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.

Multiplication-free and hardware-efficient baud-rate timing error detector for Nyquist and faster than Nyquist optical IM/DD systems.

Clock recovery (CR) algorithms that support higher baud rates and advanced modulation formats are crucial for short-distance optical interconnections, and it is desirable to push CR to operate at baud rate with minimal computing resources and power. In this Letter, we proposed a hardware-efficient and multiplication operation-free baud-rate timing error detector (TED) as a solution to meet these demands. Our approach involves employing both the absolute value of samples and the nonlinear sign operation to emphasize the clock tone, which is deteriorated by severe bandwidth limitation in Nyquist and faster than Nyquist (FTN) systems. Through experimental investigations based on a transceiver system with a 3 dB bandwidth of 30 GHz, the proposed baud-rate TED exhibits excellent performance. The proposed scheme successfully achieves clock synchronization of the received signals with the transmitted signals, including 50 GBaud PAM4/8, 80 GBaud PAM4, and up to 120 GBaud PAM4 FTN signals. To the best of our knowledge, the CR based on the proposed baud-rate TED is the most optimal solution for ultrahigh-speed short-reach IM/DD transmission, comprehensively considering the timing jitter, bit error rate (BER), and implementation complexity.

Variational autoencoder-assisted unsupervised hardware fingerprint authentication in a fiber network.

Physical-layer authentication (PLA) based on hardware fingerprints can safeguard optical networks against large-scale masquerade or active injection attacks. However, traditional schemes rely on massive labeled close-set data. Here, we propose an unsupervised hardware fingerprint authentication based on a variational autoencoder (VAE). Specifically, the triplets are generated through variational inference on unlabeled optical spectra and then applied to train the feature extractor, which has an excellent generalization ability and enables fingerprint feature extraction from previously unknown optical transmitters. The feasibility of the proposed scheme is experimentally verified by the successful classification of eight optical transmitters after a 20 km standard single-mode fiber (SSMF) transmission, to distinguish efficiently the rogue from legal devices. A recognition accuracy of 99% and a miss alarm rate of 0% are achieved even under the interference of multiple rogue devices. Moreover, the proposed scheme is verified to have a comparable performance with the results obtained from supervised learning.

Broadband ASE source-enabled self-homodyne DA-RoF fronthaul using cascaded SOAs and a multicore fiber.

Broadband amplified spontaneous emission (ASE) light sources are recognized for their cost-effective generation. However, their inherent high-intensity noise and the stringent requirement for time delay matching limits their widespread application in coherent optical telecommunication. Here we propose a broadband ASE source-enabled digital-analog radio-over-fiber (DA-RoF) mobile fronthaul architecture, leveraging semiconductor optical amplifiers (SOAs) and multicore fiber in tandem. Our proposed system uses SOAs to suppress the intensity noise of the ASE carrier and transmits the DA-RoF signal alongside an unmodulated carrier through distinct cores of an 8-core, 1-km fiber. This setup significantly enhances the signal-to-noise ratio (SNR) by 19.4 dB, boosts capacity, and enables self-homodyne detection at the receiver end. We achieve an aggregated bandwidth of 35 GHz (7 cores × 5 GHz), supporting a 2.05-Tb/s CPRI-equivalent data rate with 1024-ary quadrature-amplitude-modulated (1024-QAM) signals. Additionally, we analyze the impact of chromatic dispersion on signal-to-noise ratio for broadband source coherent detection systems. This innovative scheme offers a pragmatic solution for integrating low-cost broadband sources into cost-sensitive fronthaul systems, providing both high capacity and fidelity in massive deployment scenarios.

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.

Two-level coding for efficient digital radio-over-fiber transmission with unequal bit protection.

The digital radio-over-fiber (D-RoF) transmission with two-level coding (TLC) is proposed and demonstrated in this Letter. A joint design considering the importance of quantization bits, the protection ability of forward error correction (FEC), and the bit error ratio of quadrature amplitude modulation (QAM) symbols is realized. In TLC-based D-RoF systems, the more significant bits among quantization bits are protected by a FEC and are assigned to the least reliable bits of modulated QAM symbols. Conversely, the less significant bits, without FEC protection, are allocated to the more reliable bits of QAM symbols. Experiments on an 11-km standard single-mode fiber transmission are conducted to evaluate the performance. The results indicate that, with a maximum iteration number of 2, compared to the conventional bit-interleaved coded modulation (BICM) with all bits encoded, the D-RoF based on TLC attains nearly identical performance under the 0.34% error vector magnitude threshold of 65536QAM wireless signals, specifically achieving complexity reductions of 54.55% and 67.66% for 16QAM and 64QAM optical transmissions, respectively.

Mode-division-multiplexing self-homodyne coherent transmission over a weakly coupled few-mode fiber for optical interconnections.

Self-homodyne coherent transmission has recently received extensive investigation as a coherent lite candidate for high-speed short-reach optical networks. In this Letter, we propose a weakly coupled mode-division-multiplexing (MDM) self-homodyne coherent scheme using a multiple-ring-core few-mode fiber, in which one of the modes transmits a self-homodyne local oscillator (LO) and the rest are utilized for carrying signals. Multiple rings of index perturbations in the fiber core are applied to achieve low modal crosstalk, allowing the signals and the remote LO to be transmitted independently. We experimentally demonstrate a 7.2-Tb/s (5.64-Tb/s net rate) self-homodyne coherent transmission with an 800-Gb/s data rate for each of the nine information-bearing modes formatted in 80-GBaud probabilistic constellation-shaped 64-quadrature-amplitude modulation. To the best of our knowledge, this is the first experimental demonstration of an MDM self-homodyne coherent transmission with up to 10 spatial modes. The proposed scheme may pave the way for future high-capacity data center interconnections.

A 300†km fiber channel mapping using neural networks for Gb/s physical-layer key distribution.

Physical-layer secure key distribution (PLSKD) generally acquires highly correlated entropy sources via bidirectional transmission to share the channel reciprocity. For long-haul fiber links, the non-negligible backscattering noise (BSN) and the challenge of bidirectional optical amplification degrade the key generation performances. Since the channel reciprocity can be precisely mapped using neural networks (NNs), unidirectional PLSKD provides a feasible PLSKD for longer fiber links. Here, a final error-free key generation rate (KGR) in unidirectional PLSKD of 3.07 Gb/s is demonstrated over a 300 km fiber link using NNs. Moreover, the channel mapping is analyzed in terms of fiber distance, chromatic dispersion, the nonlinearity of random source, and BSN.

Data-driven inverse design of mode-locked fiber lasers.

The diverse applications of mode-locked fiber lasers (MLFLs) raise various demands on the output of the laser, including the pulse duration, energy, and shape. Simulation is an excellent method to guide the design and construction of an MLFL for on-demand laser output. Traditional simulation of an MLFL uses the split-step Fourier method (SSFM) to solve the nonlinear Schrödinger (NLS) equation, which suffers from high computational complexity. As a result, the inverse design of MLFLs via the traditional SSFM-based simulation method relies on the design experience. Here, a completely data-driven approach for the inverse design of MLFLs is proposed, which significantly reduces the computational complexity and achieves a fast automatic inverse design of MLFLs. We utilize a recurrent neural network to realize fast and accurate MLFL modeling, then the desired cavity settings meeting the output demands are searched via a deep-reinforcement learning algorithm. The results prove that the data-driven method enables the accurate inverse design of an MLFL to produce a preset target femtosecond pulse with a certain duration and pulse energy. In addition, the cavity settings generating soliton molecules with different target separations can also be located via the data-driven inverse design. With the GPU acceleration, the time consumption of the data-driven inverse design of an MLFL is less than 1.3 hours. The proposed data-driven approach is applicable to guide the inverse design of an MLFL to meet the different demands of various applications.

Computationally efficient composite triple beat cancellation for DML-based DA-RoF fronthaul.

The digital-analog radio-over-fiber (DA-RoF) scheme offers a high-fidelity and spectrally efficient solution for future mobile fronthaul. However, to be implemented in the low-cost directly modulated laser with direct detection (DML-DD) link, both the digital and analog parts in DA-RoF modulation would suffer from the composite second-order (CSO) and composite triple beat (CTB) caused by the chirp-dispersion interaction. In this Letter, we propose and experimentally demonstrate a computationally efficient composite triple beat cancellation (CTB-C) algorithm for DA-RoF fronthaul in the dispersion-uncompensated C-band DML-DD link. The CSO and CTB are suppressed at the receiver-side DSP based on the theoretical model of these nonlinear distortions. In the proof-of-concept experiment, a 1.2-dB improvement in the recovered signal-to-noise ratio (SNR) is obtained with 5.5-GHz 1024-QAM orthogonal frequency division multiplexing (OFDM) signal after 10-km standard single-mode fiber (SSMF) transmission. The proposed CTB-C technique does not require the training process and performs close to the Volterra-based feed-forward equalizer (VFE) under the complexity constraint.

Performance of polar coded probabilistic shaped PAM8 with systematic interleaver and identically distributed pilot in weak turbulence.

In this paper, for the first time to the best of our knowledge, we investigate the experiment of polar coded probabilistic shaped 8-ary pulse amplitude modulation (PS-PAM8) in weak turbulence. A systematic interleaver (SIL) is proposed to improve the polar code performance for PS-PAM8, compatible with the 5 G channel coding standard. Considering the effects of turbulence and shaped constellations, the pilot with identical distributions as the transmitted data is used for dynamic channel estimation to avoid demodulation failure. Moreover, the application of hybrid equalization with nonlinear and linear equalizers effectively reduces the receiver sensitivity. In 25 GBd transmission over a 4 m free-space link, the transmission performance of polar coded PAM8 schemes with SIL is better than that of the low-density parity check code by 1.0 dB, and the power budget is further saved by 0.72∼0.83 dB after linear equalization. Meanwhile, the shaping gains of polar coded PS-PAM8 with SIL and hybrid equalization are up to 2.0 dB at 1.5 bits/channel use. In addition, different weak turbulence conditions can be generated inside a chamber, and the observed channel fading is consistent with the log-normal model. The results show that the proposed polar coded PS scheme can improve the Q-factor by 0.49∼1.74 dB in different turbulence conditions.

Fast polarization state tracking for dual-polarization direct detection with Jones-space field recovery.

Direct detection system is expected to possess the phase and polarization diversity in order to achieve high spectral efficiency and fiber impairment compensation such as chromatic dispersion and polarization rotation. In this Letter, we theoretically extend the concept of the proposed Jones-space field recovery (JSFR) to include a dynamic polarization rotation matrix and experimentally demonstrate the rapid polarization state tracking ability of the JSFR receiver based on a 3 × 3 optical coupler. Under a rotation of the state of polarization at a rate of 1 Mrad/s, we successfully transmit 59-GBd dual-polarization 16-ary quadrature-amplitude-modulation signals over an 80-km standard single-mode fiber based on a decision-directed least mean square (DD-LMS) or a recursive least square (DD-RLS), with a bit-error rate below the 14% hard-decision forward error correction threshold of 1 × 10-2. The experimental results indicate that the legacy polarization tracking algorithms designed for coherent optical communication are also applicable for this direct detection scheme. To our best knowledge, this work demonstrates the first polarization rotation-tolerant direct detection system with phase and polarization diversity, providing a low-cost and high-speed solution for short-reach communications.

Signal-to-noise ratio degradation analysis for optoelectronic feedback-based chaotic optical communication systems.

Chaotic optical communication encrypts transmitted signals through physical noise; this ensures high security while causing a certain decrease in the signal-to-noise ratio (SNR). Thus, it is necessary to analyze the SNR degradation of decrypted signals after chaotic encryption and the minimum requirements for the SNR of the fiber channel to meet the required bit error rate (BER) performance. Accordingly, an SNR model of decrypted signals for optoelectronic feedback-based chaotic optical communication systems is proposed. Under different channel SNRs, the SNR degradation of 40 Gbit/s phase chaos and intensity chaos models is investigated by simulation and experiment, respectively, with a 15 GHz wideband chaotic carrier. Comparing decrypted signals with original signals, the simulation results show that there is a 2.9 dB SNR degradation for both intensity chaos and phase chaos. Further, in experiments, SNR degradation from 4.5 dB to 5.6 dB, with various channel SNRs for intensity chaos, is analyzed, while there is an SNR degradation from 7.1 dB to 8.3 dB for phase chaos. The simulation and experimental results provide guidance for long-distance transmission chaotic optical communication systems.

Low-complexity amplitude-division irregular QAM formats for short-reach unamplified coherent optical systems.

A low-complexity scheme is proposed to realize irregular uniform quadrature amplitude modulation (QAM) formats with Gray mapping, which are named amplitude-division irregular QAM (AD-Ir-QAM) formats. Compared to conventional probabilistic shaping (PS) with the Maxwell-Boltzmann (MB) distribution (PS-MB), irregular QAM formats show a smaller peak-to-average power (PAPR) and achieve a better performance in systems with the peak-power constraint. Compared with irregular QAM formats realized by PS (PS-Ir-QAM), AD-Ir-QAM formats realize a more flexible rate adaptation and have a lower implementation complexity. Experimental results obtained in an unamplified coherent optical system show that, at a generalized mutual information (GMI) of 4.5 bits/2D-symbol, AD-Ir-100QAM achieves gains of 2.1 and 0.5 dB in the power budget over PS-MB-100QAM and PS-Ir-100QAM, respectively.

Digital pre-distortion using a Gauss-Newton-based direct learning architecture for coherent optical transmitters.

Digital pre-distortion (DPD) is a powerful technique to mitigate transmitter nonlinear distortion in optical transmissions. In this Letter, the identification of DPD coefficients based on the direct learning architecture (DLA) using the Gauss-Newton (GN) method is applied in optical communications for the first time. To the best of our knowledge, this is the first time that the DLA has been realized without training an auxiliary neural network to mitigate optical transmitter nonlinear distortion. We describe the principle of the DLA using the GN method and compare the DLA with the indirect learning architecture (ILA) that uses the least-square (LS) method. Extensive numerical and experimental results indicate that the GN-based DLA is superior to the LS-based ILA, especially in a low signal-to-noise ratio scenario.

Spectral broadening scheme for suppressing SBS effects based on time-domain optimized chirp-like signals.

We propose a novel (to our knowledge) driving scheme to suppress the stimulated Brillouin scattering (SBS) effect in master oscillator power amplification (MOPA) systems based on an external high-order phase modulation. Since seed sources with the linear chirp can uniformly broaden the SBS gain spectrum with a high SBS threshold, a chirp-like signal was designed by applying further editing and processing to the piecewise parabolic signal. Compared with the traditional piecewise parabolic signal, the chirp-like signal has similar linear chirp characteristics and can reduce the driving power and sampling rate requirements, enabling more efficient spectral spreading. The SBS threshold model is constructed theoretically based on the three-wave coupling equation. The spectrum modulated by the chirp-like signal is compared with the flat-top and Gaussian spectra in terms of the SBS threshold and the bandwidth-distribution normalized threshold, and a considerable improvement is demonstrated. Meanwhile, the experimental validation is carried out in a watt-class amplifier based on the MOPA structure. At a 3 dB bandwidth of ∼10 GHz, the SBS threshold of the seed source modulated by the chirp-like signal is improved by 35% compared to the flat-top spectrum and 18% compared to the Gaussian spectrum, respectively, and the normalized threshold is also the highest among them. Our study shows that the SBS suppression effect is not only related to the power distribution of the spectrum but also can be improved by the time domain design, which provides a new idea for analyzing and improving the SBS threshold of narrow-linewidth fiber lasers.

10 Gb/s physical-layer key distribution in fiber using amplified spontaneous emission.

High-speed physical-layer secure key generation and distribution (SKGD) schemes via channel reciprocity are achieved using external electro-optical modulation or random source distribution via additional fiber links. Here, we propose and demonstrate an SKGD scheme using the fluctuation of polarization states from an amplified spontaneous emission (ASE) source, without any external electro-optical modulation or additional fiber link. Experimentally, an error-free key generation rate (KGR) of 10.1 Gb/s is achieved over a 10-km standard single-mode fiber (SSMF), with true randomness originating from ASE. Moreover, the single fiber channel can be shared for SKGD as well as data transmission, allowing the integration of the proposed SKGD with the deployed fiber infrastructure.

Low-complexity full-field ultrafast nonlinear dynamics prediction by a convolutional feature separation modeling method.

The modeling and prediction of the ultrafast nonlinear dynamics in the optical fiber are essential for the studies of laser design, experimental optimization, and other fundamental applications. The traditional propagation modeling method based on the nonlinear Schrödinger equation (NLSE) has long been regarded as extremely time-consuming, especially for designing and optimizing experiments. The recurrent neural network (RNN) has been implemented as an accurate intensity prediction tool with reduced complexity and good generalization capability. However, the complexity of long grid input points and the flexibility of neural network structure should be further optimized for broader applications. Here, we propose a convolutional feature separation modeling method to predict full-field ultrafast nonlinear dynamics with low complexity and strong generalization ability with high accuracy, where the linear effects are firstly modeled by NLSE-derived methods, then a convolutional deep learning method is implemented for nonlinearity modeling. With this method, the temporal relevance of nonlinear effects is substantially shortened, and the parameters and scale of neural networks can be greatly reduced. The running time achieves a 94% reduction versus NLSE and an 87% reduction versus RNN without accuracy deterioration. In addition, the input pulse conditions, including grid point numbers, durations, peak powers, and propagation distance, can be generalized accurately during the predicting process. The results represent a remarkable improvement in ultrafast nonlinear dynamics prediction and this work also provides novel perspectives of the feature separation modeling method for quickly and flexibly studying the nonlinear characteristics in other fields.

Optical filtering impairment monitoring based on model fusion for optical networks.

Reconfigurable optical add-and-drop multiplexer (ROADM) is a key element in optical networks. As several ROADMs are cascaded over long paths, the penalty induced by ROADM has become non-negligible due to the tight optical filtering. In this case, for efficient and reliable network planning and operation, accurate monitoring of optical filtering penalty is very important. In this paper, we propose a real-time optical filtering monitoring scheme based on model fusion. We combine an analytical model based on the digital communications theory of band-limited channels with linear equalization and a data-driven model implemented using artificial neural network (ANN). The scheme can achieve high accuracy and interpretability. Moreover, since the input features are extracted from configuration parameters and receiver digital signal processing (DSP), no additional devices are needed, which is attractive for practical deployment. Extensive simulations and experiments are conducted to investigate the performance of the scheme, and the results show the superior performance.

Probabilistically shaped polar-coded MIMO-FSO communication systems with spatially correlated fading.

In this paper, the probabilistically shaped polar-coded multiple-input multiple-output free-space optical (MIMO-FSO) communication system with or without spatially correlated (SC) fading is investigated to improve transmission performance. The designed shaping-polar encoder can flexibly generate three typical shapes of distribution via shaping bits and be decoded in the conventional method. The achievable information rate (AIR) of MIMO-FSO systems with or without SC fading is evaluated to determine the number of shaping bits for the shaping-polar encoder. The non-pairwise distributions are demonstrated to be more suitable for turbulence channels than other distributions. The results show that the AIR of the shaped 4 × 4 systems even exceeds that of the uniform 4 × 5 systems in the low signal-to-noise ratio regions over strong turbulence channels. In terms of bit error rate performance, more than 15 dB shaping gains can be achieved by the shaped 4 × 4 systems compared to the uniform single-input single-output polar-coded systems. In addition, the shaped 4 × 4 systems outperform the uniform ones ranging from 1 dB to 1.9 dB over different atmospheric turbulence channels with or without SC fading, comparable to the uniform MIMO systems with one more physical receiver.