Coherent Optical Communication Systems Research Articles

Capacity enhancement through entropy loading with probabilistically shaped signals in a frequency comb-based transmission system.

We demonstrate a multichannel entropy loading mechanism in an optical frequency comb-based coherent communication system. In high-capacity wavelength division multiplexing communications, the individual laser sources can be replaced by an optical frequency comb, thus reducing the complexity and energy consumption of the transmitter. However, the power variation among different comb lines will lead to performance discrepancies. Spectral flattening filters can be adopted to suppress the variation at the expense of an additional system loss. Alternatively, by applying probabilistic shaping, we have implemented multichannel entropy loading to facilitate a continuous adaptation of the source entropy. The data rate can be dynamically allocated according to the performance of each channel. Through the loading scheme, the non-uniform performances across the channels are effectively mitigated, achieving a capacity enhancement of 34.91 Gbit/s.

Combined modulation format identification and optical signal-to-noise ratio monitoring with high accuracy and generalizability based on a proposed fused module few-shot learning algorithm in dynamic coherent optical transmissions

Modulation format identification (MFI) and optical signal-to-noise ratio (OSNR) monitoring are important portions of optical performance monitoring (OPM) for future dynamic optical networks. In this paper, we proposed a fusion module few-shot learning (FMFSL) algorithm as an improvement upon the ordinary few-shot learning algorithms for image recognition with the specialty in adopting a combination of a dilated convolutional group and an asymmetric convolutional group to advance the feature extraction. FMFSL algorithm is applied in MFI and OSNR monitoring in coherent optical communication systems with its performance investigated in both back-to-back and fiber transmission scenarios using small-scale constellation diagrams. The results show that FMFSL algorithm can achieve 100% accuracy in MFI and higher OSNR monitoring accuracy compared to the few-shot learning algorithms Deep Nearest Neighbor Neural Network (DN4) and Prototypical Nets (PN) with 2.14% and 4.28% for 64QAM and 3.38% and 8.06% for 128QAM, respectively, without much increase in time consumption. Furthermore, the trained FMFSL algorithm remains excellent in MFI and OSNR monitoring without retraining while employed in back-to-back transmission scenarios with smaller OSNR intervals and fiber transmission scenarios with different amounts of Kerr nonlinearity, demonstrating its high capabilities in generalization and robustness. FMFSL algorithm provides a potential solution for OPM in future dynamic optical networks as a novel machine learning tool.

Exploration of Four-Channel Coherent Optical Chaotic Secure Communication with the Rate of 400 Gb/s Using Photonic Reservoir Computing Based on Quantum Dot Spin-VCSELs

In this work, we present a novel four-channel coherent optical chaotic secure communication (COCSC) system, incorporating four simultaneous photonic reservoir computers in tandem with four coherent demodulation units. We employ a quartet of photonic reservoirs that capture the chaotic dynamics of four polarization components (PCs) emitted by a driving QD spin-VCSEL. These reservoirs are realized utilizing four PCs of a corresponding reservoir QD spin-VCSEL. Through these four concurrent photonic reservoir structures, we facilitate high-quality wideband-chaos synchronization across four pairs of PCs. Leveraging wideband chaos synchronization, our COCSC system boasts a substantial 4 × 100 GHz capacity. High-quality synchronization is pivotal for the precise demasking or decoding of four distinct signal types, QPSK, 4QAM, 8QAM and 16QAM, which are concealed within disparate chaotic PCs. After initial demodulation via correlation techniques and subsequent refinement through a variety of digital signal processing methods, we successfully reconstruct four unique baseband signals that conform to the QPSK, 4QAM, 8QAM and 16QAM specifications. Careful examination of the eye diagrams, bit error rates, and temporal trajectories of the coherently demodulated baseband signals indicates that each set of baseband signals is flawlessly retrieved. This is underscored by the pronounced eye openings in the eye diagrams and a negligible bit error rate for each channel of baseband signals. Our results suggest that delay-based optical reservoir computing employing a QD spin-VCSEL is a potent approach for achieving multi-channel coherent optical secure communication with optimal performance and enhanced security.

Investigation of Costas loop phase deviation effect on BER performance of space downlink coherent communication system with DPSK scheme

The Costas loop is an important technology for synchronous demodulation in space coherent communication. However, due to the limitation of the loop device and processing technology, it is difficult to achieve high-precision locking, which results in the Costas loop phase deviation and further affects the quality of the demodulation signal. In this paper, a closed-form bit error rate (BER) model is derived to evaluate the Costas loop phase deviation effect on BER performance in the space differential phase shift keying (DPSK) modulation and heterodyne detection communication system, considering laser phase noise, atmospheric turbulence, and detector noise. Based on the BER model, analytical solution simulation is conducted. The results show that the BER performance deteriorates varying with the increase of the Costas loop phase deviation. In addition, we research how to better balance the laser linewidth and Costas loop accuracy in the system design to ensure good communication status. We find that the wider the laser linewidth, the more stringent the Costas loop accuracy. Furthermore, the BER performance versus the Costas loop phase deviation under different satellite-to-ground communication system parameter settings including divergence angle, receiving aperture, signal laser power, and data rate are analyzed. This work provides valuable references for space optical coherent communication systems design.

Transformer-Based Nonlinear Equalization for DP-16QAM Coherent Optical Communication Systems

Transformer-Based Nonlinear Equalization for DP-16QAM Coherent Optical Communication Systems

DACNN-aided nonlinear equalizer for a probabilistic shaping coherent optical communication system.

The probabilistic shaping (PS) technique is a key technology for fiber optic communication systems to further approach the Shannon limit. To solve the problem that nonlinear equalizers are ineffective for probabilistic shaping optical communication systems with non-uniform distribution, a distribution alignment convolutional neural network (DACNN)-aided nonlinear equalizer is proposed. The approach calibrates the equalizer using the probabilistic shaping prior distribution, which reduces the training complexity and improves the performance of the equalizer simultaneously. Experimental results show nonlinear equalization of 120Gb/s PS 64QAM signals in a 375km transmission scenario. The proposed DACNN equalizer improves the receiver sensitivity by 2.6dB and 1.1dB over the Volterra equalizer and convolutional neural network (CNN) equalizer, respectively. Meanwhile, DACNN converges with fewer training epochs than CNN, which provides great potential for mitigating the nonlinear distortion of PS signals in fiber optic communication systems.

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.

Wide and Deep Learning-Aided Nonlinear Equalizer for Coherent Optical Communication Systems

In this study, we developed a wide and deep network-based nonlinear equalizer to compensate for nonlinear impairment in coherent optical communication systems. In our proposed equalizer, the power feature factor and inter-symbol feature sequence in the received signal are analyzed by two combined networks, wide and deep, respectively, so that the information contained in the signal can be fully utilized. We designed an experiment using a 120 Gbit/s 64-quadrature amplitude modulation (64-QAM) coherent optical communication system over a 375 km standard single-mode fiber (SSMF) to verify the performance of the proposed wide and deep network-based nonlinear equalizer. The experimental results showed that the proposed wide and deep network-based nonlinear equalizer achieved better performance at lower complexity compared with the traditional neural network-based nonlinear equalizer. The proposed equalizer significantly improved the equalization effect at a cost of a 0.3% increase in parameters, which indicates the potential of the proposed method for application in coherent optical communication systems.

Generalized Rayleigh quotient optimization method for inter-channel nonlinearity compensation in coherent optical communication systems.

Inter-channel nonlinearity compensation plays a crucial role in wavelength division multiplexing (WDM) systems for improving transmission capacity and distance. In this work, we propose a novel, to the best of our knowledge, inter-channel nonlinearity compensation method called generalized Rayleigh quotient optimization (GRQO) method with two different working modes. In an 8 × 64 GBaud 16-ary quadrature amplitude modulation (16-QAM) experimental system over 1600 km standard single-mode fiber (SSMF), the proposed method shows a 0.40 dB Q2 factor improvement over nonlinear polarization cross talk canceller (NPCC) with a moderately low computational complexity of about 2000 real multiplications per bit (RMb).

16QAM optical signal generation scheme based on weighted optimal Euclidean distance.

A two-dimensional signal constellation scheme for binary uniform memoryless source transmission in optical fiber channels is studied in this paper. In geometric shaping (GS), optimization algorithms are usually used to change the overall position of constellation points while maintaining the probability of constellation points unchanged. Different optimization functions are used to allocate the position of constellation symbols, thereby improving constellation performance. A 16 quadrature amplitude modulation (QAM) optical signal generation scheme based on weighted optimal Euclidean distance is proposed in this paper. In order to obtain the best constellation diagram and increase the shaping gain, the weighted optimal Euclidean distance that can minimize the bit error rate (BER) over multiple iterative optimizations is used as the objective function. On the one hand, the proposed 16QAM optical signal generation scheme based on weighted optimal Euclidean distance always outperforms the uniform square 16QAM and the uniform circle 16QAM schemes in the back to back (BTB) transmission. On the other hand, after analyzing the simulation demonstration in a 50GBaud coherent optical communication system over 3000km, results demonstrate that the optical signal to noise ratio (OSNR) performance of this system is better than that of the uniform square 16QAM and the uniform circle 16QAM, which is improved by 0.52dB and 0.85dB, respectively. In addition, the proposed 16QAM system increases the transmission distance by 989km and 741km, respectively, compared to the other two systems. The performance confirms that the proposed novel 16QAM scheme, to the best of our knowledge, can effectively improve the reliability and transmission distance. Therefore, the proposed scheme has a certain development prospect in the future long-distance transmission of high-speed optical fiber communication.

Nonlinear compensation for few-mode fiber MDM-WDM systems using probabilistic neural network

In this paper, we propose for the first time to apply probabilistic neural network (PNN) to fiber nonlinear compensation (NLC) in a high-speed coherent optical communication system that combines few-mode fiber (FMF) mode division multiplexing (MDM) with wavelength division multiplexing (WDM). By training on a small number of symbols, the PNN equalizer can compute the statistical distribution of the signal nonlinearity, make decisions on test symbols, and thereby compensate for the nonlinear impairments of the signals. To verify the effectiveness of the proposed scheme, we construct a MDM-WDM simulation system with 28 GBaud polarization division multiplexing (PDM) 16-quadrature amplitude modulation(QAM) and 64 GBaud PDM-64QAM, 6 spatial mode signals are transmitted over 11 wavelength channels with link lengths of 1500 km and 400 km, respectively. The results show that the PNN equalizer can make nonlinear judgments on received signals and effectively compensate the signal impairments caused by Kerr nonlinearity and device nonlinearity in a large launch power range after undergoing carrier phase recovery (CPR). Meanwhile, this scheme exhibits strong robustness against residual linear mode coupling (LMC), differential mode group delay (DMGD), and amplified spontaneous emission (ASE) noise. Finally, by the computational complexity comparison, it is proved that the complexity of the probabilistic neural network nonlinear compensation (PNN NLC) scheme is lower than that of digital back propagation (DBP) with comparable performance, which is on the order O(N).

Fast fiber nonlinearity compensation method for PDM coherent optical transmission systems based on the Fourier neural operator.

Fiber nonlinearity compensation (NLC) is likely to become an indispensable component of coherent optical transmission systems for extending the transmission reach and increasing capacity per fiber. In this work, we introduce what we believe to be a novel fast black-box neural network model based on the Fourier neural operator (FNO) to compensate for the chromatic dispersion (CD) and nonlinearity simultaneously. The feasibility of the proposed approach is demonstrated in uniformly distributed as well as probabilistically-shaped 32GBaud 16/32/64-ary quadrature amplitude modulation (16/32/64QAM) polarization-division-multiplexed (PDM) coherent optical communication systems. The experimental results demonstrate that about 0.31 dB Q-factor improvement is achieved compared to traditional digital back-propagation (DBP) with 5 steps per span for PDM-16QAM signals after 1600 km standard single-mode fiber (SSMF) transmission at the optimal launched power of 4 dBm. While, the time consumption is reduced from 6.04 seconds to 1.69 seconds using a central processing unit (CPU), and from 1.54 seconds to only 0.03 seconds using a graphic processing unit (GPU), respectively. This scheme also reveals noticeable generalization ability in terms of launched power and modulation format.

Influence of atmospheric turbulence on coherent detection performance of space coherent optical communication

Space coherent optical communication technology is considered to be an important way to overcome the bottleneck in current high-speed space communication. However, atmospheric turbulence seriously limits its realization. Based on the Huygens-Fresnel principle and the low-frequency compensation power spectrum inversion method, this work first investigates the random distribution characteristics of the amplitude and phase of a Gaussian beam after it has been transmitted through atmospheric turbulence. Then, using the coherent mixing efficiency and communication bit error rate model, the influence of atmospheric turbulence on the performance of spatial coherent optical communication systems is obtained. Finally, a laser heterodyne detection experimental system is built to quantitatively study the influence of atmospheric turbulence on the coherent detection performance of spatial coherent optical communication. The conclusions drawn from this study are as follows. 1) The spatial phase distortion caused by the weak turbulence channel is relatively small and will hardly affect the light intensity distribution characteristics of the Gaussian beam. In the case of weak turbulence, the influence of weak turbulence on the performance of coherent optical communication system is almost negligible. The communication bit error rate will decrease rapidly with the increase of the number of single bit data photons. The communication signal-to-noise ratio can be better than 10<sup>–5</sup> when the number of single-bit photons is greater than 10. 2) Moderate turbulence will change the intensity distribution characteristics of the Gaussian beam, but will not cause a serious shift in the center of the spot. Under moderate turbulence conditions, the coherent mixing efficiency decreases rapidly as the turbulence intensity continues to increase, but the communication bit error rate still decreases rapidly with the increase of the number of single bit data photons. At this time, increasing the number of single-bit photons can suppress the negative influence of moderate intensity turbulence on the performance of coherent optical communication systems. 3) Strong turbulence will cause severe spatial phase distortion of the beam, destroy the consistency of the light intensity distribution, and cause a serious shift in the center of the spot. Under strong turbulence conditions, the coherent mixing efficiency of coherent optical communication systems approaches zero, and increasing the number of single bit data photons cannot significantly reduce the bit error rate, seriously affecting the quality of coherent optical communication. Atmospheric turbulence is an important limiting factor for developing space coherent optical communication. This study can provide useful references for evaluating the performance of space coherent optical communication systems.

Performance of quantum-dash mode-locked lasers (QD-MLLDs) for high-capacity coherent optical communications.

We investigate the capabilities and limitations of quantum-dash mode-locked lasers (QD-MLLDs) as optical frequency comb sources in coherent optical communication systems. We demonstrate that QD-MLLDs are on par with conventional single-wavelength narrow linewidth laser sources and can support high symbol rates and modulation formats. We manage to transmit 64 quadrature amplitude modulation (QAM) signals up to 80 GBd over 80 km of standard single-mode fiber (SSMF), which highlights the distinctive phase noise performance of the QD-MLLD. Using a 38.5 GHz (6 dB bandwidth) silicon photonic (SiP) modulator, we achieve a maximum symbol rate of 104 GBd with 16QAM signaling and a maximum net rate of 416 Gb/s per carrier in a single polarization setup and after 80 km-SSMF transmission. We also compare QD-MLLD performance with commercial narrow-linewidth integrable tunable laser assemblies (ITLAs) and explore their potential for use as local oscillators (LOs) and signal carriers. The QD-MLLD has 45 comb lines usable for transmission at a frequency spacing of 25 GHz, and an RF linewidth of 35 kHz.

Flexible Phase Synchronization for Wireless Optical Coherent Communication System With Adaptive Fractionally-Spaced Blind Equalization Combined With Adaptive Kalman Filter

Flexible Phase Synchronization for Wireless Optical Coherent Communication System With Adaptive Fractionally-Spaced Blind Equalization Combined With Adaptive Kalman Filter

Complex principal component analysis-based complex-valued fully connected NN equalizer for optical fibre communications

An increasing number of scholars have proposed many schemes to mitigate the Kerr nonlinearity effect restricting the transmission capacity of optical fibres. In this paper, we proposed a complex principal component analysis-based complex-valued fully connected neural network (P-CFNN) model aided by perturbation theory and demonstrated it experimentally on a dual-polarization 64-quadrature-amplitude modulation coherent optical communication system. What we believe to be a novel complex principal component analysis (CPCA) algorithm applied to complex-valued fully connected neural network (CFNN) is designed to further reduce the computational complexity of the model. Meanwhile, an equivalent real-valued fully connected neural network (RFNN) with the same time complexity as a CFNN is proposed for fair performance comparison. Under all launched optical powers, the performance of the P-CFNN equalizer is the best among all comparison algorithms, and the maximum ΔQ-factor compared to without employing the nonlinear compensation algorithm reaches 3.94 dB. In addition, under the constraint of the same Q-factor, we confirmed that the proposed P-CFNN obtained a 40% reduction in time complexity and a 70% reduction in space complexity compared with the PCA-based RFNN, which also proved the very large application prospect of the P-CFNN equalizer in optical fibre communication systems.

Demonstration of 120 Gbit/s turbulence-resilient coherent optical communication employing cylindrical vector beam multiplexing

Free space optical (FSO) communication has gained widespread attention due to its advantages, including high confidentiality, high communication capacity, and no limitation of spectrum. One of the great challenges in FSO communication is the transmission performance degradation in atmospheric turbulence channel due to wavefront distortion and scintillation. Here, we proposed and experimentally demonstrated a 120 Gbit/s vector beam multiplexed coherent optical communication system with turbulence-resilient capacity. Four multiplexed vector beams, each carrying a 30 Gbit/s quadrature phase-shift keying signal, propagate through different turbulence conditions. The influence of turbulence channel on the vector beam impairments is experimentally investigated. Under the weaker turbulence conditions, the system bit error rates are below the forward error correction threshold of 3.8 × 10−3. In comparison with the Gaussian mode, the communication interruption probability of the vector beams system decreases from 36% to 12%-18% under stronger turbulence conditions.

Real-time low-complexity diversity combining algorithm for free space coherent optical communication systems over atmospheric turbulence channel.

A novel diversity combining scheme, in conjunction with the complex-valued decision-directed least mean square (CV-DD-LMS) algorithm, is evaluated, and a real-time experimental validation is presented. This proposed scheme employs the CV-DD-LMS algorithm to concurrently perform beam combination and carrier phase recovery (CPR), thereby effectively reducing the overall complexity of digital signal processing. Furthermore, in the numerical simulation, under a low signal-to-noise ratio (SNR), a scheme utilizing the CV-DD-LMS algorithm effectively avoids cycle slips (CS) and outperforms schemes employing independent CPR modules. We experimentally validate this novel scheme by implementing it on an FPGA in a real-time 2.5Gb/s QPSK diversity-receiving system with three inputs. The back-to-back sensitivity is assessed using static received optical power, while the dynamic performance is evaluated by employing variable optical attenuators (VOAs) to simulate a power fluctuation at a frequency of 100kHz. The result proves that the implementation of the CV-DD-LMS algorithm yields stable performance while effectively reducing computational complexity.

BER analysis of an optimum MIMO linear receiver in optical SDM systems with mode-dependent loss.

Multiple-input multiple-output (MIMO) receivers designed to optimize the minimum mean square error (MMSE) are a common choice in coherent optical communication systems based on spatial division multiplexing (SDM). This kind of receivers naturally integrate both MIMO equalization and matched filtering functions. However, when the optical channel exhibits significant mode-dependent loss (MDL) and/or mode-dependent gain (MDG), the impact of inter-symbol interference (ISI) and crosstalk that arise, even using an ideal MIMO MMSE linear receiver, is barely analyzed. Moreover, due to the random nature of the MDL/MDG model, the resulting ISI, crosstalk, and bit error rate (BER) also become random variables and, hence the system performance is more unpredictable. In this paper, we first evaluate the residual distortion (ISI and crosstalk) after the MIMO receiver and then we study the validity of assuming it as an additional Gaussian noise term independent of the channel noise. Next, the probability density distribution (PDF) of the BER is analyzed, from both an analytical perspective and numerical simulations. For the latter, we use a single-carrier 2-PAM (pulse amplitude modulation) system, with pulse shaping, and the MIMO MMSE receiver implementation by means of a MIMO fractionally-spaced equalizer (FSE). We carry out simulations of the system under different conditions of MDL/MDG level and signal to noise ratio (SNR), measured at the receiver input. Additionally, we address possible fits of the BER PDF to known closed-form distributions, among which the Generalized Extreme Value (GEV) family of distributions is selected, and polynomial functions are proposed that relate the system parameters with the GEV PDF parameters. Finally, we present contour maps of BER according to a giving target of system outage probability (OP) that depend on the MDL/MDG and SNR conditions.

Hybrid Constellation Shaping 64QAM Based on Hexagonal Lattice of Constellation Subset

Increasing demand for higher-speed and large-capacity data communications has driven the development of constellation shaping technology. This paper proposes a hybrid constellation shaping scheme for 64-quadrature amplitude modulation (64QAM) based on hexagonal lattice of a constellation subset. The proposed scheme aims to enhance the nonlinear tolerance of higher-order modulated signals and further improve the constellation shaping gain. The initial quantitative characterization of the constellation is firstly performed based on the hexagonal lattice structure. Then, the objective function of maximizing constellation figure of merits (CFM) is utilized to determine the position distribution of constellation points, resulting in the generation of the geometric shaping-64QAM (GS-64QAM) signal. Finally, according to concentric hexagonal layers, all constellation points are divided into multiple subsets where points within the same subset are assigned the same probability, and the hybrid shaping-64QAM (HS-64QAM) signal is generated. To validate the effectiveness of the proposed scheme, the experimental verification was demonstrated in a 120 Gbit/s multi-span coherent optical communication system. Experimental results indicate that, at the soft-decision forward error correction threshold, HS-64QAM achieves an optical signal-to-noise ratio (OSNR) gain of 1.9 dB and 4.1 dB over uniform GS-64QAM in back-to-back and 375 km transmission scenarios, respectively. Furthermore, HS-64QAM achieves an OSNR gain of 2.7 dB and 7.6 dB over uniform Square-64QAM in back-to-back and 375 km transmission scenarios, respectively.