Digital Backpropagation Research Articles

Digital Back Propagation With Optimal Step Size for Polarization Multiplexed Transmission

A digital back propagation (DBP) scheme with optimal step size for polarization division multiplexed transmission system is proposed. For a fixed number of steps in DBP, the optimum step size is calculated by minimizing the mismatch between the area under the exponentially increasing nonlinearity profile and its stepwise approximation. In simulations, the vector nonlinear Schodinger equation or Manakov equations are used for forward propagation and Manakov equations are used for backward propagation. The simulation results show that the proposed scheme using the optimum step size outperforms that using the uniform step size at the same computational cost.

Nonlinear effects compensation in Optical Coherent PDM-QPSK Systems

Nonlinear effects has been appointed as the main limitation in coherent optical fiber transmission. Digital Back-Propagation algorithms and Maximum Likelihood Sequence Estimation are two of the current studied methods to cope with such impairment and extend the systems maximum reach. In this article, we analyzed both methods in a 112 Gb/s Dual Polarization Quadrature Phase Shifting Keying (DP-QPSK) optical coherent system through simulations and experimental results. In order to reduce the huge required computational complexity, a modified back-propagation algorithm is also analyzed.

Ideal optical backpropagation of scalar NLSE using dispersion-decreasing fibers for WDM transmission

An ideal optical backpropagation (OBP) scheme to compensate for dispersion and nonlinear effects of the transmission fibers is proposed. The scheme consists of an optical phase conjugator (OPC), N spans of dispersion-decreasing fibers (DDFs) and amplifiers, placed at the end of the fiber optic link. In order to compensate for the nonlinear effects of the transmission fibers exactly, the nonlinear coefficient of the backpropagation fiber has to increase exponentially with distance or equivalently the power in the backpropagation fiber should increase exponentially with distance if the nonlinear coefficient is constant. In this paper, it is shown that a combination of DDFs and amplifiers can compensate for the nonlinear effects exactly. An analytical expression for the dispersion profile of the DDF is derived. Numerical simulation of a long haul wavelength division multiplexing (WDM) fiber optic system with the proposed OBP scheme shows that the system reach can be enhanced by 54% as compared to digital backpropagation (DBP).

On nonlinearly-induced noise in single-channel optical links with digital backpropagation

In this paper, we investigate the performance limits of electronic chromatic dispersion compensation (EDC) and digital backpropagation (DBP) for a single-channel non-dispersion-managed fiber-optical link. A known analytical method to derive the performance of the system with EDC is extended to derive a first-order approximation for the performance of the system with DBP. In contrast to the cubic growth of the variance of the nonlinear noise-like interference, often called nonlinear noise, with input power for EDC, a quadratic growth is observed with DBP using this approximation. Finally, we provide numerical results to verify the accuracy of the proposed approach and compare it with existing analytical models.

An integral split-step fourier method for digital back propagation to compensate fiber nonlinearity

In optical fiber transmission systems, the split-step Fourier method (SSFM) has been widely used in digital back propagation (DBP) to compensate fiber nonlinearity. In this paper, by using the Lagrange's Integral Mean Value Theorem (LIMVT), we derive an analytical expression to calculate the optimal value of the nonlinearity calculation position (NLCP) for different systems and we propose an integral SSFM (I-SSFM) based on the expression. The I-SSFM can be performed more accurately and efficiently without parameter optimization. Simulations of various transmission links show that the I-SSFM outperforms the conventional asymmetric SSFM (A-SSFM) and the symmetric SSFM (S-SSFM) significantly, especially when we employ less amount of steps to ensure computation efficiency. The computation effort of the I-SSFM reaches as low as 50% of that of the S-SSFM.

Error vector magnitude based parameter estimation for digital filter back-propagation mitigating SOA distortions in 16-QAM

We investigate the performance of digital filter back-propagation (DFBP) using coarse parameter estimation for mitigating SOA nonlinearity in coherent communication systems. We introduce a simple, low overhead method for parameter estimation for DFBP based on error vector magnitude (EVM) as a figure of merit. The bit error rate (BER) penalty achieved with this method has negligible penalty as compared to DFBP with fine parameter estimation. We examine different bias currents for two commercial SOAs used as booster amplifiers in our experiments to find optimum operating points and experimentally validate our method. The coarse parameter DFBP efficiently compensates SOA-induced nonlinearity for both SOA types in 80 km propagation of 16-QAM signal at 22 Gbaud.

Nonlinear Digital Back Propagation compensator for coherent optical OFDM based on factorizing the Volterra Series Transfer Function

We introduce an efficient and accurate nonlinear compensator (NLC) for digital back-propagation (DBP) of coherent optical OFDM receivers, based on a factorization procedure for the Volterra Series Transfer Function (VSTF) with 3N degrees of freedom for N frequency samples. The O(N2) nonlinear compensation complexity of generic Volterra evaluation (normalized per-subcarrier) is reduced to 28 + 6logN. Our analysis and simulations indicate that this NLC system outperforms previous VSTF-based non-linear compensation methods. Compared to a most recent VSTF-based method, the new method incurs 52% extra computational complexity in return for improved nonlinear tolerance of ~2 dB for the particular analyzed link.

Implication of Parameter Values on Low-Pass Filter Assisted Digital Back Propagation for DP 16-QAM

The low-pass filter (LPF) assisted digital back propagation (DBP) algorithm is investigated for 112 Gb/s dual-polarization 16-ary quadrature-amplitude-modulation transmission up to 2400 km. The performance implications of the parameter values for the LPF-DBP algorithm are considered in detail through determining the dependence of the bit error ratio (BER) on the number of nonlinear compensation (NLC) steps per span for optimum parameter values and the sensitivity of the BER to nonoptimum parameter values. The sensitivity to nonoptimum values is investigated as well for different transmission lengths and launch powers. It is shown that the optimum parameter values depend on the NLC step size, but that for a given step size representative values can be used for a range of transmission lengths and channel launch powers.

Analytical Evaluation of Practical DBP-Based Intra-Channel Nonlinearity Compensators

We derive an analytical expression for the transmission performance of intra-channel nonlinearity compensated and dispersion unmanaged orthogonal frequency-divison multiplexing (OFDM) systems using practical digital back propagation (DBP) with span-length step size. The analytical expression is verified by numerical simulations with evaluation inaccuracy less than 0.4 dB for 1000-km 16-QAM modulated polarization division multiplexed-OFDM transmissions. Using the derived theory, the dependence of performance and optimum nonlinear compensation coefficient on system parameters is identified. The limitation of processing bandwidth on the performance improvement using practical intra-channel DBP is also investigated. Analytical results show that for achieving 1-dB improvement on maximum <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> factor, the processing signal bandwidth of span-length step size DBP should be within 55 GHz for 2000-km SSMF transmissions over 62.5-km spans.

Performance comparison between digital back propagation (DBP) and pilot-aided method for fiber nonlinearity compensation in different fiber links

We numerically investigate and compare the performance of fiber nonlinearity compensation using digital back propagation (DBP) method and pilot-aided method in coherent optical transmission systems using different fiber links. Simulations for wavelength division multiplexed (WDM) 112Gb/s polarization division multiplexed quadrature phase shift keying (PDM-QPSK) systems with dispersion unmanaged (no DM) and dispersion managed (DM) fiber links are implemented. System Q-factor and maximum transmission distance at bit error rate (BER) of 3.8ÿ10⿿3 are calculated for performance comparison. The results show that, for system with no DM fiber link, DBP method outperforms pilot-aided method, because DBP method has better performance for intra-channel fiber nonlinearity compensation. However, for system with DM fiber link where inter-channel fiber nonlinearity plays an important role, pilot-aided method performs better than DBP method, because of its ability for inter-channel fiber nonlinearity compensation.

400 Gbit/s 256 QAM-OFDM transmission over 720 km with a 14 bit/s/Hz spectral efficiency by using high-resolution FDE

We demonstrate 400 Gbit/s frequency-division-multiplexed and polarization-division-multiplexed 256 QAM-OFDM transmission over 720 km with a spectral efficiency of 14 bit/s/Hz by using high-resolution frequency domain equalization (FDE) and digital back-propagation (DBP) methods. A detailed analytical evaluation of the 256 QAM-OFDM transmission is also provided, which clarifies the influence of quantization error in the digital coherent receiver on the waveform distortion compensation with DBP.

Per-symbol-based digital back-propagation approach for PDM-CO-OFDM transmission systems

For polarization-division-multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) systems, we propose a per-symbol-based digital back-propagation (DBP) approach which, after cyclic prefix removal, conducts DBP for each OFDM symbol. Compared with previous DBP, this new proposal avoids the use of inefficient overlap-and-add operation and saves one fast Fourier transform (FFT) module, therefore simplifying the hardware implementation. Transmitting a 16-QAM, 42.8-Gb/s PDM-CO-OFDM signal over 960-km standard single mode fiber (SSMF), we compare the previous and the proposed DBP approaches with different receiver's sampling rates and different step lengths in each DBP iteration, and found that the proposed DBP can achieve a similar performance as that of the previous DBP while enjoying a simpler implementation. We have also specifically introduced a small self-phase modulation (SPM) model for DBP and demonstrated its feasibility with the same experimental setup.

Nonlinearity Compensation of 224 Gb/s Dual-Polarization 16-QAM Transmission Over 2700 km

Long-haul transmission for distances greater than 2000 km is investigated for a 224 Gb/s dual-polarization 16-ary quadrature-amplitude-modulation signal, using ultralarge effective area fiber with span lengths of 75.5 km and distributed Raman amplification. By using nonlinear compensation (NLC) based on the low-pass filter (LPF) assisted digital back propagation (DBP) algorithm, a transmission distance of 2700 km is demonstrated with moderate complexity (0.25 backpropagation steps/span) and good robustness to deviation of the algorithm parameters from their optimum values. Compared to the standard DBP algorithm, the LPF assisted DBP algorithm can allow a reduction in the number of NLC steps/span, but with an increased computational complexity for each step. The two DBP algorithms are compared in terms of the number of real multiplications per bit, thus allowing the algorithm with lower complexity to be determined for a given level of performance.

Nonlinear Tolerant Spectrally-Efficient Transmission Using PDM 64-QAM Single Carrier FDM With Digital Pilot-Tone

We propose nonlinear tolerant single carrier frequency-division-multiplexing (SC-FDM) signal enhanced by digital pilot-tone for future high speed Ethernet transport like 400 G Ethernet. First, we discuss system configuration and the wavelength-division-multiplexed (WDM) transmission of SC-FDM signals employing polarization-division-multiplexed (PDM) 64-ary quadrature amplitude modulation (64-QAM). Next, we describe the long-haul transmission characteristics of 50 GHz-spaced 538 Gb/s × 7 ch WDM signals. We compare digital back-propagation (DBP) and digital pilot-tone for nonlinearity compensation and experimentally show that digital pilot-tone can effectively compensate the phase noise induced by inter-channel nonlinear effects with less computational complexity than DBP. Then we discuss a high-capacity transmission experiment employing 548 Gb/s PDM-64QAM SC-FDM; 102.3 Tb/s (224 × 548 Gb/s) C- and extended L-band WDM transmission is demonstrated over 240 km (3 × 80 km) of pure-silica-core fiber (PSCF) with all-Raman amplification. Thanks to the high nonlinear tolerance enhanced by pilot-tone, we can employ the 80 km repeater spacing used in conventional terrestrial systems. Assuming 20% forward error correction (FEC) overhead, a spectral efficiency of 9.1 b/s/Hz is achieved.

Assessment of Intrachannel Nonlinear Compensation for 112 Gb/s Dual-Polarization 16QAM Systems

For 112 Gb/s dual-polarization 16-ary quadrature amplitude modulation systems, the performance and complexity of the low-pass filter (LPF)-assisted digital back-propagation (DBP) algorithm for mitigating intrachannel fiber nonlinearity are investigated. Comparison is made with both linear equalization and the standard DBP algorithm for single-channel transmission (simulation and experiment) and for wavelength division multiplexed (WDM) transmission with channel spacings of 50 and 35 GHz (simulation). With optimized values for the algorithm parameters, the simulation results show that, compared to linear equalization, the 0.2 steps/span LPF-assisted DBP algorithm can increase the transmission distance by 84%, 40%, and 17% for a single-channel, 50 GHz channel-spaced WDM, and 35 GHz channel-spaced WDM transmission, respectively. These improvements in the transmission distance are 54%, 75%, and 77% of those achieved with the 4 steps/span standard DBP algorithm but at considerably lower complexity. Single-channel experimental results show that the 0.25 steps/span LPF-assisted DBP algorithm can increase the transmission distance by 43%, which is 68% of the improvement achieved with the 4 steps/span standard DBP algorithm. Compared to the standard DBP algorithm, the LPF-assisted DBP algorithm can allow a reduction in the number of steps/span, but with an increased computational complexity for each step. The two DBP algorithms are compared in terms of the number of real multiplications per bit, thus allowing the algorithm with lower complexity to be determined at a given level of performance.

Assessment of dispersion map impact on the digital back propagation of long-haul fibre-optic links

The back propagation algorithm is one of the best methods known for simultaneous linear and nonlinear impairment mitigation in long-haul fibre-optic links. Better understanding the full potential of such algorithm is key to improve the capacity of future links, whose design is likely to depend on the algorithm performance under different link configurations. In this paper, we carry out a novel and pertinent comparison in terms of the computational complexity requirements of both symmetric and asymmetric back-propagation implementation approaches for different dispersion map configurations, using simple single channel transmission, which results in the proposal of several design rules for the optimized deployment of ultra-long haul optical transport systems. In particular, it is concluded that dispersion unmanaged transmission is preferable in the sense of compatibility with different link design configurations as well as computational complexity requirements and maximum performance that can be achieved.

Fiber nonlinear tolerance comparison between 112 Gb/s coherent transmission systems using quadrature-phase-shift-keying, offset quadrature-phase-shift-keying, and minimum-shift-keying formats

We numerically investigate the nonlinear transmission perfor- mance of 112 Gb∕s coherent transmission systems using polarization multiplexed quadrature-phase-shift-keying (QPSK), offset QPSK (OQPSK) and minimum-shift-keying (MSK) formats, and compare the fiber nonlinear tolerances of the three modulation formats. Simulation results show that in both single channel and wavelength-division-multi- plexed (WDM) systems, OQPSK is slightly more resistant to fiber nonli- nearities than QPSK, and MSK has the best fiber nonlinear tolerance. The advantage of MSK format over QPSK and OQPSK is particularly nota- ble in WDM systems. When digital back propagation (DBP) is used in the digital coherent receiver for intra-channel fiber nonlinearity compensation, system performance is improved with better Q-factor, enlarged input opti- cal power range and extended transmission distance. It is found that the use of DBP brings the largest performance improvement in QPSK system and the least performance improvement in MSK system although MSK system has better fiber nonlinear tolerance.©2012 Society of Photo-Optical

EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM

We experimentally demonstrated long-distance transmission of 68.3 Gb/s wavelength-division multiplexing polarization division multiplexing (PDM)-orthogonal frequency division multiplexing (OFDM)-16QAM and 85.5 Gb/s PDM-OFDM-32QAM signals. The PDM-OFDM-16QAM signals have been successfully transmitted over 4242 km with a net spectral efficiency of 5.46 b/s/Hz. Furthermore, utilizing multiband digital back-propagation for nonlinearity compensation, the PDM-OFDM-32QAM signals at 6.84 b/s/Hz net SE have been successfully transmitted over the same distance. After transmission, both 16QAM and 32QAM signals surpassed the 20% soft-decision forward error correction threshold. To the best of our knowledge, these results correspond to the longest transmission distance for the PDM-OFDM-16QAM and PDM-OFDM-32QAM signals with SE higher than 5 and 6.5 b/s/Hz, respectively, by employing only erbium doped fiber amplifier amplification.

Marked performance improvement of 256 QAM transmission using a digital back-propagation method

We demonstrate substantial performance improvements in 256 QAM transmission in terms of both data rate and distance that we realized by using a digital back-propagation (DBP) method. 160 Gbit/s-160 km and 64 Gbit/s-560 km transmissions were successfully achieved with a polarization-multiplexed 256 QAM signal, in which the symbol rate and transmission distance were greatly increased by compensating for the interplay between dispersion and nonlinearity, which is responsible for the transmission impairment especially for a higher symbol rate and longer distance.

Optical backpropagation for fiber-optic communications using optical phase conjugation at the receiver

A fiber-optic system design with optical backpropagation that uses an optical phase conjugator, high-dispersion fibers, and highly nonlinear fibers is investigated. The proposed technique outperforms the midpoint optical phase conjugation and digital backpropagation with the same step size.