Inline Dispersion Compensation Research Articles

On the Nonlinear Shaping Gain With Probabilistic Shaping and Carrier Phase Recovery

The performance of different probabilistic amplitude shaping (PAS)techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques—namely, sphere shaping, shell mapping with different number of shells, and constant composition DM—and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1\times 180$</tex-math></inline-formula> km, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$15\times 80$</tex-math></inline-formula> km, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$27\times 80$</tex-math></inline-formula> km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm.

Probabilistically Shaped 4-PAM for Short-Reach IM/DD Links With a Peak Power Constraint

Probabilistic shaping for intensity modulation and direct detection (IM/DD) links is discussed and a peak power constraint determined by the limited modulation extinction ratio (ER) of optical modulators is introduced. The input distribution of 4-ary unipolar pulse amplitude modulation (PAM) symbols is optimized for short-reach transmission links without optical amplification nor in-line dispersion compensation. The resulting distribution is symmetric around its mean allowing to use probabilistic amplitude shaping (PAS) to generate symbols that are protected by forward error correction (FEC) and that have the optimal input distribution. The numerical analysis is confirmed experimentally for both an additive white Gaussian noise (AWGN) channel and a fiber channel, showing gains in transmission reach and transmission rate, as well as rate adaptability.

Silicon nitride chirped spiral Bragg grating with large group delay

As one of the most important optical filtering devices, Bragg gratings have been extensively used in various systems. A long Bragg grating is desired for many applications including frequency selection in semiconductor lasers and dispersion control for ultra-short pulses. As a prominent example, integrated spiral Bragg grating waveguides (SBGWs) have drawn much attention in the years. However, until now, the length of an integrated grating is still limited to a few milli-meters due to total waveguide loss. In this work, we propose and demonstrate a novel long chirped SBGW with waveguide loss as low as 0.05 dB/cm on a silicon nitride (Si3N4) platform. A 13.8 cm SBGW is fabricated, which is the longest on-chip waveguide grating reported so far. The SBGW’s reflection bandwidth is 9.2 nm from 1556.3 nm to 1565.5 nm, and it provides a total of 1440 ps group delay, that is, −156.5 ps/nm of dispersion. The group delay response shows great linearity and temperature stability. This integrated device holds great potential for various applications including in-line dispersion compensation, optical true delay phase array, and microwave photonics.

A full-duplex 40 GHz radio-over-fiber transmission system based on frequency octupling

A 10 Gbps full-duplex 40 GHz radio-over-fiber (RoF) communication system is presented in this paper. A 5 GHz input Radio Frequency signal is octupled to 40 GHz using cascaded parallel Mach–Zehnder modulators (MZMs) operating at lower modulation index (m) range of 2.5–3.5. The ROF transmission system employs symmetrical inline dispersion compensation technique using tDCF and frequency re-use concept for upstream transmission. Full-duplex transmission distance of 180 kms can be achieved with quality factor (Q) ≥ 7 for wide range of modulation index (2.5–3.5) of MZMs, reflecting that system is tolerant to biasing variations. The transmission length can be increased to 210 kms for relatively reduced modulation index range of 3.2–3.5.

Nonlinearity Mitigation in WDM Systems: Models, Strategies, and Achievable Rates

After reviewing models and mitigation strategies for interchannel nonlinear interference (NLI), we focus on the frequency-resolved logarithmic perturbation model to study the coherence properties of NLI. Based on this study, we devise an NLI mitigation strategy which exploits the synergic effect of phase and polarization noise compensation (PPN) and subcarrier multiplexing with symbol-rate optimization. This synergy persists even for high-order modulation alphabets and Gaussian symbols. A particle method for the computation of the resulting achievable information rate and spectral efficiency (SE) is presented and employed to lower-bound the channel capacity. The dependence of the SE on the link length, amplifier spacing, and presence or absence of inline dispersion compensation is studied. Single-polarization and dual-polarization scenarios with either independent or joint processing of the two polarizations are considered. Numerical results show that, in links with ideal distributed amplification, an SE gain of about 1 bit/s/Hz/polarization can be obtained (or, in alternative, the system reach can be doubled at a given SE) with respect to single-carrier systems without PPN mitigation. The gain is lower with lumped amplification, increases with the number of spans, decreases with the span length, and is further reduced by in-line dispersion compensation. For instance, considering a dispersion-unmanaged link with lumped amplification and an amplifier spacing of 60 km, the SE after 80 spans can be be increased from 4.5 to 4.8 bit/s/Hz/polarization, or the reach raised up to 100 spans (+25%) for a fixed SE.

Phase Noise Tracking and Compensation in Coherent Optical Systems Using Kalman Filter

The performance of phase-modulated coherent optical communication systems is often limited by laser and nonlinear phase noises (PN and NLPN). The laser PN and the NLPN at high launch powers degrade system performance severely. In this letter, we investigate the use of Kalman filter (KF) to estimate and track both the laser PN and the NLPN in 100-Gb/s single channel coherent optical phase-modulated systems. Initially, the KF is operated in the training mode with pilot symbols; the filter is switched to decision directed mode after training. Simulation results for single-polarization, 100-Gb/s QPSK transmission over $20\times 80$ km fiber with in-line dispersion compensation show that KF can successfully mitigate NLPN at 8-dBm launch power with 1-MHz laser linewidth. Comparison with digital backpropagation algorithm (one step/span) shows that KF provides 6-dB improvement in $Q$ -factor. Kalman estimates corresponding to the time evolution of PN and NLPN are also provided, which shows optimal tracking of both the noise processes, thereby validating our proposed scheme.

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

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.

Improving soft FEC performance for higher-order modulations via optimized bit channel mappings.

Soft forward error correction with higher-order modulations is often implemented in practice via the pragmatic bit-interleaved coded modulation paradigm, where a single binary code is mapped to a nonbinary modulation. In this paper, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed fiber-optical system without optical inline dispersion compensation. Our focus is on protograph-based low-density parity-check (LDPC) codes which allow for an efficient hardware implementation, suitable for high-speed optical communications. The optimization is applied to the AR4JA protograph family, and further extended to protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full field simulations via the split-step Fourier method are used to verify the analysis. The results show performance gains of up to 0.25 dB, which translate into a possible extension of the transmission reach by roughly up to 8%, without significantly increasing the system complexity.

Field Trial Demonstration and Evaluation of a Coherent 100G IP Over WDM Alien Wavelength Across 769 km of Multiple WDM Infrastructures Without Regeneration [Invited

We report the first successful coherent 100G IP over WDM alien wavelength field trial over WDM infrastructures spanning a total distance of 769 km, demonstrating the feasibility and robust performance of a simplified 100G IP over WDM core network architecture. Key performance aspects have been investigated including co-propagation of a 100G IP over WDM alien wavelength and native wavelengths generated from WDM transponders, polarization mode dispersion tolerance, and operation without in-line dispersion compensation modules. We also demonstrated the feasibility of a 100G IP over WDM alien wavelength over multiple WDM systems and optical router or regenerator bypass. In addition, we show evaluation results on the key performance management and monitoring functions with a coherent 100G IP over WDM optical interface in the core router.

The Gordon—Mollenauer Effect in 112 Gbit/s DP-QPSK Systems

Gordon and Mollenauer (G-M) proposed in 1990 that the interplay between the nonlinear Kerr effect and amplified spontaneous emission noise can generate an enhanced level of noise and degrade the performance of optical phase-modulated systems. We systematically investigate the G-M effect in 112 Gbit/s coherent dual polarization quaternary phase shift keying (DP-QPSK) systems through comprehensive simulation. The results show that in the presence or absence of inline dispersion compensation, the G-M effect will seriously damage the system performance. Some of our important conclusions are listed as follows: with the increase in the input power into each span, the G-M effect is enhanced simultaneously; the smaller the span length, the stronger the G-M effect caused by more inter-span interaction; for non-zero dispersion-shifted fibers, different coefficient values will cause a similar amount of G-M effect penalty; by comparing the system performance with different dispersion compensation ratios, one can conclude that different residual dispersions of the same magnitude, no matter whether they are under-compensated or over-compensated, can derogate the overall system performance to a similar degree. In brief, the G-M effect cannot be ignored. We also have a short discussion on how to reduce and compensate for the G-M effect in DP-QPSK systems.

Intra-channel nonlinearity compensation for PM-16QAM traffic co-propagating with 28Gbaud m-ary QAM neighbours

We quantify the benefits of intra-channel nonlinear compensation in meshed optical networks, in view of network configuration, fibre design aspect, and dispersion management. We report that for a WDM optical transport network employing flexible 28Gbaud PM-mQAM transponders with no in-line dispersion compensation, intra-channel nonlinear compensation, for PM-16QAM through traffic, offers significant improvements of up to 4dB in nonlinear tolerance (Q-factor) irrespective of the co-propagating modulation format, and that this benefit is further enhanced (1.5dB) by increasing local link dispersion. For dispersion managed links, we further report that advantages of intra-channel nonlinear compensation increase with in-line dispersion compensation ratio, with 1.5dB improvements after 95% in-line dispersion compensation, compared to uncompensated transmission.

Comparison of optical back propagation schemes for fiber-optic communications

Optical back propagation techniques that utilize two highly nonlinear fibers to compensate for transmission fiber nonlinear effects are analyzed. When the step-size is equal to the amplifier spacing, inline compensation of fiber nonlinearity without inline dispersion compensation provides the best performance.

Nonlinear Tolerance of 53.5-Gb/s Differential 6-ary PSK Surrounded by 10.7-Gb/s NRZ-OOK Neighbors in SMF and DSF Transmission Links

We demonstrate an optical transmission system based on a 53.5-Gb/s differential 6-ary phase-shift-keying (D6PSK) signal with copropagating 10.7-Gb/s nonreturn-to-zero (NRZ) on-off keying (OOK) channels over either 320-km-long single-mode fiber link with in-line dispersion compensation or 320-km-long dispersion-shifted fiber link, and compare its performances with that of a classical polarization-division-multiplexing differential quadrature phase-shift-keying (DQPSK)-based system. The results show that the nonlinear tolerance of the D6PSK signal outperforms that of the PDM-DQPSK signal in terms of the cross-phase modulation effect induced by the 10.7-Gb/s NRZ-OOK neighboring channels.

Scaling 112 Gb/s Optical Networks With the Nonlinear Threshold Metric

A nonlinear penalty threshold that contains the total nonlinear phase shift is examined as a criterion for scaling fiber optic links. We investigate 112 Gb/s PDM-QPSK hybrid optical networks consisting of either TrueWave (G.655) or AllWave (G.652) fiber. We establish experimental and simulation environments with robust absolute matching in both linear and nonlinear regimes. We identify both XPM and SPM penalties in 0% and 100% inline dispersion compensation schemes for the two different fiber types. Both experimental and simulation results reveal that 0% inline-compensated links operate with larger nonlinear threshold for increasing span count and readily yield simple design rules.

Performance comparison of MSK and QPSK optical long haul DWDM transmission with coherent detection

We performed long-haul WDM transmission experiments to compare 10 Gbit/s MSK and QPSK modulation with a channel grid of 12.5 GHz. A standard link setup with inline dispersion compensation was applied in combination with coherent detection and following offline signal processing. Both modulation formats showed nearly equal performance bridging about 4000 km at a BER of 10(-3).

Efficient compensation of chromatic dispersion and nonlinearities using logarithmic digital backward propagation in N-channel DWDM 1.12Tbit/s DP-QPSK transmission

We propose and numerically investigate the logarithmic step-size distribution for implementing an efficient digital backward propagation (DBP) algorithm using the split-step Fourier method (SSFM). DBP is implemented in N-channel dual-polarization quadrature-phase-shift-keying (DP-QPSK) transmission over 2000 km standard single-mode fiber (SMF) with no in-line optical dispersion compensation. This algorithm is compared with the constant step-size modified DBP (M-SSFM) algorithm in terms of efficiency, complexity and computational time. Furthermore, we investigate the same-capacity and same-bandwidth transmission systems with 14 Gbaud (GBd), 28 GBd and 56 GBd per-channel rates. The logarithmic step-size based DBP algorithm depicts efficient mitigation of chromatic dispersion (CD) and nonlinear (NL) impairment. The benefit of the logarithmic step-size is the reduced complexity and computational time for higher baud rates.

RF-Assisted DP-16-QAM 112-Gbit/s Transmission Over 824 km of G.652 Fiber With and Without Inline Dispersion Compensation

We evaluate transmission performance of a coherent 112-Gbit/s radio-frequency (RF)-assisted dual-carrier DP-16-QAM solution over 824 km of field deployed G.652 fiber. Two scenarios, with and without inline dispersion compensation, are compared. Furthermore, the effectiveness of nonlinearity mitigation using digital signal processing in the two scenarios is investigated. It is shown that good performance after 824 km can be obtained and that relatively simple nonlinearity mitigation can be very effective using the RF-assisted solution.

Impact of nonlinear and polarization effects in coherent systems

Coherent detection with digital signal processing (DSP) significantly changes the ways impairments are managed in optical communication systems. In this paper, we review the recent advances in understanding the impact of fiber nonlinearities, polarization-mode dispersion (PMD), and polarization-dependent loss (PDL) in coherent optical communication systems. We first discuss nonlinear transmission performance of three coherent optical communication systems, homogeneous polarization-division-multiplexed (PDM) quadrature-phase-shift-keying (QPSK), hybrid PDM-QPSK and on/off keying (OOK), and PDM 16-ary quadrature-amplitude modulation (QAM) systems. We show that while the dominant nonlinear effects in coherent optical communication systems without optical dispersion compensators (ODCs) are intra-channel nonlinearities, the dominant nonlinear effects in dispersion-managed (DM) systems with inline dispersion compensation fiber (DCF) are different when different modulation formats are used. In DM coherent optical communication systems using modulation formats of constant amplitude, the dominant nonlinear effect is nonlinear polarization scattering induced by cross-polarization modulation (XPolM), whereas when modulation formats of non-constant amplitude are used, the impact of inter-channel cross-phase modulation (XPM) is much larger than XPolM. We then describe the effects of PMD and PDL in coherent systems. We show that although in principle PMD can be completely compensated in a coherent optical receiver, a real coherent receiver has limited tolerance to PMD due to hardware limitations. Two PDL models used to evaluate PDL impairments are discussed. We find that a simple lumped model significantly over-estimates PDL impairments and show that a distributed model has to be used in order to accurately evaluate PDL impairments. Finally, we apply system outage considerations to coherent systems, taking into account the statistics of polarization effects in fiber.

Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP

A field trial of 100-Gbit/s Ethernet over an optical transport network (OTN) is conducted using a real-time digital coherent signal processor. Error free operation with the Q-margin of 3.2 dB is confirmed at a 100 Gbit/s Ethernet analyzer by concatenating a low-density parity-check code with a OTN framer forward error correction, after 80-ch WDM transmission through 6 spans x 70 km of dispersion shifted fiber without inline-dispersion compensation. Also, the recovery time of 12 msec is observed in an optical route switching experiment, which is achieved through fast chromatic dispersion estimation functionality.

Pilot-based cross-phase modulation compensation for coherent optical orthogonal frequency division multiplexing long-haul optical communications systems

A pilot-based nonlinearity compensator (PB-NLC) is shown in this Letter to be an effective method for compensating cross-phase modulation (XPM) in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. An unmodulated pilot tone is transmitted at the center of each OFDM channel to detect phase errors caused by the Kerr effect, which converts intensity fluctuations from all channels to phase errors. The pilots are then used to cancel the XPM phase errors for each OFDM channel at the receiver after each channel's self-phase modulation (SPM) has been compensated, using its intensity waveform to determine its SPM. Numerical simulations of a 58 Gb/s single polarization 2375 km system with inline dispersion compensation show that the signal quality, Q, at the optimal launch power is increased by 2.4 dB if SPM compensation is used before the PB-NLC. This contrasts with only a 0.9 dB improvement if the PB-NLC is used without an SPM compensator for the same link. This shows the PB-NLC can effectively mitigate XPM but not SPM.