Digital Backward Propagation Research Articles

Hybrid optical-electronic compensation of fiber nonlinearity for long-haul coherent optical transmission

Abstract From the concepts of the dispersion-folded digital backward propagation (DBP) and optical phase conjugation (OPC), a hybrid optical-electronic nonlinearity-compensation scheme is proposed to enhance the system performance of the dispersion-managed transmission. The computational complexity of the proposed scheme, compared with that of the conventional DBP method, is reduced significantly while the performance penalty is negligible. The compensation efficiency of the proposed scheme has been validated in a 5 (and 9)-channel PM-16QAM system at 256 Gbit/s.

Research on Key Technologies of large capacity and long distance optical transmission systems

In recent years, with the rapid development of high-bandwidth applications and the rapid growth of Internet data services, the capacity of communication networks is growing rapidly. Optical fiber has become an ideal transmission medium for communication networks due to its advantages such as large bandwidth and low loss. Large-capacity and long-distance optical fiber communication networks have become the key research directions of optical communication systems. In this paper, the main technical means to achieve large-capacity and long-distance optical transmission are investigated. First, the application of orthogonal frequency division multiplexing (OFDM) technology in large-capacity transmission is briefly introduced, including its principle, main structure, advantages and disadvantages. Subsequently, wavelength division multiplexing (WDM) technology based on optical frequency comb is introduced. Finally, the methods to realize long-distance transmission are discussed, including Digital Backward Propagation (DBP), Phase-Conjugate Twin Wave (PCTW) and advanced modulation format.

Digital Back Propagation via Sub-Band Processing in Spatial Multiplexing Systems

An advanced digital backward-propagation (DBP) method using a separate-channels approach (SCA) is investigated for the compensation of inter-channel nonlinearities in spatial- and wavelength-multiplexed systems. Compared to the conventional DBP, intra-, and inter-mode cross-phase modulation can be efficiently compensated by including the effect of the inter-channel walk-off in the nonlinear step of the split-step Fourier method. We found that the SCA-DBP relaxes the step size requirements by a factor of 10, while improving performance by 0.8 dB for large walk-off and strong linear coupling. For the first time, it is shown that in spatial multiplexed systems transmission performance can be improved by sub-band processing of back propagated channels.

Compensation of Nonlinear Impairments Using Inverse Perturbation Theory With Reduced Complexity

We propose a modification of the conventional perturbation-based approach of fiber nonlinearity compensation that enables straight-forward implementation at the receiver and meets feasible complexity requirements. We have developed a model based on perturbation analysis of an inverse Manakov problem, where we use the received signal as the initial condition and solve Manakov equations in the reversed direction, effectively implementing a perturbative digital backward propagation enhanced by machine learning techniques. To determine model coefficients we employ machine learning methods using a training set of transmitted symbols. The proposed approach allowed us to achieve 0.5 dB and 0.2 dB $Q^2$ -factor improvement for 2000 km transmission of 11 × 256 Gbit/s DP-16QAM signal compared to chromatic dispersion equalization and one step per span two samples per symbol digital back-propagation technique, respectively. We quantify the trade-off between performance and complexity.

Linear and Nonlinear Compensation for 8-QAM SC-400G Long-Haul Transmission Systems

Digital signal processing (DSP) with both linear equalization and nonlinear compensation for the single-carrier 400G system based on 84-GBaud polarization-division multiplexing 8QAM signals is studied in this paper. The 8QAM signals are generated and preprocessed with pre-equalization and lookup table predistortion at the transmitter (Tx)-side. The implementation principles of training-based adaptive equalization and predistortion are presented in this paper with experimental studies on the tap and memory length. At the receiver (Rx)-side, fiber-nonlinearity compensation based on digital backward propagation is also utilized to further improve the transmission performance. Thanks to the Tx-side and Rx-side DSPs, eight channels of 400G are successfully transmitted over 2125 km SSMF with EDFA-only amplification.

Advanced linear and nonlinear compensations for 16QAM SC-400G unrepeatered transmission system

Digital signal processing (DSP) with both linear equalization and nonlinear compensations are studied in this paper for the single-carrier 400G system based on 65-GBaud 16-quadrature amplitude modulation (QAM) signals. The 16-QAM signals are generated and pre-processed with pre-equalization (Pre-EQ) and Look-up-Table (LUT) based pre-distortion (Pre-DT) at the transmitter (Tx)-side. The implementation principle of training-based equalization and pre-distortion are presented here in this paper with experimental studies. At the receiver (Rx)-side, fiber-nonlinearity compensation based on digital backward propagation (DBP) are also utilized to further improve the transmission performances. With joint LUT-based Pre-DT and DBP-based post-compensation to mitigate the opto-electronic components and fiber nonlinearity impairments, we demonstrate the unrepeatered transmission of 1.6Tb/s based on 4-lane 400G single-carrier PDM-16QAM over 205-km SSMF without distributed amplifier.

All-optical and digital non-linear compensation algorithms in flex-coherent grouped and un-grouped contiguous spectrum based networks

We have evaluated that in-line non-linear compensation schemes decrease the complexity of digital backward propagation and enhance the transmission performance of 40/112/224 Gbit/s mixed line rate network. Multiple bit rates, i.e. 40/112/224 Gbit/s and modulation formats (i.e. DP-QPSK and DP-16QAM) are transmitted over 1280 km of Large \(\hbox {A}_{eff}\) Pure-Silica core fiber. Both grouped and un-grouped spectral allocation schemes are investigated. Optical add-drop multiplexers are used to drop the required wavelength for signal processing in the transmission link. Moreover, hybrid mid-link spectral inversion and in-line non-linear compensation methods are also analyzed. This gives us enhanced system performance and DBP step-size of 400 km in WDM 224 Gbit/s DP-16QAM system, significantly reducing the complexity of digital backward propagation.

Hybrid opto-digital signal processing in 112 Gbit/s DP-16QAM and DP-QDB transmission for long-haul large- $$\hbox {A}_\mathrm{eff}$$ A eff pure-silica-core fiber links

By means of numerical simulations, we demonstrated that all-optical signal processing methods (XPM-suppressor module and in-line nonlinear equalization) significantly increase the system performance of digital nonlinear compensation (digital backward propagation) and improve the system performance in five-channel 112 Gbit/s DP-16QAM and DP-QDB transmission over 2400 km large- effective-area pure-silica-core fiber ($$\hbox {LA}_\mathrm{eff}$$LAeff-PSCF). The system performance is quantified with the help of Q-factor (dB) for both dispersion-managed and nondispersion-managed fiber links.

Adaptive digital backward propagation based on variance of intensity noise

An adaptive digital backward propagation (ADBP) algorithm is proposed and experimentally demonstrated based on the variance of the intensity noise. The proposed algorithm can self-determine the unknown nonlinear coefficient γ and the nonlinear compensation parameter ξ. Compared to the scheme based on the variance of phase noise, the proposed algorithm can avoid the repeated frequency offset compensation and carrier phase recovery. The simulation results show that the system’s performance compensated by the proposed method is comparable to conventional ADBP schemes. The performance of the proposed algorithm is simulated in 40/112 Gb/s polarization-division multiplexing (PDM)-quadrature phase-shift keying (QPSK) and 224 Gb/s PDM-16-quadrature amplitude modulation (QAM) systems and further experimentally verified in a 40 Gb/s PDM-QPSK coherent optical communication system over a 720 km single-mode fiber.

Timing and phase jitter suppression in coherent soliton transmission.

We have revisited soliton transmission in the new context of coherent optical detection optimizing and comparing digital backward propagation and in-line optical filtering as a means to suppress soliton timing and phase jitter. We find that in-line optical filtering allows one to improve the reach of the soliton system by up to the factor of 2. Our results show that nonlinear propagation can lead to performance beyond the nonlinear Shannon limit.

Digital compensation of cross-phase modulation distortions using perturbation technique for dispersion-managed fiber-optic systems

A digital compensation scheme based on a perturbation theory for mitigation of cross-phase modulation (XPM) distortions is developed for dispersion-managed fiber-optic communication systems. It is a receiver-side scheme that uses a hard-decision unit to estimate data for the calculation of XPM fields using the perturbation technique. The intra-channel nonlinear distortions are removed by intra-channel digital backward propagation (DBP) based on split-step Fourier scheme before the hard-decision unit. The perturbation technique is shown to be effective in mitigating XPM distortions. However, wrong estimations in the hard-decision unit result in performance degradation. A hard-decision correction method is proposed to correct the wrong estimations. Numerical simulations show that the hybrid compensation scheme with DBP for dispersion and intra-channel nonlinear impairments compensation and the perturbation technique for XPM compensation brings up to 3.7 dBQ and 1.7 dBQ improvements as compared with the schemes of linear compensation only and intra-channel DBP, respectively. The perturbation technique for XPM compensation requires only one-stage (or two-stage when hard-decision correction is applied) compensation and symbol-rate signal processing.

Multi-channel nonlinearity compensation of PDM-QPSK signals in dispersion-managed transmission using dispersion-folded digital backward propagation

We demonstrate nonlinearity compensation of 37.5-GHz-spaced 128-Gb/s PDM-QPSK signals using dispersion-folded digital-backward-propagation and a spectrally-sliced receiver that simultaneously receives three WDM signals, showing mitigation of intra-channel and inter-channel nonlinear effects in a 2560-km dispersion-managed TWRS-fiber link. Intra-channel and adjacent inter-channel nonlinear compensation gains when WDM channels are fully populated in the C-band are estimated based on the GN-model.

Nonlinearity and Phase Noise Mitigation Using Feed-forward Carrier Phase Estimation and Digital Backward Propagation in Coherent QAM Transmission

We numerically investigate the performance of Viterbi-Viterbi (VV) carrier phase estimation (CPE) and feed-forward decision directed (DD) CPE along with digital backward propagation (DBP) to mitigate laser phase noise, linear and nonlinear fiber impair- ments for polarization multiplexed (PM) 4 and 16-ary quadrature amplitude modulation (QAM) coherent systems. For 16-QAM, DD-CPE is compared with quadrature phase shift keying (QPSK) partitioning method that is based on the modification of VV-CPE. When the laser phase noise is negligible, both CPE methods exhibit a similar performance when employed after DBP. However, in the presence of phase noise, non-decision directed VV-CPE (for 4-QAM) and QPSK partitioning (for 16-QAM) methods outper- form DD-CPE with greater phase noise tolerance and reduced complexity.

Experimental demonstration of simultaneous SPM and XPM mitigation using combined techniques of optical compensation and multichannel single‐stage DBP

A novel system mitigating self-phase and cross-phase modulation effects simultaneously using optical dispersion compensation at optical nodes and multichannel single-stage digital backward propagation (DBP) is proposed. Experiments demonstrate 2.4 dB Q-factor improvements with both self-phase modulation and cross-phase modulation compensation.

Digital Nonlinear Compensation Based on the Modified Logarithmic Step Size

In this paper, we investigate the digital backward propagation (DBP) nonlinear compensation (NLC) based on the modified logarithmic step size distribution. Different from regular constant step size, we use the logarithmic non-constant step size distribution in DBP. The compensation performance is investigated with Nyquist wavelength division multiplexing (NWDM) system. The modified logarithmic step size distribution is proposed and studied by introducing an attenuation adjusting factor k. As a proof of the concept, the optimal k factor is studied by simulation results with the noise figure, the input power, the transmission distance, the fiber attenuation, the span length, the step number per span, the dispersion value, the baud rate, the calculated sub-channels, the pulse shape and the modulation formats. Reduced complexity and improved performance is observed by using the modified logarithmic step size distribution. Compared with constant step nonlinear compensation, the improved bit-error-ratio (BER) performance and Q-value for our scheme is demonstrated by 3 × 50-Gb/s NWDM polarization division multiplexing quadrature phase shift keying (PDM-QPSK) signal with 1120-km single-mode fiber-28 (SMF-28) transmission and Erbium-doped fiber amplifier (EDFA)-only amplification.

Hybrid mid-link spectral inverter to compensate for linear and nonlinear distortions for efficient transmission performance in 224 Gbit/s DP-16QAM system

The hybrid mid-link spectral inversion (H-MLSI) and digital signal processing techniques to compensate for the optical Kerr effects in 224 Gbit/s DP-16QAM transmission over 640 km of single-mode fiber are numerically evaluated. Digital signal processing methods, i.e., electronic dispersion compensation (EDC) and digital backward propagation (DBP) techniques, are implemented. The system is evaluated for diverse signal input launch powers for both single-channel and multichannel transmission in which five channels are multiplexed with a channel spacing of 100 GHz with central wavelength at 1550 nm. The system performance is enumerated by monitoring the bit error ratio. From the results, it is clear that the nonlinear threshold point is improved by 2 and 3 dBm signal power by using H-MLSI and DBP, respectively, with 20 steps per fiber span as compared to EDC. Furthermore, we have also evaluated the DBP complexity as compared to H-MLSI and the resultant impact on maximum transmission distance. Moreover, the performance penalty coming from the span-offset of H-MLSI can be reduced by employing DBP to compensate for the residual Kerr effects.

Advanced perturbation technique for digital backward propagation in WDM systems

An improved digital backward propagation (DBP) is proposed to compensate inter-nonlinear effects and dispersion jointly in WDM systems based on an advanced perturbation technique (APT). A non-iterative weighted concept is presented to replace the iterative in analytical recursion expression, which can dramatically simplify the complexity and improve accuracy compared to the traditional perturbation technique (TPT). Furthermore, an analytical recursion expression of the output after backward propagation is obtained initially. Numerical simulations are executed for various parameters of the transmission system. The results indicate that the advanced perturbation technique will relax the step size requirements and reduce the oversampling factor when launch power is higher than -2 dBm. We estimate this technique will reduce computational complexity by a factor of around seven with respect to the conventional DBP.

Evaluation of correlative coding and DP-16QAM n-channel 112Gbit/s coherent transmission: digital non-linear compensation perspective

We numerically report on the complexity reduction of digital backward propagation (DBP) by utilizing correlative encoded transmission (dual-polarization quadrature duobinary) at a bit-rate of 112Gbit/s over 1640km fiber link. The single channel (N=1) and multi-channel (N=10) transmission performances are compared in this paper. In case of multi-channel system, 10 transmitters are multiplexed with 25GHz channel spacing. The fiber link consists of Large A(eff) Pure-Silica core fiber with 20 spans of 82km each. No in-line optical dispersion compensator is employed in the link. The system performances are evaluated by monitoring the bit-error-ratio and the forward error correction limit corresponds to bit-error-ratio of 3.8×10(-3). The DBP algorithm is implemented after the coherent detection and is based on the logarithmic step-size based split-step Fourier method. The results depict that dual-polarization quadrature duobinary can be used to transmit 112Gbit/s signals with an spectral efficiency of 4-b/s/Hz, but at the same time has a higher tolerance to nonlinear transmission impairments. By utilizing dual-polarization quadrature duobinary modulation, comparative system performance with respect to dual-polarization 16-quadrature amplitude modulation transmission can be achieved with 60% less computations and with a step-size of 205km.

Nonlinear mitigation using carrier phase estimation and digital backward propagation in coherent QAM transmission

We investigate the performance of carrier phase estimation (CPE) and digital backward propagation (DBP) in compensating fiber nonlinearity for 224 Gbps polarization-multiplexed quadrature-amplitude-modulation coherent systems with level of 4 and 16 (PM-4-QAM and PM-16-QAM) over standard single-mode fiber (SSMF) uncompensated link. The results from numerical simulation show the individual performance of CPE and DBP as well as their mutual influence. With DBP compensation, required CPE tap number for optimal performance can be reduced by 50% for 4-QAM signal and 67% for 16-QAM signal compared to linear compensation. On the other hand, employing CPE compensation after DBP also allows to reduce DBP steps. In the mentioned PM-16-QAM system, 60% reduction in the required number of DBP steps to achieve BER=10(-3) is possible, with a step-size of 200 km, which reveals great potential to reduce the complexity for future real time implementation.

Application of a digital non-linear compensation algorithm for evaluating the performance of root-raised-cosine pulses in 112 Gbit s−1 DP-QPSK transmission

In this paper, we numerically investigate the non-linear tolerance of root-raised-cosine (RRC) pulse shaping by interpolating finite impulse response (FIR) filters in conjunction with digital backward propagation (DBP) in coherent 112 Gbit s−1 dual-polarization quadrature phase shift keying (DP-QPSK) transmission. The results depict that RRC pulses are more tolerant to intra-channel non-linearities, i.e. self-phase modulation (SPM), as compared to standard RZ-33 and NRZ pulses. The non-linear threshold point is improved by using RRC pulses by a factor of 2 dB signal input power as compared to RZ pulses and by 4 dB signal launch power as compared to NRZ pulses. The behavior of RRC pulses is also investigated with standard single mode fiber (SMF), non-zero dispersion shifted fiber (NZDSF) and next-generation large Aeff pure silica core fiber (LA-PSCF). Most importantly multi-span DBP is implemented and in the case of RRC pulses the computational efforts of the conventional DBP algorithm are reduced by 80% with a diminutive Q-penalty of 0.74 dB. The duty cycle of the RRC pulses is further optimized for efficient system performance. We have also compared the performance of single-channel transmission with the multi-channel transmission, where the performance is limited due to inter-channel non-linear effects. Furthermore, the non-linear tolerance of RRC pulses is investigated with; (a) different amplifier spacing and (b) variation in transmission link design information for the DBP algorithm.