Coherent Optical Fiber Communication Systems Research Articles

Coherent all Optical Reservoir Computing for Equalization of Impairments in Coherent Fiber Optic Communication Systems

Coherent all Optical Reservoir Computing for Equalization of Impairments in Coherent Fiber Optic Communication Systems

High-Capacity Coherent WDM Networks Empowered by Probabilistic Shaping and End-to-End Deep Learning

To optimize the functionality of coherent optical fiber communication (OFC) systems and enhance their capacity related to long-haul transmissions, wavelength-division multiplexing (WDM) and probabilistic constellation shaping (PCS) techniques have been used. This paper develops an end-to-end (E2E) deep learning (DL)-based PCS algorithm, i.e., autoencoder (AE) for a high-order modulation format WDM system that minimizes nonlinear effects while ensuring high capacity and considers system parameters, in particular those related to the OFC channel. Only the AE of the central channel is trained to meet the specified performance objective, as the system design employs identical AEs in each WDM channel. The simulation results show that the architecture should consist of two hidden layers, with thirty two nodes per hidden layer and a ”32×modulation order” batch size to obtain optimal system performance, when designing AE using a dense layer neural network. The behavior of the AE is examined to determine the optimum launch-power ranges that enhance the system's performance. The developed AE-based PCS-WDM provides a 0.4 shaping gain and outperforms conventional solutions.

Performance investigation of geometric constellation shaping-based coherent WDM optical fiber communication system supported by deep-learning autoencoder

Geometric constellation shaping (GCS) has been proposed to enhance the performance of wavelength-division multiplexing (WDM) coherent optical fiber communication (OFC) systems. This paper presents a comprehensive simulation platform to design and simulate these systems' performance using an advanced autoencoder (AE) technique. The design of the AE is based on end-to-end deep learning and takes into account the system parameters, especially those related to the OFC channel. The system design uses identical AEs, one in each WDM channel, and only the AE of the central channel is trained to achieve the required performance target. The developed AE simulation platform is capable of assessing the bit error rate characteristics, signal-to-noise ratio, and mutual information for long-haul coherent OFC-WDM systems operating with various modulation formats. The simulation results indicate that using a multilayer perceptron neural network to design AE requires four hidden layers, sixteen nodes per hidden layer, and a “16x modulation order” batch size to achieve optimum system performance. The AE's behaviour is investigated to identify the allowed ranges of the optimal launch power using two different procedures that achieve better system performance for 2D and 4D constellations.

Joint CD, DGD, and PDL Estimation Enabled by FrFT based Time-Frequency Reconstruction

A high-precision optical performance monitoring (OPM) scheme is proposed to achieve chromatic dispersion estimation (CDE), differential group delay (DGD) estimation, and polarization-dependent loss (PDL) estimation simultaneously for the long haul coherent optical fiber communication system. A time-frequency analysis method based on the fractional Fourier transformation (FrFT) is applied to the optical signal under different channel impairments to reconstruct the two-dimensional distribution images. Multi-task convolutional neural network (MT-CNN) is then adopted to extract the corresponding features of impairments and establish a solid relationship between the images and impairment quantities, thus can jointly estimate CD, DGD, and PDL. We validate in simulation the proposed estimation using 50GBaud PDM-16QAM, the mean absolute error (MAE) for CD, DGD, and PDL estimation is 114ps/nm, 0.26ps, and 0.072dB, and the monitoring window ranges from 1600∼48000ps/nm, 4∼100ps, and 0∼2dB, respectively. Simulation verification indicates that the proposed estimation method achieves high precision and robustness to ASE noise and fiber nonlinearity of self-phase modulation (SPM).

Joint monitoring of OSNR and frequency offset for coherent optical fiber communication systems based on QPSK training sequence

We propose a joint monitoring scheme of optical signal-to-noise ratio (OSNR) and frequency offset (FO) based on the analysis of a quadrature phase-shift keying training sequence (QPSK-TS) spectrum for coherent optical fiber communication systems. In the proposed scheme, the FO estimation (FOE) consists of a coarse FOE stage and a fine FOE stage. Firstly, the coarse FOE stage is operated by searching for the peak of QPSK-TS spectrum. Then, after conducting coarse FO compensation (FOC) and down-sampling process to the QPSK-TS signal, the fine FOE stage can be realized by operating fast Fourier transform (FFT) to the 4th power of the signal. Compared with the traditional FOE scheme based on FFT with 4th-power operation, the FOE range of the proposed scheme can be extended to 3 times without losing the FOE resolution. After the FOC procedure with the proposed FOE scheme, OSNR can be monitored accurately by obtaining the whole in-band amplified spontaneous emission (ASE) noise from QPSK-TS spectrum. It is noteworthy that both the proposed FOE scheme and the OSNR monitoring scheme are insensitive to chromatic dispersion (CD) and intra-channel nonlinearity (NL). Simulation results for a 28 GBaud system with 2400 km transmission length show that when the OSNR range is 10∼28 dB and FO is 10.25 GHz, the mean OSNR estimated error is < 0.9 dB and the standard deviation is < 0.3 dB. Furthermore, the back-to-back (B2B) experiment results with 20 GBaud show that when the OSNR range is 10∼26 dB and FO is 7 GHz, the mean OSNR estimated error is < 0.8 dB and the standard deviation is also < 0.3 dB.

Kalman filter polarization demultiplexing algorithm based on diagonalized matrix treatment.

When we implement the equalizations of polarization effects using a Kalman filter (KF) in a coherent optical fiber communication system, we will require to multiply many matrices. If the state vector describing the system has a dimension of n, the state error covariance matrix P will have the dimension of n × n, and other matrices used in the Kalman filter will also have the dimension of n × l (l is the dimension of the measurement vector). If n is very large, the KF-based algorithm will suffer from significant complexity, which results in an impractical KF-based polarization demultiplexing algorithm. In this paper, we propose a new structured KF-based polarization demultiplexing algorithm in which the state error covariance matrix P is diagonalized, which we call the diagonalized Kalman filter (DKF). We theoretically analyze the rationality of the DKF, and the validity of the DKF was verified in both 64 Gbaud polarization-division multiplexed (PDM) QPSK and 16QAM Nyquist coherent optical simulation systems. Compared with the conventional KF, simulation results proved that under a rotation of state of polarization from 1 to 10 Mrad/s for QPSK and 1 to 5 Mrad/s for 16QAM, a differential group delay from 15 to 75 ps, and a residual chromatic dispersion of 100 ps/nm, the OSNR penalties for the DKF are only within 0.5 dB for QPSK at the threshold BER = 3.8 × 10-3, and within 2 dB for 16-QAM at the threshold BER = 2 × 10-2, respectively, compare to the case of no impairment. In the meantime, for the proposed DKF, a computational complexity reduction of over 30% is achieved, compared with conventional KF, at the expense of about no more than 50 symbols convergence delay.

Nonlinear Coherent Optical Systems in the Presence of Equalization Enhanced Phase Noise

Equalization enhanced phase noise (EEPN) occurs due to the interplay between laser phase noise and electronic dispersion compensation (EDC) module. It degrades significantly the performance of uncompensated long-haul coherent optical fiber communication systems. In this work, a general expression accounting for EEPN is presented based on Gaussian noise model to evaluate the performance of multi-channel optical communication systems using EDC and digital nonlinearity compensation (NLC). The nonlinear interaction between the signal and the EEPN is analyzed. Numerical simulations are carried out in nonlinear Nyquist-spaced wavelength division multiplexing (WDM) coherent transmission systems. Significant performance degradation due to EEPN in the cases of EDC and NLC are observed, with and without the consideration of transceiver (TRx) noise. The validation of the analytical approach has been done via split-step Fourier simulations. The maximum transmission distance and the laser linewidth tolerance are also estimated to provide important insights into the impact of EEPN.

Fast tracking of polarization impairments using DSP algorithms in fiber for a coherent optical communication system

AbstractIn a 100G coherent optical fiber communication system, the equalization algorithm of polarization effects in fibers is generally integrated in digital signal processing (DSP) using a multiple input/multiple output (MIMO) equalizer to overcome the impairment due to the polarization effects in fiber. However, it was found in some extreme scenarios, such as the lightning strikes near the fiber cables, the Kerr effect and Faraday effect would induce very fast time‐varying state‐of‐polarization (SOP) and transient variation of principal‐state‐of‐polarization (PSP) of polarization mode dispersion (PMD) which would result in the coherent receivers unlocking. Faced with the difficulty, we propose a 3‐parameter RSOP model and design a window‐split structured Kalman filter equalization scheme instead of conventional MIMO equalizer to cope with this extreme scenario of large PMD combined with ultra‐fast rotation of SOP in presence of residual chromatic dispersion (RCD). The proposed equalization method has an excellent performance and can cope with RCD in the range of ±820 ps/nm under RSOP from 100 krad/s to 3 Mrad/s and DGD = 200 ps.

Joint OSNR and Frequency Offset Estimation Using Signal Spectrum Correlations

We propose an efficient and modulation-format-transparent method to jointly estimate optical signal-to-noise ratio (OSNR) and frequency offset (FO) by using signal spectrum correlations for coherent optical fiber communication systems. Based on the signal spectrum correlation analysis, a coarse FO estimation (FOE) and the corresponding compensation can be conducted after chromatic dispersion compensation (CDC). Then, OSNR monitoring can be accurately operated without deterioration caused by FO. Meanwhile, to realize fine FOE, down-sampling process of signal can be used to reduce the complexity of fast Fourier transform-based FOE (FFT-FOE) without losing FOE resolution. Simulation results show that when the OSNR is in the range of 10 to 30 dB, the proposed scheme presents an absolute OSNR estimation error lower than 0.18 dB. Finally, we experimentally demonstrate our scheme in an optical back-to-back (B2B) transmission link using 28 Gbaud dual-polarization (DP)-4/16/32-quadrature amplitude modulation (QAM) formats, and an absolute OSNR estimation error lower than 0.66 dB is achieved for OSNR ranging from 15 to 30 dB.

Hybrid Dy-NFIS &amp; RLS equalization for ZCC code in optical-CDMA over multi-mode optical fiber

For long haul coherent optical fiber communication systems, it is significant to precisely monitor the quality of transmission links and optical signals. The channel capacity beyond Shannon limit of Single-mode optical fiber (SMOF) is achieved with the help of Multi-mode optical fiber (MMOF), where the signal is multiplexed in different spatial modes. To increase single-mode transmission capacity and to avoid a foreseen “capacity crunch”, researchers have been motivated to employ MMOF as an alternative. Furthermore, different multiplexing techniques could be applied in MMOF to improve the communication system. One of these techniques is the Optical Code Division Multiple Access (Optical-CDMA), which simplifies and decentralizes network controls to improve spectral efficiency and information security increasing flexibility in bandwidth granularity. This technique also allows synchronous and simultaneous transmission medium to be shared by many users. However, during the propagation of the data over the MMOF based on Optical-CDMA, an inevitable encountered issue is pulse dispersion, nonlinearity and MAI due to mode coupling. Moreover, pulse dispersion, nonlinearity and MAI are significant aspects for the evaluation of the performance of high-speed MMOF communication systems based on Optical-CDMA. This work suggests a hybrid algorithm based on nonlinear algorithm (Dynamic evolving neural fuzzy inference (Dy-NFIS)) and linear algorithm (Recursive least squares (RLS)) equalization for ZCC code in Optical-CDMA over MMOF. Root mean squared error (RMSE), mean squared error (MSE) and Structural Similarity index (SSIM) are used to measure performance results.

Reduced sampling rate Kalman filters for carrier phase and frequency offset tracking in 200\xa0Gbps 16 QAM coherent communication system

We propose 1 state and 2 state multi-step Kalman filters (MKFs) to estimate and compensate CFO, LPN and NLPN in long-haul coherent fiber-optic communication systems. The proposed filters generate state estimates once every m symbols and therefore operate at a reduced sampling rate compared to conventional KFs that perform symbol by symbol processing. No computations are performed to obtain phase estimates of the intermediate m-1 samples; instead, the present and previous estimates are averaged and used to derotate the intermediate m-1 samples which are then demodulated to recover the transmitted symbols. This reduces the computational load on the receiver DSP. Further, in order to improve estimation accuracy, we adaptively vary the process noise covariance Q. Simulation results of 200 Gbps PDM 16 QAM system over 12 spans shows that the proposed 1 state MKF can reduce the sampling rate requirement by a factor of m = 20 with Q-factor degradation of 1.32 dB compared to single-step KF at linewidth of 100 kHz. The 2 state MKF tracks PN and CFO with a maximum step size of m=10 for a CFO of 100 MHz at linewidth of 100 kHz. We also study the dynamic performance of the proposed algorithms by applying step change to CFO. The 2 state MKF with adaptive Q is able to track a step change of 400 MHz of CFO with m = 1 and 3 with high estimation accuracy but slower convergence time compared to the non-adaptive 2 state MKF. Finally, we study the computational requirements of the proposed MKFs and show that they offer significant reduction in computations compared to single-step KF thus making the proposed filters suitable for hardware implementation.

A Novel Ultra-Broadband Polarization Filter Based on a Microstructured Optical Fiber with a Gold-Coated Air Hole.

In this paper, a pentagonal microstructured optical fiber polarization filter by utilizing a surface plasmon resonance effect is proposed. The characteristics of the mode-coupling and filtering of the filter are studied by making use of the full-vector finite element method. The performance of the filter is greatly affected by the structure parameters. The losses of Y and X polarization of the fiber core are 665.97 and 0.17 dB/cm at 1.55 μm, respectively, and the loss ratio is 3917.47. This shows that the filter has a greater loss ratio. Moreover, both the extinction ratio and tolerance are also researched, which shows that the proposed filter has a wider filtering bandwidth and better fabrication tolerance. The designed filter has an important role in wavelength-division multiplexing (WDM) and coherent optical fiber communication systems.

A Blind Nonlinearity Compensator Using DBSCAN Clustering for Coherent Optical Transmission Systems

Coherent fiber-optic communication systems are limited by the Kerr-induced nonlinearity. Benchmark optical and digital nonlinearity compensation techniques are typically complex and tackle deterministic-induced nonlinearities. However, these techniques ignore the impact of stochastic nonlinear distortions in the network, such as the interaction of fiber nonlinearity with amplified spontaneous emission from optical amplification. Unsupervised machine learning clustering (e.g., K-means) has recently been proposed as a practical approach to the blind compensation of stochastic and deterministic nonlinear distortions. In this work, the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is employed, for the first time, for blind nonlinearity compensation. DBSCAN is tested experimentally in a 40 Gb/s 16 quadrature amplitude-modulated system at 50 km of standard single-mode fiber transmission. It is shown that at high launched optical powers, DBSCAN can offer up to 0.83 and 8.84 dB enhancement in Q-factor when compared to conventional K-means clustering and linear equalisation, respectively.

Frequency offset estimation for nonlinear frequency division multiplexing with discrete spectrum modulation.

Although fruitful studies have been conducted on carrier frequency offset (CFO) estimations in linear coherent optical fiber communication systems, there are few studies on CFO estimations and recoveries in the systems based on the nonlinear Fourier transform (NFT). Although the CFO is originated from the linear frequency domain, it definitely has effects on nonlinear spectra, including the shift of the nonlinear frequency and the phase rotations of the scattering data, which are similar to its effects on linear spectra. This work indicates that it is feasible to estimate frequency offset (FO) by capturing symbol variations in the nonlinear frequency domain (NFD) rather than in the linear frequency domain; the latter was usually exploited in the literature. Based on a thorough investigation of the FO induced behavior that appears in a nonlinear frequency division multiplexing (NFDM) system, we proposed a nonlinear frequency domain estimation method aided by training symbols (TS) using an angle search algorithm after NFT operations at the receiver. The discussions in this paper prove that the proposed method is generally applicable to the NFDM systems regardless of whether using single or multiple eigenvalues. A performance comparison between the NFD method and the conventional method in the linear frequency domain is performed with different modulation formats for both single and multiple eigenvalue NFDM transmission systems. The analysis results show that the proposed method holds the better stability and estimation accuracy in contrast with the linear domain estimation method. The TS overhead can also be deduced dramatically, which implies better transmission efficiency. Therefore, the NFD method is more powerful for eigenvalue NFDM transmission systems, especially for the scenarios where high order modulation formats and multiple eigenvalues are utilized.

Blind Modulation Format Identification Using Differential Phase and Amplitude Ratio

We propose a blind digital modulation format identification (MFI) method for coherent optical fiber communication systems. Based on the evaluation of differential phase distribution ratio (DPDR) and average of amplitude ratio (AAR), a monitoring factor ${R}$ , the product of DPDR and AAR, is defined to distinguish whether the signal modulation format is QPSK, 16-QAM, or 64-QAM. Simulation and experimental results demonstrate that the proposed MFI can perform an identification when the OSNR of the incoming signal is greater than 12 dB. The proposed method needs no extensive training data sets and can tolerate residual chromatic dispersion (−210–210 ps/nm) and phase noise.

Laser Frequency Combs for Coherent Optical Communications

Laser frequency combs with repetition rates on the order of 10 GHz and higher can be used as multi-carrier sources in wavelength-division multiplexing (WDM). They allow replacing tens of tunable continuous-wave lasers by a single laser source. In addition, the comb's line spacing stability and broadband phase coherence enable signal processing beyond what is possible with an array of independent lasers. Modern WDM systems operate with advanced modulation formats and coherent receivers. This introduces stringent requirements in terms of signal-to-noise ratio, power per line, and optical linewidth which can be challenging to attain for frequency comb sources. Here, we set quantitative benchmarks for these characteristics and discuss tradeoffs in terms of transmission reach and achievable data rates. We also highlight recent achievements for comb-based superchannels, including >10 Tb/s transmission with extremely high spectral efficiency, and the possibility to significantly simplify the coherent receiver by realizing joint digital signal processing. We finally discuss advances with microresonator frequency combs and compare their performance in terms of flatness and conversion efficiency against state-of-the-art electro-optic frequency comb generators. This contribution provides guidelines for developing frequency comb sources in coherent fiber-optic communication systems.

Independent component analysis based digital signal processing in coherent optical fiber communication systems

In this paper, channel equalization techniques for coherent optical fiber transmission systems based on independent component analysis (ICA) are reviewed. The principle of ICA for blind source separation is introduced. The ICA based channel equalization after both single-mode fiber and few-mode fiber transmission for single-carrier and orthogonal frequency division multiplexing (OFDM) modulation formats are investigated, respectively. The performance comparisons with conventional channel equalization techniques are discussed.

Signal Processing for Fiber Optic Systems

This paper reviews the digital signal processing (DSP) methods used in coherent fiber optic communication systems. With the advances in high speed DSP, linear impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD) can be compensated for using fixed/adaptive equalizers. It is also possible to compensate for the interplay between dispersion and nonlinearity by digital back propagation (DBP), in which the virtual fibers whose signs of dispersion, loss and nonlinear coefficients are opposite of those of the transmission fiber, are realized in the digital domain by numerically solving the nonlinear Schrӧdinger equation (NLSE). DSP equalization enhances the transmission performance and error-free reach of coherent fiber optic systems significantly. Keywords: Chromatic dispersion, coherent communications, digital back propagation, digital signal processing, fiber optic communications, nonlinear fiber optics, perturbation techniques, polarization mode dispersion.

Application of local error method to SSSF simulation of vector propagation in dispersion compensated optical links

A local error method based on an analytical scheme previously developed for the scalar optical fiber channel is applied to the second-order symmetrized split-step Fourier simulation of polarization multiplexed signal propagation through dispersion compensated optical fiber links. It is found that the global simulation accuracy for the vector propagation can be satisfied using the local error bound from a scalar propagation model for the same global error over a large range of simulation accuracy, chromatic dispersion, and differential group delay. Furthermore, carefully designed numerical simulations are used to show that similar local simulation error are obtained for vector simulations and that the similar local error leads to higher computational efficiency compared to other prevalent step-size selection schemes. The scaling of the global simulation error with respect to the number of optical fiber spans is demonstrated, and global error control for multi-span simulations is proposed. Combining the local error and global error control, the developed simulation scheme can significantly speed up the time-consuming simulations in coherent optical fiber communication system analysis and design.

Coupling of a laser diode to a quadric interface lensed monomode elliptic-core step index fiber: efficiency computation with the ABCD matrix

We report what to our knowledge is the first theoretical prediction of the coupling efficiency of a laser diode emitting two wavelengths either 1.3 or 1.5 μm, to three elliptic core step index fibers with different aspect ratios via quadric interface microlens of three different focal lengths on the fiber tip. Here, quadric interface microlens contains elliptical (hemispherical included), hyperbolic and parabolic microlenses. Instead of considering special ABCD matrix for individual microlens, a simple, accurate, and popular unified transfer ABCD matrix for refraction of quadric microlens under paraxial approximation is utilized to analyze the theoretical coupling efficiency, based on Gaussian beam approximation. The coupling efficiency can reach as high as 98.63 % with optimizing structure parameters of specific lensed fiber. The analysis can give some guidance for fabricating quadric interface lensed elliptic core fiber which are mainly useful in polarisation-maintaining fiber optic sensors and coherent fiber optic communication systems.