We propose a bi-directional gated recurrent unit neural network based nonlinear equalizer (bi-GRU NLE) for coherent optical communication systems. The performance of bi-GRU NLE has been experimentally demonstrated in a 120 Gb/s 64-quadrature amplitude modulation (64-QAM) coherent optical communication system with a transmission distance of 375 km. Experimental results show that the proposed bi-GRU NLE can significantly mitigate nonlinear distortions. The Q-factors can exceed the hard-decision forward error correction (HD-FEC) limit of 8.52 dB with the aid of bi-GRU NLE, when the launched optical power is in the range of -3 dBm to 3 dBm. In addition, when the launched optical power is in the range of 0 dBm to 2 dBm, the Q-factor performances of the bi-GRU NLE and bi-directional long short-term memory neural network based nonlinear equalizer (bi-LSTM NLE) are similar, while the number of parameters of bi-GRU NLE is about 20.2% less than that of bi-LSTM NLE, the average training time of bi-GRU NLE is shorter than that of bi-LSTM NLE, the number of multiplications required for the bi-GRU NLE to equalize per symbol is about 24.5% less than that for bi-LSTM NLE.

Optical nonlinearity impairments have been a major obstacle for high-speed, long-haul and large-capacity optical transmission. In this paper, we propose a novel convolutional neural network (CNN)-based perturbative nonlinearity compensation approach in which we reconstruct a feature map with two channels that rely on first-order perturbation theory and build a classifier and a regressor as a nonlinear equalizer. We experimentally demonstrate the CNN equalizer in 375 km 120-Gbit/s dual-polarization 64-quadrature-amplitude modulation (64-QAM) coherent optical communication systems. We studied the influence of the dropout value and nonlinear activation function on the convergence of the CNN equalizer. We measured the bit-error-ratio (BER) performance with different launched optical powers. When the channel size is 11, the optimum BER for the CNN classifier is 0.0012 with 1 dBm, and for the CNN regressor, it is 0.0020 with 0 dBm; the BER can be lower than the 7 $\%$ hard decision-forward threshold of 0.0038 from −3 dBm to 3 dBm. When the channel size is 15, the BERs at −4 dBm, 4 dBm and 5 dBm can be lower than 0.0020. The network complexity is also analyzed in this paper. Compared with perturbative nonlinearity compensation using a fully connected neural network (2392-64-64), we can verify that the time complexity is reduced by about 25 $\%$ , while the space complexity is reduced by about 50 $\%$ .

In this article, a distributed optical fiber sensing system for large infrastructure temperature monitoring is proposed. To meet the requirements of monitoring networks in terms of measurement accuracy, spatial resolution, and real-time or quasireal-time performance, a quaternion wavelet transform (QWT) image denoising algorithm is proposed to address the original edge node data for the structural monitoring networks of large infrastructures. A distributed Brillouin optical time-domain analysis (BOTDA) sensing system with a 40-km sensing fiber is established. The raw Brillouin gain spectrum (BGS) image is decomposed into one magnitude image and three phase images by QWT. The phase images of the OWT are distributed randomly and disorderly with respect to the noise, while the magnitude image of the quaternion wavelet is greatly affected by the noise. The useful message energy of the magnitude image is concentrated on a small number of coefficients with large amplitude, while the noise mainly corresponds to the coefficients with smaller amplitude. Then, the Bayes shrink threshold method is introduced to filter out noise in the magnitude image. The results indicate that the signal-to-noise ratio (SNR) and the frequency uncertainty have been improved significantly. The accuracy of the retrieved Brillouin frequency shift from denoised BGS images reaches 0.2 MHz, which corresponds to a temperature error of ±0.1 °C. Less than 4 s are required to process a BGS image with 50 $\times $ 40 000 pixels by the QWT denoising technique. The uploaded data obtained from 40 M bytes of raw data are reduced to 0.08 M bytes for each measurement. We hope that with technological progress and algorithm optimization, the distributed optical fiber sensing system based on the QWT image denoising algorithm will have an important role in the real-time application of large-scale infrastructure structural health monitoring for the Internet of Things.

Atmospheric turbulence (AT) tends to impair the performance of free space optical (FSO) communication systems. Detecting AT strength is significant for turbulence effect mitigation, which can appropriately guide the selection of turbulence mitigation techniques and modulation formats. Orbital angular momentum (OAM) beam aberrations received through the turbulence channel are closely related to the turbulence strength. In this paper, we experimentally detect the AT strength using an OAM beam based on a convolutional neural network (CNN). We collect 8 kinds of superposed OAM beam intensity images after 5 levels of turbulence in the laboratory as datasets and test the AT detector performance with respect to the number of pixels, mode number of OAM beams, different AT sets and training set size. The results show that the AT detection accuracy is near 100% for 3 kinds of ATs, and the accuracy remains at approximately 85% for 5 kinds of ATs. In addition, using data augmentation methods or a hybrid dataset can improve the AT detection accuracy. The CNN-based method in this paper can help detect the AT strength in atmospheric channels and provide references for choosing appropriate techniques to mitigate turbulence effects and then enhance the OAM-FSO system performance.

An optimized principal component-based phase estimation (OPCPE) algorithm is proposed for probabilistically shaped (PS) square-quadrature amplitude modulation (QAM) systems. The optimization method is based on mirroring and partially scaling the received constellation. Numerical simulation validation shows that the proposed phase recovery algorithm outperforms the well-known blind phase search (BPS) algorithm at low signal-to-noise ratio (SNR) and solves the incompatibility between principal component-based phase estimation (PCPE) and PS at high SNR. It's worth mentioning that the proposed algorithm retains the advantages of low cycle slip rate (CSR) and low computational complexity of PCPE. Furthermore, the performance of a hybrid implementation combining the proposed algorithm and BPS is also investigated. When the shaping parameter for a PS-64QAM system is 0.05, the proposed simple and hybrid methods can achieve performance improvements around 0.34-dB and 0.61-dB respectively benchmarking the widely used two-stage BPS (2S-BPS), considering the 0.8 normalized generalized mutual information (NGMI) threshold. To the best of our knowledge, this is the first time to robustly apply PCPE algorithm to PS systems, and the proposed design has stable NGMI performance, strong cycle slip tolerance and low computational complexity, which makes it a suitable candidate for practical probabilistically-shaped transmissions.