A data-driven fiber channel modeling method based on deep learning (DL) is introduced in an optical communication system. In this study, bidirectional long short-term memory (BiLSTM) is selected from a diverse range of DL algorithms to perform fiber channel modeling for on—off keying and pulse amplitude modulation 4 signals. Compared with the conventional model-driven split-step Fourier (SSF)-based method, the proposed method yields similar results based on the comprehensive comparison of multiple characteristics associated with the generated optical signals, including the optical amplitude and phase waveforms in the time domain, optical spectrum components in the frequency domain, and eye diagrams after detection in the electrical domain. Additionally, the effects of multiple factors on the modeled fiber channel have also be investigated, including fiber length, fiber nonlinearity, dispersion, data pattern, pulse shaping, and sample rate. The satisfactory fitting results and acceptable mean square errors indicate that the approximate transfer function of the fiber channel is learned by the BiLSTM. Moreover, compared with repetitive iteration SSF, the computing time is significantly reduced by the BiLSTM owing to its independence on fiber length and insensitivity to data size and launch power. Our aim is to demonstrate the BiLSTM is comparable with the conventional model-driven SSF-based method for direct-detection optical fiber system. We think the proposed method could be a supplementary technique that can be used for the existing simulation system and could also be a potential option for future simulation methods.

A novel low-complexity and nonlinearity-tolerant modulation format identification (MFI) using random forest (RF) is proposed for the flexible coherent receivers (FCRs). The RF-based MFI takes the advantage of distinct features from the amplitude histograms (AHs) and the swarm intelligence of RF to significantly reduce the computational complexity compared with the deep learning-based method. Both numerical simulation and experiments are conducted. The simulation results of polarization multiplexed (PM) 4/8/16/32/64 quadrature amplitude modulation (QAM) wavelength division multiplexing (WDM) systems demonstrate its feasibility and identification performance. In the presence of nonlinear effects, with lower complexity than three other machine learning algorithms (k-nearest neighbors, support vector machine, and deep neural networks), the RF-based MFI can obtain 100% accuracy at the OSNR values greater than or equal to the respective soft decision forward error correction (SD-FEC) threshold. The identification accuracy versus total launch power is experimentally investigated in PM-4/16/32QAM WDM coherent systems. In the case of obvious nonlinear impairments, 100% accuracy can also be achieved above the OSNR corresponding to the SD-FEC threshold. The superiority of the proposed MFI method makes it highly desirable for applications in modulation format-adaptive FCRs.

In this paper, we propose and demonstrate a low-complexity fiber nonlinearity impairments compensation (NLC) scheme based on simple recurrent neural network (SRNN), combining with the triplets derived from the first-order perturbation solution of the coupled nonlinear Schrodinger equation. Benefitting from the time memory of SRNN, the proposed NLC can reduce the computational complexity without sacrificing the compensation performance compared with the schemes based on memoryless feedforward neural networks. To verify the feasibility of the proposed NLC, the simulation systems of single channel and three channel 30 GBaud polarization division multiplexing (PDM) 16 quadrature amplitude modulation (QAM) over 2400 km standard single mode fiber transmission are constructed respectively. Comprehensive numerical simulation results demonstrate that although the NLC performance of proposed scheme is inferior to that of digital back propagation (DBP) with much higher complexity and impracticality, it can still achieve the competitive NLC performance with lower computational complexity compared to the schemes based on deep neural network (DNN) and artificial neural network (ANN). Moreover, it is further proved that using triplets as the feature required for NLC can cause the pattern of pseudo random bit sequence to be destroyed, resulting in the neural network-based NLC scheme not suffering from the problem of overestimation for performance. Additionally, the time memory of SRNN enables the number of triplets in training set required by the SRNN-based NLC to be reduced by 169% compared to that of DNN and ANN. The experimental results of 16 GBaud PDM-16QAM wavelength division multiplexing coherent systems demonstrate that compared to with ANN and DNN, the comparable NLC performance can also be achieved by the proposed scheme with lower complexity.

A frequency domain (FD) 4×2 multi-input and multi-output (MIMO) equalizer based on radially directed equalizer is proposed to compensate receiver in-phase/quadrature (IQ) imbalances of M-ary quadrature amplitude modulation signals. This algorithm has a significantly lower complexity compared with a conventional time-domain 4×2 MIMO equalizer. Furthermore, each of imperfection estimations is derived from the converged discrete frequency response of the FD 4×2 MIMO equalizer. The simulation and experimental results indicated that the receiver (Rx) IQ imbalances were fully compensated by the proposed equalizer and precisely estimated by estimators, even for long-haul transmission with Rx IQ imbalances varying over a wide range.

In this paper, a novel joint symbol rate-modulation format identification (SR-MFI) and optical signal-to-noise ratio (OSNR) estimation scheme using the low-bandwidth coherent detecting and random forest (RF)-based ensemble learning is proposed for intermediate nodes in the flexible dense wavelength division multiplexing (F-DWDM) networks. By leveraging low-bandwidth coherent detecting with small bulk wavelength scanning, no chromatic dispersion compensation and low-complexity RF, the proposed scheme could serve as a reduced-complexity and cost-effective option to realize joint SR-MFI and OSNR estimation at intermediate nodes in F-DWDM networks. To verify the feasibility of the proposed scheme, the comprehensive simulations of 8/16 GBaud polarization division multiplexing (PDM)-4/16/32/64 quadrature amplitude modulation (QAM) systems are conducted. The simulation results show that the identification accuracy of SR-MFI reaches 100% and the mean absolute error of OSNR estimation is within 1 dB. Moreover, the proposed monitoring scheme is verified by 8/16 GBaud PDM-4/16/32QAM coherent transmission experiments.

In future elastic optical networks, hardware-efficient and multi-format frequency offset estimation (FOE) is critical for digital coherent receivers (DCRs) to alleviate the requirement of wavelength matching while reducing the power consumption as well as the footprint of digital signal processing units. Here, we propose a blind feedforward and low-complexity FOE algorithm based on the techniques of extended QPSK partitioning and quasi-linear approximation. With processing in polar coordinates, a simple novel error function is first defined to measure the phase deviation induced by frequency offset so that robust FOE can be directly determined by the quasi-linear relationship between the phase deviation and the corresponding offset distance. Besides, a multi-timespan estimation method is also introduced to further mitigate the phase noise impact on FOE. Not only the simulation results of 4/16/32/64-quadrature amplitude modulation (QAM) demonstrate its feasibility and versatility, but also the complexity analyses show that hardware complexities are significantly reduced. The bit error rate versus OSNR performance is experimentally investigated in double-polarization 4/16/32-QAM measurements. The superiority of the proposed FOE makes it highly desirable for application in practical multi-format DCRs.