and gains in the achievable information rate are obtained by considering more sophisticated four-dimensional (4D) distributions. We also show that for nonlinear channels, gains in the achievable information rate can also be achieved by estimating the mean values of the received constellation in four dimensions. The highest gain for such channels is seen for a 4D correlated Gaussian distribution.

A Robust Adaptive Pre-Distortion Method for Optical Communication Transmitters

Abstract: Present and next generation optical communication systems are constantly being developed to operate at higher baud rates and higher modulation formats. It then becomes inevitable to consider the various linear and nonlinear effects due to the imperfect components at the transmitter. State-of-the-art digital-to-analog converters, high bandwidth driver amplifiers, and dual-polarization (DP) Mach–Zehnder modulators are far from being ideal and present distortions in the form of bandwidth limitation, transmitter I/Q skew, and nonlinear effects. In this letter, we propose a new robust pre-distortion method to mitigate the undesirable linear and non-linear distortions of all electrical and optical transmitter components simultaneously. A step-by-step derivation and implementation of the algorithm are discussed and put forward. The performance of the algorithm is experimentally assessed across DP-4QAM, DP-8QAM, DP-16QAM, DP-32QAM, and DP-64QAM up to the signaling rates of 56 GBd. Significant improvements in the required optical signal-to-noise ratio at bit-error rate (BER) of $10^{-2}$ are demonstrated.

Long-Haul Transmission of PM-16QAM-, PM-32QAM-, and PM-64QAM-Based Terabit Superchannels Over a Field Deployed Legacy Fiber

Abstract: Increase in transmission symbol-rate as well as order of quadrature amplitude modulation (QAM) is identified as the most economical way to reduce cost per transmitted bit. In particular, next generation transponders aim at supporting data-rates up to 1 Tb/s employing superchannels due to electrical components’ bandwidth limitations. Furthermore, the introduction of a flexible-grid architecture can maximize throughput by minimizing spectral gaps in available optical spectrum. Keeping in view these design options, we conducted several high capacity experiments with tier1 operator Orange using their field deployed standard single mode fiber (SSMF, G.652), having a total length of 762 km, connecting the cities Lyon and Marseille in France. In particular we employed four subcarriers per Tb/s superchannel, each modulated by PM-16QAM, PM-32QAM, and PM-64QAM with per carrier symbol-rates of 41.2 GBd, 33 GBd, and 34 GBd, respectively. The subcarrier spacing was 50 GHz for the PM-16QAM case and 37.5 GHz for both the PM-32QAM and PM-64QAM cases allowing in total 24 $\times$ 1.0, 32 $\times$ 1.0, and 32 $\times$ 1.2 Tb/s superchannels over C-band and resulting in potential C-band capacities of 24.0, 32.0, and 38.4 Tb/s, respectively. After field transmission the maximum available $\rm {OSNR_{0.1\,nm}}$ margin compared to the required $\rm {OSNR_{0.1\,nm}}$ at forward error correction (FEC) threshold was 8.2, 5.4, and 4.2 dB for PM-16QAM, PM-32QAM, and PM-64QAM, respectively. The transmission reach for PM-16QAM and PM-32QAM modulated superchannels was extended to $\sim$ 1571 and $\sim$ 1065 km using erbium doped fiber amplified SSMF spans of $\sim$ 101 km length.

400G single carrier transmission in 50 GHz grid enabled by adaptive digital pre-distortion

Abstract: An adaptive digital pre-distortion method to enable single carrier 400G DP-128QAM transmission over 328 km fiber with 30% FEC is presented. Experimental comparison in reach and spectral efficiency is made with 400G DP-64QAM.

Improved achievable information rates by optimized four-dimensional demappers in optical transmission experiments

Abstract: We experimentally study different four-dimensional demappers in a dispersion-managed fiber system. The proposed blind algorithm is shown to offer gains of 0.2 bits per 4D symbol for DP-16QAM.

Experimental Analysis of Correlations in the Nonlinear Phase Noise in Optical Fiber Systems

Abstract: A dual-link self-homodyne receiver is used to measure the phase correlations introduced by the interplay of dispersion and fiber nonlinearities. The dependence of the memory on the WDM setup, signal power and transmission distance is experimentally demonstrated.

Multi-flex field trial over 762km of G.652 SSMF using programmable modulation formats up to 64QAM

Abstract: We demonstrate next-generation network upgrade scenarios using flexi-format (PM-QPSK→PM-64QAM) and flexi-rate (100G→300G) transmission over field-deployed fiber (762km). The back-to-back penalties are limited to ∼2.6dB, whereas after transmission, available margin in excess of ∼7.6dB is reported.

Comparison of single carrier 200G 4QAM, 8QAM and 16QAM in a WDM field trial demonstration over 612 km SSMF

Abstract: We present results of a field trial carried on Telecom Italia EDFA-only legacy link with 0.3 dB/km average fiber attenuation. Single carrier 200G WDM DP-4QAM, DP-8QAM and DP-16QAM were successfully transmitted with system margin of 4.1 dB, 4.3 dB and 2.6 dB respectively.

Improved achievable information rates by optimized four-dimensional demappers in optical transmission experiments

Abstract: We experimentally study different four-dimensional demappers in a dispersion-managed fiber system. The proposed blind algorithm is shown to offer gains of 0.2 bits per 4D symbol for DP-16QAM.

On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear Fiber Channel

Abstract: Different aspects of probabilistic shaping for a multi-span optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input probability mass functions (PMFs) for a range of signal-to-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR. It is shown that if a small penalty of at most 0.1 dB SNR to the full shaping gain is acceptable, just two shaped PMFs are required per quadrature amplitude modulation (QAM) over a large SNR range. For a multi-span wavelength division multiplexing (WDM) optical fiber system with 64QAM input, it is shown that just one PMF is required to achieve large gains over uniform input for distances from 1,400 km to 3,000 km. Using recently developed theoretical models that extend the Gaussian noise (GN) model and full-field split-step simulations, we illustrate the ramifications of probabilistic shaping on the effective SNR after fiber propagation. Our results show that, for a fixed average optical launch power, a shaping gain is obtained for the noise contributions from fiber amplifiers and modulation-independent nonlinear interference (NLI), whereas shaping simultaneously causes a penalty as it leads to an increased NLI. However, this nonlinear shaping loss is found to have a relatively minor impact, and optimizing the shaped PMF with a modulation-dependent GN model confirms that the PMF found for AWGN is also a good choice for a multi-span fiber system.

Multi-dimensional demappers for optical fiber systems with soft-decision forward error correction

Abstract: We study the impact of demappers using various channel statistics, including circularly symmetric and multi-dimensional Gaussian, in fiber-optic communication systems. In nonlinear dispersion-managed fiber systems, an improvement in achievable information rate (AIR) and bit error ratio (BER) after decoding is obtained from using multi-dimensional non-circularly symmetric Gaussian statistics at the demapper. For fiber systems without in-line dispersion compensation, only minor gains are obtained.