Simultaneous wireless mm-wave transmission of both SC-modulated and OFDM-modulated high-order QAM signals enabled by bandpass delta-sigma modulation.

The application of dual vector millimeter-wave (mm-wave) signals in radio-over-fiber (RoF) systems represents a significant opportunity to enhance spectrum efficiency, transmission capacity, and access flexibility. In addition, facing the increasingly intricate application scenarios, the comprehensive exploitation of high-order quadrature-amplitude-modulation (QAM) signals with hybrid single-carrier (SC) and orthogonal-frequency-division-multiplexing (OFDM) modulation is also vital to rich systematic connotation. Based on bandpass delta-sigma modulation (BP-DSM) and heterodyne detection, we propose what we believe to be a novel scheme for the simultaneous wireless mm-wave transmission of both SC-modulated and OFDM-modulated high-order QAM signals. The innovation lies in the modulation-agnostic nature, accommodating both SC-modulated and OFDM-modulated vector radio-frequency (RF) signals. The BP-DSM is utilized to digitize two independent SC-modulated and OFDM-modulated high-order QAM signals into relatively simple sequences at the transmitter side. With the aid of an optical I/Q modulator, we can integrate both signals after BP-DSM to generate the desired optical quadrature-phase-shift keying (QPSK) signal carrying both information of two original high-order QAM signals. Facilitated by heterodyne detection and a single photodetector (PD), our scheme attains prowess in the detection of both SC-modulated and OFDM-modulated high-order signals. Based on our proposed scheme, we experimentally demonstrate the simultaneous wireless mm-wave transmission of both SC-modulated and OFDM-modulated 512QAM signals at 30-GHz mm-wave band, demonstrating bit-error-rates (BERs) below the hard decision forward error correction (HD-FEC) threshold of 3.8 × 10-3 after transmission over 10-km single-mode fiber (SMF) link and 1-m wireless link. In addition, we further investigate the performance impact between SC-modulated and OFDM-modulated high-order QAM signals, and experiment results indicate that the impact is virtually negligible. Moreover, the performance of the generated QPSK mm-wave signal is transparent to the QAM modulation formats of both SC-modulated and OFDM-modulated signals in our proposed scheme.

ExtraTrees-hidden Markov model based equalizer for mode division multiplexing ring-core fiber communication with non-orthogonal MultiCAP modulation.

This paper presents an orbital angular momentum mode division multiplexing (OAM-MDM) ring-core fiber transmission method based on non-orthogonal multiband carrierless amplitude and phase (NMCAP) modulation with an extremely randomized trees-hidden Markov model (ExtraTrees-HMM)-based equalizer. The ExtraTrees-HMM equalizer uses the statistical characteristics of the received distorted signals to model the nonlinear channel of the system to classify these distorted signals into corresponding constellation classes. Experiments were conducted using a 216 Gbit/s OAM-MDM NMCAP modulation optical fiber communication system with 2 km ring-core fiber transmission and the results show that compared with a conventional Volterra nonlinear equalizer (VNE), the proposed ExtraTrees-HMM equalizer could improve the receiver sensitivity by 1 dB for OAM mode l = + 2, and 0.6 dB for OAM mode l = + 3. In addition, the computational complexity of the proposed equalizer was reduced by 43.94% compared with the VNE. In brief, the ExtraTrees-HMM is a promising equalization candidate for ultra-high-capacity inter-data-center interconnections.

SC and OFDM hybrid coherent optical transmission scheme based on 1-bit bandpass delta-sigma modulation.

High-order quadrature amplitude modulation (QAM) can effectively improve the capacity and spectral efficiency of coherent optical transmission systems. However, as the modulation order increases, the signal becomes less tolerant to noise and nonlinear effects during transmission, and the implementation cost also increases. We propose a single carrier (SC) and orthogonal frequency division multiplexing (OFDM) hybrid coherent optical transmission scheme based on a 1-bit bandpass (BP) delta-sigma modulation (DSM). The driving I-channel and Q-channel signals for the optical in-phase/quadrature (I/Q) modulator carry SC-modulated and OFDM-modulated transmitter data, respectively. Optical quadrature-phase-shift-keying (QPSK) modulation is realized by the 1-bit DSM quantizer and I/Q modulator, which can effectively suppress quantization noise and reduce the complexity of digital signal processing (DSP) and the performance requirements of optoelectronic devices. In addition, the hybrid transmission of SC and OFDM can balance the advantages of both to meet the variable channel conditions and complex application scenarios. High-fidelity transmission of SC 512QAM and OFDM 512QAM hybrid signals, in the form of a 60 Gbaud optical QPSK signal, over 60 km single-mode fiber-28 (SMF-28) is verified by offline experiments, and the bit error rates (BERs) of both SC 512QAM and OFDM 512QAM are below the hard-decision forward-error correction (HD-FEC) threshold of 3.8e-3.

Hybrid transmission of PS-GS4QAM and QPSK data in the form of a PS-16QAM mm-wave signal enabled by optical asymmetrical dual-SSB modulation.

The independent optical dual-single-sideband (dual-SSB) signal generation and detection can be achieved by an optical in-phase/quadrature (I/Q) modulator and one single photodiode (PD). The dual-SSB signal is able to carry two different information. After PD detection, the optical dual-SSB signal can be converted into an electrical millimeter-wave (mm-wave) signal. Therefore, the optical dual-SSB signal generation and detection technique can be employed in the radio-over-fiber (RoF) system to achieve higher system spectral efficiency and reduce system architecture complexity. However, the I/Q modulator's nonideal property results in the amplitude imbalance of the optical dual-SSB signal, and then the crosstalk can occur. Moreover, after PD detection, the generated mm-wave signal based on the optical dual-SSB modulation has a relatively low signal-to-noise ratio (SNR), which restricts the system performance. In this paper, we propose an optical asymmetrical dual-SSB signal generation and detection scheme based on the probabilistic shaping (PS) technology, to decrease the influence of the optical dual-SSB signal's amplitude imbalance and to enhance the system performance in the scenario of the limited SNR. The dual-SSB in our scheme is composed of the left sideband (LSB) in probabilistic-shaping geometric-shaping 4-ary quadrature amplitude modulation (PS-GS4QAM) format and the right sideband (RSB) in quadrature phase-shift keying (QPSK) format. The transmitter digital signal processing (DSP) generates a dual-SSB signal to drive the optical I/Q modulator. The I/Q modulator implements an electrical-to-optical conversion and generates an optical dual-SSB signal. After PD detection, the optical dual-SSB signal is converted into a PS-16QAM mm-wave signal. In our simulation, compared with the normal 16QAM scenario, the PS-16QAM scenario exhibits a ∼1.2 dB receiver sensitivity improvement at the hard-decision forward error correction (HD-FEC) threshold of 3.8×10-3. Therefore, in our experiment, based on the PS technology, we design a dual-SSB signal including a 5 Gbaud LSB-PS-GS4QAM at -15 GHz and a 5 Gbaud RSB-QPSK at 20 GHz. After 5 km standard single-mode fiber (SSMF) transmission and PD detection, the dual-SSB signal is converted into a 5 Gbaud PS-16QAM mm-wave signal at 35 GHz. Then, the generated PS-16QAM signal is sent into a 1.2 m single-input-single-output (SISO) wireless link. In the DSP at the receiver end, the dual-SSB signal can be recovered from the mm-wave signal, and the PS-GS4QAM and QPSK data carried by the dual-SSB signal can be separated. The bit error rates (BERs) of the LSB-PS-GS4QAM and the RSB-QPSK in our experiment can be below the HD-FEC threshold of 3.8×10-3. The results demonstrate that our scheme can tolerate the I/Q modulator's nonideal property and performs well in the scenario of a relatively low SNR.

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.

Dual high-order QAM-modulated mm-wave signal transmission in the Q-band enabled by simple IM/DD architecture and bandpass delta-sigma modulation.

The intensity-modulation (IM)/direct-detection (DD) systems have been proven effective and low-cost due to their simple system architecture. However, the Mach-Zehnder modulator (MZM) of the IM/DD systems only reserves its driving signal intensity. Therefore, the IM/DD systems are generally unable to transmit vector signals and have a restricted spectrum efficiency and channel capacity. Similarly, the radio-over-fiber (RoF) transmission systems based on IM/DD are limited by their simple architecture and generally cannot transmit high-order quadrature amplitude modulation (QAM) signals, which hinders the improvement of their spectrum efficiency. To address the challenges, we propose a novel, to the best of our knowledge, scheme to simultaneously transmit the dual independent high-order QAM-modulated millimeter-wave (mm-wave) signals in the RoF system with a simple IM/DD architecture, enabled by precoding-based optical carrier suppression (OCS) modulation and bandpass delta-sigma modulation (BP-DSM). The dual independent signals can carry different information, which increases channel capacity and improves spectrum efficiency and system flexibility. Based on our proposed scheme, we experimentally demonstrate the dual 512-QAM mm-wave signal transmission in the Q-band (33-50 GHz) under three different scenarios: 1) dual single-carrier (SC) signal transmission, 2) dual orthogonal-frequency-division-multiplexing (OFDM) signal transmission, and 3) hybrid SC and OFDM signal transmission. We achieve high-fidelity transmission of dual 512-QAM vector signals over a 5 km single-mode fiber (SMF) and a 1-m single-input single-output (SISO) wireless link operating in the Q-band, with the bit error rates (BERs) of all three scenarios below the hard decision forward error correction (HD-FEC) threshold of 3.8 × 10-3. To the best of our knowledge, this is the first time dual high-order QAM-modulated mm-wave signal transmission has been achieved in a RoF system with a simple IM/DD architecture.

Dual vector millimeter-wave signal generation based on optical carrier suppression modulation and direct detection with one photodetector.

We propose a novel, to the best of our knowledge, scheme for dual vector millimeter-wave (mm-wave) signal generation and transmission, based on optical carrier suppression (OCS) modulation, precoding, and direct detection by a single-ended photodiode (PD). At the transmitter side, two independent vector radio frequency (RF) signals with precoding, generated via digital signal processing (DSP), are used to drive an in-phase/quadrature (I/Q) modulator operating at the optical OCS modulation mode to simultaneously generate two independent frequency-doubling optical vector mm-wave signals, which can reduce the bandwidth requirement of transmitter's components and enhance spectral efficiency. With the aid of the single-ended PD and subsequent DSP at the receiver side, two independent frequency-doubling vector mm-wave signals can be separated and demodulated without data error. Based on our proposed scheme, we experimentally demonstrate the generation, transmission, and detection of 2-Gbaud 30-GHz quadrature-phase-shift-keying (QPSK) and 2-Gbaud 46-GHz QPSK signals over 10-km single-mode fiber-28 (SMF-28) and 1-m wireless transmission. The results indicate that the bit-error ratio (BER) of the dual vector mm-wave signals can each reach the hard-decision forward-error-correction (HD-FEC) threshold of 3.8 × 10-3.

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.

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 120 Gb/s PS 64QAM signals in a 375 km transmission scenario. The proposed DACNN equalizer improves the receiver sensitivity by 2.6 dB and 1.1 dB 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.

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 3000 km, 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 0.52 dB and 0.85 dB, respectively. In addition, the proposed 16QAM system increases the transmission distance by 989 km and 741 km, 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.

Ultra-low complexity random forest for optical fiber communications.

In this paper, we present an efficient equalizer based on random forest for channel equalization in optical fiber communication systems. The results are experimentally demonstrated in a 120 Gb/s, 375 km, dual-polarization 64-quadrature magnitude modulation (QAM) optical fiber communication platform. Based on the optimal parameters, we choose a series of deep learning algorithms for comparison. We find that random forest has the same level of equalization performance as deep neural networks as well as lower computational complexity. Moreover, we propose a two-step classification mechanism. We first divide the constellation points into two regions and then use different random forest equalizers to compensate the points in different regions. Based on this strategy, the system complexity and performance can be further reduced and improved. Furthermore, due to the plurality voting mechanism and two-stage classification strategy, the random forest-based equalizer can be applied to actual optical fiber communication systems.

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.

Data rate measurement method with selectable range in linear optical sampling.

Linear optical sampling (LOS) is one of the most powerful techniques for high-speed signal monitoring. To measure the data-rate of signal under test (SUT) in optical sampling, multi-frequency sampling (MFS) was proposed. However, the measurable data-rate range of the existing method based on MFS is limited, which makes it very difficult to measure the data-rate of high-speed signals. To solve the above problem, a range selectable data-rate measurement method based on MFS in LOS is proposed in this paper. Through this method, the measurable data-rate range can be selected to match the data-rate range of SUT and the data-rate of SUT can be measured precisely, independently of the modulation format. What's more, the sampling order can be judged using the discriminant in the proposed method, which is key for plotting eye diagrams with correct time information. We experimentally measure the baud-rates of PDM-QPSK signal from 800 MBaud to 40.8 GBaud in different ranges and judge the sampling orders. The relative error of measured baud-rate is less than 0.17% while the error vector magnitude (EVM) is less than 0.38. Compared with the existing method, under the same sampling cost, our proposed method realizes the selectivity of the measurable data-rate range and the judgment of sampling order, greatly extends the measurable data-rate range of SUT. Hence, the data-rate measurement method with selectable range has great potential for high-speed signal data-rate monitoring.

Bayesian generative adversarial network emulator based end-to-end learning strategy of the probabilistic shaping for OAM mode division multiplexing IM/DD transmission.

Orbital angular momentum (OAM) mode division multiplexing (MDM) has emerged as a new multiplexing technology that can significantly increase transmission capacity. In addition, probabilistic shaping (PS) is a well-established technique that can increase the transmission capacity of an optical fiber to close to the Shannon limit. However, both the mode coupling and the nonlinear impairment lead to a considerable gap between the OAM-MDM channel and the conventional additive white Gaussian noise (AWGN) channel, meaning that existing PS technology is not suitable for an OAM-MDM intensity-modulation direct-detection (IM-DD) system. In this paper, we propose a Bayesian generative adversarial network (BGAN) emulator based on an end-to-end (E2E) learning strategy with probabilistic shaping (PS) for an OAM-MDM IM/DD transmission with two modes. The weights and biases of the BGAN emulator are treated as a probability distribution, which can be accurately matched to the stochastic nonlinear model of OAM-MDM. Furthermore, a BGAN emulator based on an E2E learning strategy is proposed to find the optimal probability distribution of PS for an OAM-MDM IM/DD system. An experiment was conducted on a 200 Gbit/s two OAM modes carrierless amplitude phase-32(CAP-32) signal over a 5 km ring-core fiber transmission, and the results showed that the proposed BGAN emulator outperformed a conventional CGAN emulator, with improvements in modelling accuracy of 29.3% and 26.3% for the two OAM modes, respectively. Moreover, the generalized mutual information (GMI) of the proposed E2E learning strategy outperformed the conventional MB distribution and the CGAN emulator by 0.31 and 0.33 bits/symbol and 0.16 and 0.2 bits/symbol for the two OAM modes, respectively. Our experimental results demonstrate that the proposed E2E learning strategy with the BGAN emulator is a promising candidate for OAM-MDM IM/DD optic fiber communication.

Secure key real-time update and dynamic DNA encryption for CO-OFDM-PON based on a hybrid 5-D chaos.

A double key (DK) real-time update and hybrid five-dimensional (5-D) hyperchaotic deoxyribonucleic acid (DNA) dynamic encryption scheme is proposed, which can ensure the security in the orthogonal frequency division multiplexing passive optical network (OFDM-PON). Chaotic sequences for DNA dynamic encryption are produced using a four-dimensional (4-D) hyperchaotic Lü system and a one-dimensional (1-D) logistic map. In this scheme, the DK consists of an external key set, which is stored locally, and an internal key, which is associated with the plaintext and external key. In addition, a pilot cluster is used as the carrier of key transmission and key embedding is achieved by converting key to phase information of the pilot. To verify the feasibility of the scheme, a simulation validation is performed on a 46.5Gb/s 16 quadrature amplitude modulation (QAM) coherent OFDM-PON system transmitted over an 80 km transmission distance. The results show that the proposed scheme can improve the security performance of OFDM-PON at a low OSNR cost of 0.3 dB and the key space is expanded to (8.514 × 10102)S. When the correlation redundancy (CR) G⩾7, the 0 bit error rate (BER) of key can be achieved and the key can be updated and distributed in real-time without occupying additional secure channels.

400 Gbit/s 4 mode transmission for IM/DD OAM mode division multiplexing optical fiber communication with a few-shot learning-based AffinityNet nonlinear equalizer.

Nonlinear impairment in a high-speed orbital angular momentum (OAM) mode-division multiplexing (MDM) optical fiber communication system presents high complexity and strong stochasticity due to the massive optoelectronic devices. In this paper, we propose an Affinity Network (AffinityNet) nonlinear equalizer for an OAM-MDM intensity-modulation direct-detection (IM/DD) transmission with four OAM modes. The labeled training and testing signals from the OAM-MDM system can be regarded as "small sample" and "large target", respectively. AffinityNet can be used to build an accurate nonlinear model using "small sample" based on few-shot learning and can predict the stochastic characteristic nonlinearity of OAM-MDM with a high level of generalization. As a result, the AffinityNet nonlinear equalizer can effectively compensate the stochastic nonlinearity in the OAM-MDM system, despite the large difference between the training and testing signals due to the stochastic nonlinear impairment. An experiment was conducted on a 400 Gbit/s transmission with four OAM modes using a pulse amplitude modulation-8 (PAM-8) signal over a 2 km ring-core fiber (RCF). Our experimental results show that the proposed nonlinear equalizer outperformed the conventional Volterra equalizer with improvements in receiver sensitivity of 1.7, 1.8, 3, and 3.3 dB for the four OAM modes at the 15% forward error correction (FEC) threshold, respectively. In addition, the proposed equalizer outperformed a convolutional neural network (CNN) equalizer with improvements in receiver sensitivity of 0.8, 0.5, 0.9, and 1.4 dB for the four OAM modes at the 15% FEC threshold. In the experiment, a complexity reduction of 37% and 83% of the AffinityNet equalizer is taken compared to the conventional Volterra equalizer and CNN equalizer, respectively. The proposed equalizer is a promising candidate for a high-speed OAM-MDM optical fiber communication system.

Hidden conditional random field-based equalizer for the 3D-CAP-64 transmission of OAM mode-division multiplexed ring-core fiber communication.

As a key technique for achieving ultra-high capacity optical fiber communications, orbital angular momentum (OAM) mode-division multiplexing (MDM) is affected by severe nonlinear impairments, including modulation related nonlinearities, square-law nonlinearity and mode-coupling-induced nonlinearity. In this paper, an equalizer based on a hidden conditional random field (HCRF) is proposed for the nonlinear mitigation of OAM-MDM optical fiber communication systems with 20 GBaud three-dimensional carrierless amplitude and phase modulation-64 (3D-CAP-64) signals. The HCRF equalizer extracts the stochastic nonlinear feature of the OAM-MDM 3D-CAP-64 signals by estimating the conditional probabilities of the hidden variables, thereby enabling the signals to be classified into subclasses of constellation points. The nonlinear impairment can then be mitigated based on the statistical probability distribution of the hidden variables of the OAM-MDM transmission channel in the HCRF equalizer. Our experimental results show that compared with a convolutional neural network (CNN)-based equalizer, the proposed HCRF equalizer improves the receiver sensitivity by 2 dB and 1 dB for the two OAM modes used here, with l = + 2 and l = + 3, respectively, at the 7% forward error correction (FEC) threshold. When compared with a Volterra nonlinear equalizer (VNE) and CNN-based equalizer, the computational complexity of the proposed HCRF equalizer was found to be reduced by 30% and 41%, respectively. The bit error ratio (BER) performance and reduction in computational complexity indicate that the proposed HCRF equalizer has great potential to mitigate nonlinear distortions in high-speed OAM-MDM fiber communication systems.

Adaptive Bayesian neural networks nonlinear equalizer in a 300-Gbit/s PAM8 transmission for IM/DD OAM mode division multiplexing.

The strong stochastic nonlinear impairment induced by random mode coupling appears to be a long-standing performance-limiting problem in the orbital angular momentum (OAM) mode division multiplexing (MDM) of intensity modulation direct detection (IM/DD) transmission systems. In this Letter, we propose a Bayesian neural network (BNN) nonlinear equalizer for an OAM-MDM IM/DD transmission with three modes. Unlike conventional Volterra and convolutional neural network (CNN) equalizers with fixed weight coefficients, the weights and biases of the BNN nonlinear equalizer are regarded as probability distributions, which can accurately match the stochastic nonlinear model of the OAM-MDM. The BNN nonlinear equalizer is capable of adaptively updating its weights and biases sample-by-sample, according to the probability distribution. An experiment was conducted on a 300-Gbit/s PAM8 signal with three modes over a 2.6-km OAM-MDM RCF transmission. The experimental results demonstrate that the proposed BNN nonlinear equalizer exhibits promising solutions to effectively mitigate nonlinear distortions, which outperforms conventional Volterra and CNN equalizers with receiver sensitivity improvements of 1.0 dBm and 2.5 dBm, respectively, under hard-decision forward error correction (HD-FEC) thresholds. Moreover, compared with the Volterra and CNN equalizers, the complexity of the OAM-MDM is significantly improved through the BNN nonlinear equalizer. The proposed BNN nonlinear equalizer is a promising candidate for the high capacity inter-data center interconnects.

Photonic-aided W-band dual-vector RF signal generation and detection enabled by bandpass delta-sigma modulation and heterodyne detection.

We propose a photonic-aided dual-vector radio-frequency (RF) signal generation and detection scheme enabled by bandpass delta-sigma modulation and heterodyne detection. With the aid of the bandpass delta-sigma modulation, our proposed scheme is transparent to the modulation format of the dual-vector RF signals and can support the generation, wireless transmission, and detection of both single-carrier (SC) and orthogonal-frequency-division-multiplexing (OFDM) vector RF signals with high-level quadrature-amplitude-modulation (QAM) modulation. With the aid of the heterodyne detection, our proposed scheme can support up to W-band (75-110 GHz) dual-vector RF signal generation and detection. For the validation of our proposed scheme, we experimentally demonstrate the simultaneous generation of a SC-64QAM signal at 94.5 GHz and a SC-128QAM signal at 93.5 GHz and their error-free high-fidelity transmission over a 20-km single-mode fiber 28 (SMF-28) and a 1-m single-input single-output (SISO) wireless link at the W-band. To the best of our knowledge, this is the first time that delta-sigma modulation has been introduced into a W-band photonic-aided fiber-wireless integration system to achieve flexible and high-fidelity dual-vector RF signal generation and detection.

Low-complexity characterized-long-short-term-memory-aided channel modeling for optical fiber communications.

In this work, a low-complexity data-driven characterized-long-short-term-memory (C-LSTM)-aided channel modeling technique is proposed for optical single-mode fiber (SMF) communications. To fully utilize the sequence correlation learning ability of traditional long short-term memory (LSTM) networks and solve the gradient explosion problem, the feature information is introduced into the traditional LSTM input layer to better characterize the intersymbol interference caused by dispersion in SMF modeling. The simulation results show that the proposed C-LSTM can effectively alleviate the gradient explosion problem with a stable and ultimately lower mean square error (MSE) than traditional LSTM. Compared with the split-step Fourier method (SSFM) and the conditional generative adversarial network (CGAN), the proposed C-LSTM has superior computational complexity. Moreover, due to the sequence correlation learning ability inherent to C-LSTM, coupled with the flexibility of feature information selection, the proposed C-LSTM-aided modeling technique has a higher modeling accuracy than traditional LSTM. Moreover, the C-LSTM-aided modeling technique can be effectively extended to other channel modeling applications with strong sequence correlations.