High-order Modulation Formats Research Articles

High-fidelity sub-petabit-per-second self-homodyne fronthaul using broadband electro-optic combs

With the exponential growth in data density and user ends of wireless networks, fronthaul is tasked with supporting aggregate bandwidths exceeding thousands of gigahertz while accommodating high-order modulation formats. However, it must address the bandwidth and noise limitations imposed by optical links and devices in a cost-efficient manner. Here we demonstrate a high-fidelity fronthaul system enabled by self-homodyne digital-analog radio-over-fiber superchannels, using a broadband electro-optic comb and uncoupled multicore fiber. This self-homodyne superchannel architecture not only offers capacity boosting but also supports carrier-recovery-free reception. Our approach achieves a record-breaking 15,000 GHz aggregated wireless bandwidth, corresponding to a 0.879 Pb/s common public radio interface (CPRI) equivalent data rate. Higher-order formats up to 1,048,576 quadrature-amplitude-modulated (QAM) are showcased at a 100 Tb/s class data rate. Furthermore, we employ a packaged on-chip electro-optic comb as the sole optical source to reduce the cost, supporting a data rate of 100.5 Tb/s with the 1024-QAM format. These demonstrations propel fronthaul into the era of Pb/s-level capacity and exhibit the promising potential of integrated-photonics implementation, pushing the boundaries to new heights in terms of capacity, fidelity, and cost.

Overcoming laser phase noise for low-cost coherent optical communication

Artificial-intelligence-generated content has driven explosive data traffic growth in data-center interconnects. Traditional direct detection solutions struggle with limited spectral efficiency and distance, prompting the shift to coherent optics for cost-sensitive short-reach links. One specific challenge is integrating low-cost lasers while overcoming severe phase noise on high-order modulation formats. Here, we propose a residual carrier modulation scheme for precise and efficient carrier frequency and phase recovery. The residual optical carrier can continuously track phase fluctuations without redundancy compared with discrete time-domain pilots, and address the digital-to-analog convertor resolution reduction issue of frequency-domain digital pilots. In proof-of-concept experiments, we transmit a net 1-Tb/s probabilistic-shaped 256-ary quadrature amplitude modulated (PS-256-QAM) signal using a 3 MHz distributed feedback (DFB) laser. Our scheme improves bitrate by 41% compared to conventional time-domain pilots, achieving a record laser linewidth sum and symbol duration product of 6.89 × 10−5. This approach supports MHz linewidth DFB lasers in low-cost coherent optical communications.

Bit weight-aware high-fidelity digital RoF fronthaul based on dual-drive MZM and chirp-dispersion Interaction.

Digital radio-over-fiber (D-RoF) quantizes the wireless waveform to improve the noise tolerance in fronthaul links. Unlike conventional data transmission, the quantization bits exhibit different weights, offering a new strategy to protect the high-weight bits. By introducing a dual-drive MZM (DD-MZM)-based optical transmitter, the interaction between frequency chirp and chromatic dispersion (CD) results in eye closure/open. Such an effect would potentially achieve higher fidelity of the reconstructed wireless signal in the SNR-limited region. In this paper, we first establish a theoretical model for chirp and dispersion-induced eye closure/open, characterizing the influence of fiber length and baud rate on the constellation interval. We then propose two protection schemes for 4-level pulse amplitude modulation (PAM-4), in which the high- and low-weight bits are interleaved and loaded onto the upper or lower arms of DD-MZM to leverage the negative or positive chirp. Furthermore, we extend to high-order modulation formats and propose two uneven optical PAM-8 schemes with different frequency chirps, which protect one or two of the three bits in each PAM-8 symbol, respectively. The chirp-dispersion interaction-enabled uneven optical PAM-4/8 schemes are experimentally demonstrated in intensity modulation and direct detection (IM-DD) D-RoF system. We compare the performance with chirp-free PAM-4/8 schemes generated by differential-driven mode. Then, we adopt the µ-law quantizer to verify the effectiveness of the proposed schemes and the Lloyd-Max algorithm-based quantizer to maximize the signal-to-noise ratio (SNR). With the help of chirp-dispersion interaction-enabled uneven optical PAM-4/8 schemes, the experimental results show 11.3-dB and 4.8-dB SNR gains of the wireless signal after 5-km fiber transmission, respectively.

Efficient Error-Rate Estimation for Optical Transmission Systems Using Artificial Neural Networks

ABSTRACT With the advancement in modulation formats, optical transmission systems are becoming more adaptable and dynamic. Predicting bit errors of higher-order modulation formats is a challenging problem for the optimum design of communication systems. The existing simulation methods have persisted by employing iterative procedures that frequently incur high computing expenses and time consumption. On the other hand, deep learning (DL) algorithms have demonstrated remarkable efficacy as practical computing tools, presenting a viable approach to accelerate modulation simulations. In this paper, an artificial neural network (ANN) based bit error rate (BER) estimation scheme is proposed for the popular modulation forms including 56 Gbps 16-quadrature amplitude modulation (16QAM), 100 Gbps 32QAM, and 120 Gbps 64QAM optical system. Based on constellation diagrams (CDs) acquired with different launch power, laser linewidth, transmission distance, and OSNR, amplitude histograms (AHs) are generated via a manual preprocessing method. The properly trained ANN architecture exhibits a computational speed that surpasses traditional simulation methods by a factor exceeding 347. Moreover, the design considerations including the number of layers, nodes, activation functions, learning rate, optimizers, and evolution epochs are also investigated in detail. This research paves the way for optical transmission systems to use fast DL-based optimization strategies.

Phase-locking-free all-optical matching system for 100 Gbaud QPSK optical signal.

Photonic firewall is a monitoring protection device that will directly detect and locate optical network attacks at the optical layer, which can effectively ensure the security of optical networks. An all-optical matching system is the core part of photonic firewall, which determines the performance of a photonic firewall, so it is of great significance to research and develop all-optical matching system for high-speed and high-order modulation formats signals. At present, an all-optical matching system for binary modulation formats is relatively mature, but the all-optical matching system for high-order phase modulation format signals is still limited by how to solve the problem of phase synchronization. In this paper, a new all-optical matching system based on self-interference matching is proposed for quadrature phase shift keying (QPSK) optical signal, which avoids the introduction of local target sequence optical signals and phase-locking circuits. The theoretical analysis and simulation verification are conducted for the designed system. The results demonstrate that the system can accurately identify and locate 4-symbol or 8-symbol target sequences in the input QPSK optical signals with 16-symbol and 32-symbol data sequences at a data rate of 100 Gbaud.

Block-length aware enumerative sphere shaping for probabilistic shaping optical transmission system.

Due to its large transmission capacity and low complexity, probabilistic shaping (PS) technology has been attracting increasing attention. The commonly used constant composition distribution matching (CCDM) in PS technology, which generates amplitude sequences with a fixed empirical distribution, exhibits higher rate loss for short block lengths. In this paper, we present a block-length aware enumerative sphere shaping (BA-ESS) designed to implement probability shaping within high-order modulation formats, which can transition between static (BA-ESS-S) and dynamic (BA-ESS-D) modes based on the block length. When dealing with short block lengths, it will be switched to the static mode. On the contrary, for longer block lengths, the algorithm will be transitioned to dynamic mode, which is a real-time coding method that effectively reduces storage complexity. We validate the transmission performance of this scheme through a 28 GBaud PS-64QAM simulation system and an 8 GBaud PS-64QAM transmission experiment. Through the analysis of simulation results, it can be observed that BA-ESS achieves handsome gains over ESS and optimum ESS (OESS). When all three schemes reach the NGMI threshold, for a block length of 40, BA-ESS provides OSNR gains of 0.88 dB and 0.34 dB compared to ESS and OESS, respectively. Additionally, experimental results indicate that for a block length of 20, the BA-ESS scheme offers an OSNR gain of 0.97 dB relative to ESS.

On the multipath interference mitigation for high-speed IM-DD transmissions with Nyquist subcarrier modulation.

The performance of high-speed intensity modulation direct detection (IM-DD) transmissions is severely degraded due to the occurrence of multipath interference (MPI), especially when a higher-order modulation format is utilized. Here, we propose and demonstrate, for the first time to the best of our knowledge, that a Nyquist subcarrier modulation (Nyquist-SCM) format inherently exhibits resistance to the MPI. We experimentally evaluate the MPI tolerance by transmitting 56 Gbit/s PAM-4 signals and Nyquist-SCM 16QAM signals over the 2 km standard single-mode fiber (SSMF) when the C-band semiconductor laser with a linewidth of 1.7 MHz is utilized. In comparison with the PAM-4 format, the Nyquist-SCM 16QAM format can lead to an enhanced MPI tolerance of 4 dB at the KP4-FEC threshold of BER = 2 × 10-4. In addition, even with the help of MPI mitigation for the PAM-4 signals based on two newly reported methods, the utilization of Nyquist-SCM 16QAM signal can still guarantee an improved MPI tolerance of 1 dB.

High-Capacity Coherent WDM Networks Empowered by Probabilistic Shaping and End-to-End Deep Learning

To optimize the functionality of coherent optical fiber communication (OFC) systems and enhance their capacity related to long-haul transmissions, wavelength-division multiplexing (WDM) and probabilistic constellation shaping (PCS) techniques have been used. This paper develops an end-to-end (E2E) deep learning (DL)-based PCS algorithm, i.e., autoencoder (AE) for a high-order modulation format WDM system that minimizes nonlinear effects while ensuring high capacity and considers system parameters, in particular those related to the OFC channel. Only the AE of the central channel is trained to meet the specified performance objective, as the system design employs identical AEs in each WDM channel. The simulation results show that the architecture should consist of two hidden layers, with thirty two nodes per hidden layer and a ”32×modulation order” batch size to obtain optimal system performance, when designing AE using a dense layer neural network. The behavior of the AE is examined to determine the optimum launch-power ranges that enhance the system's performance. The developed AE-based PCS-WDM provides a 0.4 shaping gain and outperforms conventional solutions.

Experimental demonstration of optical waveform transmission with multiple-eigenvalue 16-APSK modulation.

The multi-eigenvalue multiplexing-based discrete spectrum-modulated nonlinear frequency-division multiplexing (DS-NFDM) system with higher-order modulation format has been demonstrated experimentally. After designing the coefficients of the eigenvalue set and the constellation point distribution of 16-amplitude phase shift keying (16-APSK), the realizations of 14-, 30-, and 46-eigenvalue multiplexed DS-NFDM signals have been implemented. The results show that 46-eigenvalue and 30-eigenvalue multiplexed DS-NFDM signals can transmit 50 km and 400 km over a nonzero dispersion-shifted fiber (NZDSF) under soft-decision forward error correction (SD-FEC) threshold of 2.4E-2, respectively. This demonstration shows for the first time, to the best of our knowledge, the record for multiplexed eigenvalue number and data rate of the multiple-eigenvalue-based DS-NFDM system.

Noise equalization scheme based on probabilistic shaping and complex-valued ANN for dual-polarization continuous spectrum NFDM system with high-order modulation formats

In dual-polarization continuous spectrum nonlinear frequency division multiplexing (DP-CS NFDM) systems, the presence of noise destroys the independence between subcarriers in the nonlinear spectral domain (NSD). Additionally, as the modulation order and the number of subcarriers increase, the signal power increases and the effect of noise on the performance of the system becomes more severe. In this paper, we propose a noise equalization scheme based on probabilistic shaping (PS) and complex-valued neural network (c-ANN) for dual-polarization transmission CS NFDM system with high-power signals. The scheme utilizes PS to reduce the distribution probability of high-power constellation points of the signal with high-order modulation format, to decrease the peak-to-average power ratio of the continuous spectrum subcarriers and the average power of the signal, which can achieve the suppression and equalization of the amplifier spontaneous emission (ASE) noise and the processing noise. In addition, the scheme uses the c-ANN to effectively reduce the correlation between subcarriers caused by the noise and improve the system performance. The effectiveness of the proposed scheme is verified in the DP-CS NFDM system, and the simulation results show that the Q-factor gain is enhanced by roughly 1.1 dB and 0.8 dB for the number of subcarriers of 128 and 256, respectively, compared to the classic nonlinear Fourier transform (NFT) scheme. Among them, with different noise figure (NF) and satisfying the 7% forward error correction (FEC) threshold, the 512QAM signal with an entropy of 8 after equalization increase the transmission distance by 80 km longer than that of uniform 256QAM signals for the number of subcarriers of 128. Compared with the joint scheme based on PS and real-valued neural network (r-ANN), this scheme has better equalization performance at the same complexity, and the complexity can be reduced by 50% under the same performance.

Improved carrier phase recovery for high-capacity optical communication systems with high-order modulation formats

A modified Viterbi-Viterbi (MVV) carrier phase recovery (CPR) algorithm is comprehensively studied based on the quadrature phase-shift-keying (QPSK) partition scheme. By improving the QPSK partition scheme for the 16-ary quadrature amplitude modulation (16QAM), MVV algorithm is developed for the optical fiber communication systems with the modulation formats of dual-polarization 64-QAM (DP-64QAM) and DP-256QAM. Numerical simulations have been carried out in a 9-channel Nyquist-spaced 32-Gbaud optical transmission system for different modulation formats and the performance of MVV CPR with respect to pilot-aided (PA) CPR has been examined. Results show that MVV CPR can significantly mitigate the laser phase noise in the system using high-order modulation formats. Compared to PA CPR, MVV CPR performs better with the increase of the transmission distance, where the impact of equalization enhanced phase noise has to be taken into account. Furthermore, MVV has been compared with other CPR approaches in terms of the performance and the computational complexity.

Reconfigurable all-optical pattern recognition for PSK and QAM signals in high-speed optoelectronic firewalls.

In the fifth generation fixed networks (F5G) era, full-fiber-connected optical networks support emerging bandwidth-hungry services. However, optical networks are vulnerable to attack by tapping or other methods, which has been paid more and more attention in modern optical infrastructure. Therefore, high-speed optoelectronic firewalls appear as one of the promising technologies to guarantee security. The most significant and challenging component of a high-speed optoelectronic firewall is all-optical pattern recognition, especially for more advanced high-order modulation formats such as phase shift keying (PSK) or quadrature amplitude modulation (QAM) to satisfy efficient enhanced fixed broadband in F5G. In this paper, what we believe to be a novel reconfigurable all-optical pattern recognition system for PSK and QAM signals is proposed with two implementation architectures. The proposed system mainly consists of a generalized XNOR (GXNOR) and a recirculating loop. The two implementation architectures are precisely two realization methods of the GXNOR part. One employs two cascaded IQ Mach-Zehnder modulators and the other is implemented by the four-wave mixing. The numerical simulation results demonstrate that the two implementation architectures can both achieve all-optical pattern recognition for the reconfigurable high-order modulation formats of QPSK, 8PSK, and 16QAM with the recorded baud rate of 260GBaud.

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.

ISRS impact-reduced routing, modulation, band, and spectrum allocation algorithm in C + L-bands elastic optical networks

C + L-bands elastic optical networks (EONs) cope with growing traffic demands by leveraging the C and L bands of deployed optical fibers. In this scenario, the inter-band stimulated Raman scattering (ISRS) becomes more serious and degrades the quality of transmission (QoT) of services, and should be considered to guarantee the lightpaths establishment for services in the routing, modulation, band, and spectrum allocation (RMBSA). In this paper, we propose an ISRS impact-reduced RMBSA algorithm that reduces the ISRS impact on services at the RMBSA process. In the routing phase, selecting the route with more available contiguous aligned frequency slots (FSs) and shorter transmission distance, the less ISRS impact of requests can be suffered and the spectrum resources of each link can be used as much as possible. In the modulation phase, the lower-order modulation format which can achieve the least required FSs and has higher OSNR tolerance is selected. In the band and spectrum allocation phase, allocation of higher-order modulation format requests to the C-band to reduce the ISRS impact from C-band to L-band. Meanwhile, centralized assignment of more required FSs requests to reduce the ISRS impact of these requests on other requests. Simulation results indicate that the proposed RMBSA algorithm can effectively decrease the blocking probability, improve the resource utilization and request average optical signal-to-noise ratio.

Adaptive feedback-driven probabilistic shaping for high-order modulation formats in a fiber–THz seamless integration system at 320 GHz

In this Letter, we propose a novel, to the best of our knowledge, adaptive feedback-driven probabilistic constellation-shaping (FBD-PCS) method based on the robustness evaluation criteria and employ variational autoencoder (VAE)-based equalizers to implement polarization demultiplexing and nonlinear equalization for the recovery of high-order PCS-QAM signals. We experimentally demonstrate the fiber–THz 2 times 2 MIMO system with a net rate of 366.4 Gbit/s using dual-polarization 40 Gbaud PCS-64QAM signal over a 20 km SSMF and 6 m wireless link. Specifically, the feedback mechanism drives the fiber–THz system to solve optimization problems, adaptively matching the optimized distribution of transmitted symbols that maximizes normalized generalized mutual information (NGMI). We also examine six scenarios to explore nonlinear resistances of FBD-PCS symbols and the robustness of VAE-based equalizers. The results demonstrate the superiority of FBD-PCS over the Maxwell–Boltzmann (M–B) distributions in practical nonlinear-dominant systems. Additionally, the FBD-PCS signals can break limitations for ultrahigh rate transmission with the help of advanced equalizers.

Experimental demonstration of 480 Gbit/s coherent transmission using a nanosecond switching tuneable laser

Fast-switching tuneable lasers with a wide wavelength coverage and with noise and linewidth levels suitable for high-order modulation formats can facilitate the implementation of highly flexible and reconfigurable optical metro, access and inter/intra data center networks. In this work, we show the characterization of a tuneable laser capable of covering a wavelength range of 35 nm in the C-band with nanosecond switching time and low linewidth and use it to demonstrate 480 Gbit/s 16QAM transmission over 25 km of single-mode fiber for a wavelength range of 19 nm.

23.1-Gb/s 135-GHz Wireless Transmission Over 4.6-Km and Effect of Rain Attenuation

In this article, we have experimentally demonstrated a fiber-wireless-integration <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$D$</tex-math> </inline-formula> -band (110–170 GHz) transmission system. To extend the wireless transmission distance while maintaining the wireless bit rate as high as possible, we designed high-gain lens horn antenna modules consisting of a pair of dielectric plano-convex lenses and horn antennas for long-haul wireless links. In addition, we employ the Volterra nonlinear equalization (VNE) algorithm based on the multiple-input–multiple-output (MIMO) structure to precisely compensate for the in-phase/quadrature (I/Q) imbalance and nonlinear impairment of quadrature amplitude modulation (QAM) signals mainly caused by photoelectric (O-E) conversion and electric-photo (E-O) conversion. Meanwhile, one of the methods adopted in our experiment to decrease the influence of nonlinearity on high-order QAM signals is coupling the high-order modulation format with the probabilistic shaping (PS) technology. As a result of outdoor field experimental verification, the demonstration at 135 GHz carrier with a net rate of 23.1 Gb/s over 10 km optic-fiber and 4.6 km wireless transmission distance has been successfully carried out. It is, as we know, the first time that a record-breaking product of net bit rate and wireless transmission distance, i.e., 23.1 Gb/s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> 4.6 km <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> 106.3 Gb/s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot$</tex-math> </inline-formula> km, has been accomplished based on a fiber-wireless-integration system. Also, for the first time, we have measured the effect of rain attenuation for the 135 GHz millimeter-wave (mm-wave) wireless link and established more accurate rainfall models for the Shanghai region of China by comparing them with multiple rainfall models. This work can be used as a complement to the International Telecommunication Union-Radiocommunication sector (ITU-R) recommendations.

Clone-comb-enabled high-capacity digital-analogue fronthaul with high-order modulation formats

Clone-comb-enabled high-capacity digital-analogue fronthaul with high-order modulation formats

Joint-Transceiver Equalization Technique over a 1.4 km Multi-Mode Fiber Using Optical MIMO Technique in IM/DD Systems

In optical fiber communication, recent advances in multiple-input and multiple-output (MIMO) systems using space-division multiplexing have helped achieve higher spectral efficiency and data rates. Propagating higher-order modulation formats over MIMO systems further strengthens the capacity of the transmission link. In the optical-MIMO system, the dispersion impairments originating from a 1.4 km long multi-mode fiber (MMF) are mitigated using the proposed joint-transceiver equalization technique. A numerical convex optimization algorithm is used to compute and optimize the pre- and post-equalization (PPE) coefficients jointly restricted by cost and power budgets. The potential of the proposed joint-PPE technique is tested on an MMF link, which is severely degraded by dispersion compared to a single-mode fiber channel. From the experimental results, the average optical received power gain necessary to reach 10−4 bit-error rate is improved by nearly 2.5 dB using the joint-PPE compared to the post-equalization only based on the minimum mean-squared error principle. When the efficiency of the conventional zero-forcing (ZF) principle-based PPE and the joint-PPE is compared, the joint-PPE scheme outperforms the ZF-PPE by approximately 1.5 dB. The enhancement in the transmission quality is observed with experimentally measured eye diagrams using the joint-PPE scheme. Under the analyzed scenarios, computer simulation also confirms the hypothesis, which establishes the effectiveness of the proposed joint-transceiver equalization over the conventional ZF-PPE scheme. Moreover, the simulated performance benefits of the joint-PPE are evaluated using the singular value decomposition (SVD) technique. Improvement of ≈3.86 dB in the average optical received power gain required to reach 10−4 bit-error rate is witnessed with the PAM-4 format. Overall, the joint-transceiver equalization technique is proven to be beneficial in optical MIMO systems.

High Spectral Efficiency Photonics-Based Polarization Multiplexing OFDM Signal Delivery at W-Band

We have implemented a large-capacity, long-haul, and high spectral efficiency photonics-based polarization multiplexing communication system at W-band. The signal delivery up to 119.1 Gb/s with spectral efficiency of 9.9 bit/s/Hz is achieved over a 10 km optic-fiber link and 4600 m wireless link. In our study, we utilize an orthogonal frequency division multiplexing (OFDM) scheme to compensate for the signal impairments caused by the dispersion effect and the wireless multipath effect. Based on a pair of antennas, the antenna polarization multiplexing technique is used to realize the polarization-multiplexed mm-wave signal delivery. Also, only one communication link is required, instead of the complex 2×2 line-of-sight multiple-input multiple-output (MIMO) link. Instead of Cassegrain antennas, the combination of plano-convex lens and horn antenna greatly extends the wireless distance. For increasing the spectral efficiency and throughput of the communication system, we employ higher-order modulation formats, probabilistic shaping (PS) techniques, and a series of equalization algorithms. Based on photonics technology, we have created a record-setting distance-rate product of 547.9 Gb/s•km (119.1 Gb/s × 4.6 km) for an independent channel at W-band.