Nonlinear Impairments Research Articles

Spectrally efficient DWDM system using DQPSK modulation

Abstract DWDM technology is gaining popularity in fiber-optic communication due to high-speed transmission channel capacity demands. The adoption of this system has been driven by this demand. Researchers focus on optimizing data transmission parameters within channel characteristics for maximum performance. The signal’s form typically influences the optical channel capacity, the guiding medium’s dispersive and non-linear characteristics, and interference from multiple sources. This study investigates how efficient modulated systems control linear and non-linear impairments in optical channel capacity due to high data rates transmitted over optical communication networks, aiming to circumvent current issues. The selection of pulse shape and modulation format is crucial for an effective DWDM optical communication system due to the rigorous specifications of the optical channel. Modulation formats like intensity and phase have become viable network design technologies, allowing for network creation that operates to the designer’s satisfaction. This academic study examines the theoretical properties of various models used to analyze and recreate high-speed optical communication links, aiming to understand the impact of system components and modulation techniques.

End-to-end learning of joint noise shaping and probabilistic shaping for OAM mode division multiplexing transmission.

Intensity modulation direct detection (IM/DD) orbital angular momentum (OAM) mode division multiplexing (MDM) technology can greatly expand the capacity of a communication system, which is a promising solution for the next generation of high-speed passive optical networks (PONs). However, there are serious obstacles such as mode coupling, device nonlinear impairment, and quantization noise in an IM/DD OAM-MDM system with a low-resolution digital-to-analog converter (DAC). In this Letter, we propose a novel, to the best of our knowledge, end-to-end (E2E) learning scheme based on a double residual feature decoupling network (DRFDnet) emulator with joint probabilistic shaping (PS) and noise shaping (NS) for the OAM-MDM IM/DD transmission. Our DRFDnet emulator can accurately build a complex nonlinear model of an OAM-MDM system by separating the signal impairments into linear and nonlinear. Meanwhile, a DRFDnet-based E2E scheme for joint PS and NS is presented with the aim of compensating the signal impairment for the OAM-MDM IM/DD system. An experiment is carried out on a 200 Gbit/s PON system based on the OAM-MDM IM/DD transmission. The experimental results demonstrate that the proposed DRFDnet-based joint PS and NS scheme is a promising solution to effectively mitigate nonlinear distortions and outperforms the CGAN-based joint PS and NS scheme and traditional joint PS and NS scheme with receiver sensitivity improvements of 1.2 dBm and 2.5 dBm under hard-decision forward error correction (HD-FEC) thresholds, respectively. Our experimental results demonstrate that the proposed DRFDnet emulator-based E2E learning scheme is a viable candidate for future PON.

Impact of dispersion-shifted fiber on optical communications link through orthogonal channels

Dispersion-Shifted Fiber (DSF) is essential for reducing chromatic dispersion in high-speed optical communication systems. This study investigates the influence of Four Wave Mixing (FWM) on the quality of signals in orthogonal channels. We examine the advantages of DSF technology and analyze the impact of modulation formats such as On-Off Keying with Return-to-Zero (OOK-RZ) and Duo Binary Modulation class-1 (DBM-1) on transmission performance at different distances. This research assesses the efficacy of orthogonal channels in mitigating four-wave mixing (FWM) effects and improving the overall performance of eight-channel systems at distances of 100 km and 200 km through computer simulations. The results of our study show notable enhancements, namely in optimizing the Q-factor (a metric for signal quality) and reducing bit error rates when employing orthogonal channels compared to previous work. By integrating orthogonal channels with OOK-RZ modulation, we achieved higher performance and reduced nonlinear impairments in a simulated eight-channel system with 50 GHz spacing and 80 Gb/s data rates. This effect was particularly pronounced at high input power levels. At an input power of 20 dBm and a distance of 200 km, this particular combination yielded a maximum Q-factor of 27.25 and a minimum FWM power of −54 dBm. In comparison, under the same conditions, the use of OOK-RZ alone resulted in an FWM power of −24 dBm and a Q-factor of only 1.63. This research provides vital insights into enhancing the efficiency and dependability of optical communication systems, hence facilitating breakthroughs in high-speed data transfer and network scalability.

Quadruple impact of SPM, XPM, FWM and SRS nonlinear impairments on the performance of DWDM-PON

Recently, dense wavelength division multiplexing passive optical networks (DWDM-PONs) have become a considerable choice for 5G and beyond fronthaul implementations. Formerly, we have proposed a full-duplex bidirectional DWDM-PON architecture convenient for those implementations and analyzed the combined dual impact of four-wave mixing (FWM) and stimulated Raman scattering (SRS) nonlinear impairments on the proposed architecture. Meanwhile, a detailed literature analysis showed us that the combined quadruple impact of self phase modulation (SPM), cross phase modulation (XPM), FWM and SRS on the performance of bidirectional DWDM-PONs have never been researched up to now. In this paper, quadruple impact of SPM, XPM, FWM and SRS on the performance of both uplink channels (ULCs) and downlink channels (DLCs) of the formerly proposed DWDM-PON has been analyzed with simulations. Simulations have been performed in O-band region for ULCs and in C-band region for DLCs of 2 × 15- and 2 × 63-channel DWDM-PONs having 12.5 GHz, 25 GHz, 50 GHz, 100 GHz equally-spaced channels. The quadruple impact of optical nonlinear impairments on the DWDM-PON performance has been analyzed with signal-to-crosstalk ratio (SXR) simulations performed under varying channel input powers and channel lengths. Results show that under the quadruple nonlinear impact reliable bidirectional transmission with an SXR over 23 dB can be achieved for channel input powers below 0.58 mW and 0.16 mW in 2 × 15- and 2 × 63-channel DWDM-PONs, respectively, for all channel spacing values and 25 km transmission lengths. Moreover, results also imply that variations in channel lengths do not significantly affect SXR at both ULCs and DLCs of 2 × 15- and 2 × 63-channel DWDM-PONs for lengths exceeding 50 km. The thorough analysis presented in the paper will give a new insight for analysis of conventional and next generation PONs.

Advanced Neural Network-Based Equalization in Intensity-Modulated Direct-Detection Optical Systems: Current Status and Future Trends

Intensity-modulated direct-detection (IM/DD) optical systems are most widely employed in short-reach optical interconnects due to their simple structure and cost-effectiveness. However, IM/DD systems face mixed linear and nonlinear channel impairments, mainly induced by the combination of square-law detection and chromatic dispersion, as well as the utilization of low-cost non-ideal transceivers. To solve this issue, recent years have witnessed a growing trend of introducing machine learning technologies such as neural networks (NNs) into IM/DD systems for channel equalization. NNs usually present better system performance than traditional approaches, and various types of NNs have been investigated. Despite the excellent system performance, the associated high computational complexity is a major drawback that hinders the practical application of NN-based equalizers. This paper focuses on the performance and complexity trade-off of NNs employed in IM/DD systems, presenting a systematic review of the current status of NN-based equalizers as well as a number of effective complexity reduction approaches. The future trends of leveraging advanced NN in IM/DD links are also discussed.

Nonlinear RF impairments modeling with OFDM symbol-based parallel Wiener–Hammerstein structure

In the paper, a novel orthogonal frequency division multiplexing (OFDM) symbol-based parallel Wiener–Hammerstein structure is proposed to deal with the problem of nonlinear radio frequency (RF) impairments modeling for a cyclic prefix OFDM (CP-OFDM) waveform in telecommunication systems. The aforementioned structure is an equivalent linear-in-parameters representation of the parallel Wiener–Hammerstein structure in the considered problem. The structure is formally derived enabling the usage of identification algorithms compared with the artificial neural network (ANN) approach. The solution is compliant with current telecommunication standards.

Weight-adaptive joint mixed-precision quantization and pruning for neural network-based equalization in short-reach direct detection links.

Neural network (NN)-based equalizers have been widely applied for dealing with nonlinear impairments in intensity-modulated direct detection (IM/DD) systems due to their excellent performance. However, the computational complexity (CC) is a major concern that limits the real-time application of NN-based receivers. In this Letter, we propose, to our knowledge, a novel weight-adaptive joint mixed-precision quantization and pruning approach to reduce the CC of NN-based equalizers, where only integer arithmetic is taken into account instead of floating-point operations. The NN connections are either directly cutoff or represented by a proper number of quantization bits by weight partitioning, leading to a hybrid compressed sparse network that computes much faster and consumes less hardware resources. The proposed approach is verified in a 50-Gb/s 25-km pulse amplitude modulation (PAM)-4 IM/DD link using a directly modulated laser (DML) in the C-band. Compared with the traditional fully connected NN-based equalizer operated with standard floating-point arithmetic, about 80% memory can be saved at a minimum network size without degrading the system performance. Quantization is also shown to be more suitable to over-parameterized NN-based equalizers compared with NNs selected at a minimum size.

Nonlinear impairment compensation in multi-channel communication systems based on correlated digital backpropagation with separation of walk-off effect

Digital backpropagation (DBP) is a commonly used method to compensate for the nonlinear impairments of optical fiber channels in the electrical domain, offering a new approach to enhancing the data capacity without affecting the system performance. However, due to the repeated Fourier transform and inverse transform of the split-step Fourier method (SSFM), the complexity of DBP algorithm has increased significantly. In this paper, a correlated backpropagation algorithm with the separation of the walk-off effect is developed, which improves the computational step and significantly reduces the complexity of the algorithm. Simulation results demonstrate that in a 6-channel PDM-16QAM system, the proposed hybrid algorithm reduces the computational complexity by 73.96 % compared to the traditional DBP algorithm for an 800 km transmission.

Minimization of dispersion and non-linear effects in WDM based long-haul high capacity optical communication systems

Abstract Chromatic dispersion and nonlinear impairments pose challenges in high-capacity optical transmission systems, leading to signal distortions, channel interference and diminished the transmission performances. This paper explores the utilization of dispersion compensating fibers (DCF) using different schemes to mitigate the dispersion that accumulates along the length of a fiber in a 16 × 10 Gbps high-capacity long haul WDM system over a range of 500 km. When different wavelengths of light pulses are transmitted through an optical fiber, they experience varying speeds due to the refractive index’s wavelength dependency. As a result, the light pulses become temporally spread out as they travel through the fiber, and this dispersion persists throughout the fiber’s length. Considering non-linear effects such as self-phase modulation (SPM) and cross-phase modulation (XPM), this paper analyze and compare the three compensation schemes of DCF in a 16 channel WDM system. Moreover the impact of non-linearities based on fiber length are also analyzed and compared. The results are evaluated by comparing metrics such as Q-factor, bit error rate (BER) and eye height. The analysis concludes that the symmetrical compensation scheme of DCF outperforms the pre- and post-compensation scheme. This finding suggests that the symmetrical compensation method offers a promising solution for high-capacity access networks, providing high spectral efficiency, cost-effectiveness, and improved flexibility.

Distributed reservoir computing based nonlinear equalizer for VCSEL based optical interconnects

We propose a distributed reservoir computing based nonlinear equalizer for 106 Gbps VCSEL based optical interconnects. By comparing with neural network and Volterra series based equalizers, the computational complexity of this proposed nonlinear equalizer is significantly reduced in the training, prediction and inference process. 106 Gbps PAM4 short-range optical transmission is demonstrated by experiment, using a VCSEL-based co-packaged optical transmitter to verify the performance of the equalizer and key parameters that affect the nonlinear compensation performance are carefully investigated. We believe that by incorporating such simplified nonlinear equalizers, it is possible to compensate for nonlinear impairments while preserving the inherent advantages of VCSEL-based optical interconnects. This optical interconnect will become a promising paradigm to overcome I/O performance penalty when communication leaving packages.

End-to-end learning strategy based on a frequency domain feature decoupling network emulator with joint probabilistic shaping and equalization for a 300-Gbit/s OAM mode division multiplexing transmission

Mode coupling and device nonlinear impairment appear to be a long-standing challenge in the orbital angular momentum (OAM) mode division multiplexing (MDM) of intensity modulation direct detection (IM/DD) transmission systems. In this paper, we propose an end-to-end (E2E) learning strategy based on a frequency domain feature decoupling network (FDFDnet) emulator with joint probabilistic shaping (PS) and equalization for an OAM-MDM IM/DD transmission with three modes. Our FDFDnet emulator can accurately build a complex nonlinear model of an OAM-MDM system by separating the signal into features from different frequency domains. Furthermore, a FDFDnet-based E2E strategy for joint PS and equalization is presented with the aim of compensating the signal impairment for the OAM-MDM IM/DD system. An experiment is carried out on a 300 Gbit/s carrierless amplitude phase-32 (CAP-32) signal with three OAM modes over a 10 km ring-core fiber transmission, and the results show that the proposed FDFDnet emulator outperforms the traditional CGAN emulator, with improvements in the modelling accuracy of 30.8%, 26.3% and 31% for the three OAM modes. Moreover, the receiver sensitivity of the proposed E2E learning strategy is higher than for the CGAN emulator by 3, 2.5, 2.2 dBm and the real channel by 5.5, 5.1, and 5.3 dBm for the three OAM modes, respectively. Our experimental results demonstrate that the proposed FDFDnet emulator-based E2E learning strategy is a promising contender for achieving ultra-high-capacity interconnectivity between data centers.

Discrete wavelet transform assisted convolutional neural network equalizer for PAM VLC system.

With the deepening of research and the further differentiation of damage types, and to compensate for both linear and nonlinear damage in visible light communication systems (VLCs), we propose a novel discrete wavelet transform-assisted convolutional neural network (DWTCNN) equalizer that combines the advantages of wavelet transform and deep learning methods. More specifically, wavelet transform is used in DWTCNN to decompose the signal into diverse coefficient series and employ an adaptive soft-threshold method to eliminate redundant information in the signal. The coefficients are then reconstructed to achieve complete signal compensation. The experimental results show that the proposed DWTCNN equalizer can significantly reduce nonlinear impairment and improve system performance with the bit error rate (BER) under the 7% hard-decision forward error correction (HD-FEC) limit of 3.8 × 10-3. We also experimentally compared DWTCNN with the Long Short-Term Memory (LSTM) and entity extraction neural network (EXNN) equalizer, the Q factor has been improved by 0.76 and 0.53 dB, and the operating ranges of the direct current (DC) bias have increased by 4.76% and 23.5%, respectively.

FrFT-based estimation of linear and nonlinear impairments using Vision Transformer

To comprehensively assess the conditions of an optical fiber communication system, it is essential to implement joint estimation of the following four critical impairments: nonlinear signal-to-noise ratio (SNRNL), optical signal-to-noise ratio (OSNR), chromatic dispersion (CD), and differential group delay (DGD). However, current studies only achieve identifying a limited number of impairments within a narrow range, due to a lack of high-performance computing algorithms and a unified representation of impairments. To address these challenges, we adopt time-frequency signal processing based on the fractional Fourier transform (FrFT) to achieve the unified representation of impairments, while employing a Transformer-based neural network (NN) to break through network performance limitations. To verify the effectiveness of the proposed estimation method, numerical simulations were conducted on a five-channel polarization-division-multiplexed quadrature phase shift keying (PDM-QPSK) long haul optical transmission system with the symbol rate of 50 GBaud per channel. The mean absolute error (MAE) for SNRNL, OSNR, CD, and DGD estimation is 0.091 dB, 0.058 dB, 117 ps/nm, and 0.38 ps, and the monitoring window ranges from 0−20dB, 10−30dB, 1700−51,000ps/nm, and 0−100ps, respectively. Our proposed method achieves accurate estimation of linear and nonlinear impairments over a broad range, representing a significant advancement in the field of optical performance monitoring (OPM).

Nonlinear fiber effects in ultra-high power 10 × 10 Gbit/s WDM-IM free-space systems for satellite links.

We investigate an unexplored type of nonlinear impairments that will take place in a very short fiber after the booster amplifier in a Free Space Optical (FSO) system for space communications. In Earth-satellite links, optical power levels up to 100 W could be required at the transmitter side to achieve the foreseen 100 Gbit/s capacity, because of the extremely high losses. These systems thus need an optical booster amplifier having very high optical power and it should be connected to the transmitting telescope by means of a short fiber (few meters). Here, we discuss and investigate the impact of the nonlinear fiber effects by means of numerical simulations, and estimate the impairments in a Wavelength Division Multiplexing (WDM) 10 × 10 Gbit/s system with intensity modulation. The obtained results clearly indicate that, in this system, the most relevant effect is Four Wave Mixing. We proved that this can be observed as soon as the total power exceeds 20 W. Due to the short fiber length, the system impairments are not affected by chromatic dispersion or channel spacing. We demonstrate that an effective means to reduce the impact is by adopting Polarization Interleaving, i.e., odd and even channels with orthogonal state of polarization. This solution could not work in long terrestrial links because of polarization mode dispersion, yet it can be effectively exploited in short fiber patch cords. These results can be used as a guideline to control this type of impairment in high-power FSO systems for satellite links.

Analysis of the resilience of 32-channels system to nonlinear impairments based on different modulation formats and bit rates

Abstract Designing a DWDM system for fiber optic transmissions requires optimizing some important parameters to enable the system to be more tolerant to nonlinear impairments. This paper proposes a simulation of a 32-channels system with different bit rates per channel, for different modulation formats (RZ, NRZ, 4-QAM, and DQPSK) then the Gaussian (Gauss) and Hyperbolic Secant (Sech) pulses. The main goal is to investigate the resilience of the designed system to nonlinear effects, taking into account the different modulation formats and bit rates used. Thus, several comparisons were taken into account in the different simulations carried out with the optisystem software. The results reveal that for a bit rate of 40 Gbps per channel, the order of performance is NRZ, Sech, 4-QAM, RZ, and DQPSK; whereas for a bit rate of 100 Gbps per channel, the order becomes NRZ, DQPSK, 4-QAM, Sech, and RZ. For a bit rate of 100 Gbps without nonlinear effects, the 4-QAM format would be more efficient than other modulation formats for the input powers considered (−10 dBm to 10 dBm). While this same 4-QAM format is more vulnerable to nonlinear effects beyond an input power of 5 dBm. At a bit rate of 100 Gbps, the DQPSK format would be more resilient to nonlinear effects for input powers between −10 dBm and 8 dBm for the simulated system.

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.

Evaluating DNN and LSTM nonlinear compensators for enhanced performance in DCO-OFDM system

Abstract This study proposes a deep neural network (DNN) and long-short-term memory (LSTM) nonlinear compensators method for direct current (DC)-biased optical orthogonal frequency division multiplexing (DCO-OFDM) in indoor visible light communication (VLC) conventional to handle the nonlinearity and retrieve the high-fidelity signals, and compared in terms of performance and complexity. Unlike the data training after fast Fourier transform in existing deep neural network schemes, this study proposes a scheme that uses the time domain waveform data output by photodiodes for direct equalization. The OFDM signal at the receiving end is equalized, which can mitigate hybrid linear and nonlinear impairments and save spectrum resources without requiring the pilots’ assistance. Compared with conventional receivers based on different guide frequencies and existing DL-based reception methods, the proposed adaptive receiver approach yields better bit error rate performance at different signal-to-noise ratios. This research reveals the extreme sensitivity of the LSTM’s performance to system SNR. LSTM outperforms DNN in high signal-to-noise ratio (SNR) situations, but at low SNR, even with high complexity, LSTM falls short of DNN’s performance.

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).

OAM mode-division multiplexing IM/DD transmission at 4.32 Tbit/s with a low-complexity adaptive-network-based fuzzy inference system nonlinear equalizer.

Stochastic nonlinear impairment is the primary factor that limits the transmission performance of high-speed orbital angular momentum (OAM) mode-division multiplexing (MDM) optical fiber communication systems. This Letter presents a low-complexity adaptive-network-based fuzzy inference system (LANFIS) nonlinear equalizer for OAM-MDM intensity-modulation direct-detection (IM/DD) transmission with three OAM modes and 15 wavelength division multiplex (WDM) channels. The LANFIS equalizer could adjust the probability distribution functions (PDFs) of the distorted pulse amplitude modulation (PAM) symbols to fit the statistical characteristics of the WDM-OAM-MDM transmission channel. Therefore, although the transmission symbols in the WDM-OAM-MDM system are subjected to a stochastic nonlinear impairment, the proposed LANFIS equalizer can effectively compensate the distorted signals. The proposed equalizer outperforms the Volterra equalizer with improvements in receiver sensitivity of 2, 1.5, and 1.3 dB for three OAM modes at a wavelength of 1550.12 nm, respectively. It also outperforms a CNN equalizer, with improvements in receiver sensitivity of 1, 0.5, and 0.3 dB, respectively. Moreover, complexity reductions of 67%, 74%, and 99.9% are achieved for the LANFIS equalizer compared with the Volterra, CNN, and ANFIS equalizers, respectively. The proposed equalizer has high performance and low complexity, making it a promising candidate for a high-speed WDM-OAM-MDM system.

Gradient-descent noise whitening techniques for short-reach IM-DD optical interconnects with severe bandwidth limitation.

Bandwidth limitation in optoelectrical components and the chromatic dispersion-induced power fading phenomenon cause severe inter-symbol interference (ISI) in high-speed intensity modulation and direct detection (IM-DD) optical interconnects. While the equalizer implemented in the receiver's digital signal processing procedure can mitigate ISI, it also inevitably enhances the noise located in the decayed frequency region, known as equalization-enhanced colored noise (EECN). Additionally, the nonlinear impairments of the modulator and photodetector also deteriorate the performance of the IM-DD system, especially for high-order modulation formats. In this work, we propose a gradient-descent noise whitening (GD-NW) algorithm to address EECN and extend it by introducing nonlinear kernels to simultaneously mitigate EECN and nonlinear impairments. The proposed algorithms are compared with conventional counterparts in terms of the achievable baud rate and the receiver optical power sensitivity. As a proof-of-concept experiment, we validate the principles of the proposed algorithms by successfully transmitting 360-GBd on-off-keying (OOK) and 180-GBd 4-level pulse-amplitude-modulation (PAM-4) signals in the back-to-back case under a 62-GHz brick-wall bandwidth limitation. 280-GBd OOK and 150-GBd PAM-4 transmissions are also demonstrated over 1-km standard single-mode fiber with a bit error rate below 7% hard-decision forward error correction aided by the proposed approach.