High-order Modulation Research Articles

A Hybrid Genetic Algorithm with Tabu Search Using a Layered Process for High-Order QAM in MIMO Detection

In this paper, we propose a hybrid genetic algorithm (HGA) that embeds the tabu search mechanism into the genetic algorithm (GA) for multiple-input multiple-output (MIMO) detection. We modified the selection and crossover operation to maintain the diverse and wide exploration areas, which is an advantage of the GA, and the mutation operation to perform a local search for a specific region. In the mutation process, the ’tabu’ concept is also employed to prevent the repeated search of the same area. In addition, a layered detection process is applied simultaneously with the proposed algorithm, which not only improves the bit error rate performance but also reduces the computational complexity. We apply the layered HGA (LHGA) to the MIMO system with very high modulation order such as 64-quadrature amplitude modulation (QAM), 256-QAM, and 1024-QAM. Simulation results show that the LHGA outperforms conventional detection approaches. Especially, in the 1024-QAM MIMO system, the LHGA has less than 10% of computational complexity but a 6 dB signal-to-noise ratio (SNR) gain compared to the conventional GA-based MIMO detection scheme.

Highly secure 3D-FTN-NOMA scheme based on NODFT matrix precoding and multi-level chaotic perturbation.

This Letter aims to present a highly secure 3D faster-than-Nyquist non-orthogonal multiple access (3D-FTN-NOMA) scheme based on non-orthogonal discrete Fourier transform (NODFT) matrix precoding and multi-level chaotic perturbation. The NODFT matrix precoding technique is employed to operate on the 3D-NOMA system for generating the 3D-FTN-NOMA signal. To address the dual security vulnerabilities in the 3D-FTN-NOMA system, chaotic vector technology is employed to achieve multi-level perturbation of both the original information from different users and the superimposed information. With a net rate of 105.98 Gb/s, we experimentally verified the proposed scheme on a 2 km 7-core fiber system based on intensity modulation/direct detection (IM/DD). By employing NODFT precoding, the 3D-FTN-NOMA system using low-order modulation formats can achieve the transmission capacity of the 3D-NOMA signal using high-order modulation formats within the same system and bandwidth, resulting in a receiving sensitivity gain of approximately 5 dB. Moreover, our proposed encryption scheme effectively addresses the dual security vulnerabilities of 3D-FTN-NOMA and enables comprehensive secure transmission of signals.

High-order direct modulation terahertz communications with a wideband time-coding metachip modulator.

Terahertz communication technology based on on-off keying (OOK) direct modulation is vital for sixth-generation communication systems, especially in short-distance and high-rate applications. However, low-order OOK modulation often leads to suboptimal anti-interference capabilities and a heightened demodulation threshold. Here, we propose a high-order direct modulation terahertz communication framework using a wideband time-coding metachip modulator. The modulator leverages the electromagnetic resonance properties within the metaunit structure, with control enabled by gallium arsenide Schottky diodes. By manipulating the timing of voltage pulses applied to these diodes, the equivalent electromagnetic resonance distributions can be precisely regulated in the time domain. This enables independent and accurate control over the amplitude and phase of terahertz harmonics. Leveraging this technique, three high-order modulation schemes-quadrature phase-shift keying, 16-phase-shift keying, and 16-quadrature amplitude modulation- are achieved in a direct modulation and direct detection system, demonstrating the real-time image transmission. The proposed method offers an important way to develop integrated and low-complexity terahertz wireless communication systems.

Enhancing performance of end-to-end communication system using Attention Mechanism-based Sparse Autoencoder over Rayleigh fading channel

Deep learning has revolutionized communication systems by introducing innovative approaches to address channel impairments through end-to-end models. Autoencoders, a type of deep learning architecture, are adept at learning compact data representations. However, conventional autoencoders in end-to-end models can suffer from overfitting, which limits their effectiveness in noisy communication environments. To address this issue, we propose a Sparse Autoencoder-based (SAE) model that enforces sparsity and promotes the extraction of robust features. Despite its effectiveness, the SAE model may still lack the ability to focus on the most relevant features of the input data. To overcome this limitation, we further introduce an Attention Mechanism-based Sparse Autoencoder (ASA) model. This model integrates the feature extraction capabilities of a sparse autoencoder with an attention mechanism that selectively highlights informative features of the signal. Through simulations, we demonstrate that both proposed models significantly improve M-PSK and M-QAM communication system performance. When trained at 7 dB, both proposed models exhibit significant performance improvements at higher testing average SNRs. Our results show that the SAE model outperforms the conventional Maximum Likelihood Detection (MLD) model and baseline autoencoder systems but suffers from error floor issues. The SAE model suffers from an error floor at average SNRs beyond 16 dB for BPSK and 14 dB for higher-order modulation schemes. As the value of M increases, the performance gap between the MLD and the proposed SAE model narrows. The ASA model, however, effectively mitigates the error floor observed in the SAE model for all values of M and across all modulation schemes. This research highlights the benefits of integrating an attention mechanism with SAE, resulting in enhanced robustness and reliability in communication systems characterized by improved accuracy and reduced error rates.

Optical orthogonal frequency division multiplexing with differential index modulation

This paper proposes a differential index modulation (DIM) scheme to address the complex channel estimation challenges in optical orthogonal frequency division multiplexing with index modulation (OOFDM-IM). The main idea of the DIM scheme is to design a time-frequency dispersive matrix with unitary characteristics and perform index mapping based on the Lemer code principles. By applying differential operations, the DIM scheme enables decoding at the receiver without requiring channel estimation. The paper provides a detailed explanation of the design principles and theoretical bit error rate (BER) of the proposed scheme. Simulations based on the exponential Weibull atmospheric turbulence channel model are conducted to compare the DIM scheme with the existing OOFDM-IM scheme. Additionally, a carefully designed proof-of-concept experiment is performed to further validate the scheme’s effectiveness and feasibility. Both simulation and experimental results demonstrate that, compared to OOFDM-IM, the proposed scheme can entirely avoid complex channel estimation with a maximum signal-to-noise ratio (SNR) loss of no more than 4 dB, even under various turbulence intensities and higher-order modulation scenarios. This provides a valuable reference for OOFDM-IM in complex environments or where channel estimation is challenging.

Performance Enhancement for B5G/6G Networks Based on Space Time Coding Schemes Assisted by Intelligent Reflecting Surfaces with Higher Modulation Orders.

Intelligent Reflecting Surfaces (IRS) and Multiple-Input Single-Output (MISO) technologies are essential in the fifth generation (5G) networks and beyond. IRS optimizes the signal propagation and the coverage and is a viable approach to address the issues caused by fading channels that limits the spectral efficiency, while MIMO enhances data rates, reliability, and spectral efficiency by using multiple antennas at both transmitter and receiver ends. This paper proposes an IRS-assisted MISO system using the Orthogonal Space-Time Block Code (OSTBC) scheme to enhance the channel reliability and reduce the Bit Error Rate (BER) in wireless communication systems. The proposed system exploits the benefits from the transmit diversity gain of the OSTBC scheme as well as from the bit energy to noise power spectral density (Eb/No) improvement of the IRS technology. The presented work explores these combined technologies across different modulation schemes. The obtained results outperform the similar previously published works by considering higher-order modulation schemes as well as the deployment of rate ¾ OSTBC-assisted IRS. Moreover, the obtained results demonstrate that the integration of OSTBC with IRS can yield significant performance improvements in terms of Eb/No by 7 dB and 13 dB when using 16 reflecting elements and 64 reflecting elements, respectively.

Real-time demonstration of 64 × 200 Gbps UDWDM-PON downstream transmission based on silicon photonic integrated transceiver

Coherent detection, high-order modulation, and dense wavelength division multiplexing (DWDM) technologies provide solutions for increasing bandwidth demand of future access networks. We experimentally demonstrate a real-time 64 × 200-Gb/s coherent ultra-dense wavelength-division (UDWDM) coherent passive optical networks (PONs) at 75-GHz channel spacing. The demonstrated downlink transmission is realized with the dual-polarization QPSK (DP-QPSK) modulation scheme. The cost is reduced by using silicon photonic integrated coherent transceiver modules and wider grid AWGs. The power budget is evaluated when all 200 channels are launched at C band. The power budget is 26 dB after 20-km G.652D standard single mode fiber (SSMF) transmission without amplifier at the receiver side under soft-decision FEC (SD-FEC) threshold of 1 × 10−2, and can achieve 32.5 dB with pre-amplified semiconductor optical amplifier (SOA) used at the receiver side.

ОЦІНКА ЧАСТОТНО-ФАЗОВИХ СПОТВОРЕНЬ В ОПТИЧНИХ ТЕЛЕКОМУНІКАЦІЯХ З OFDM

The article proposes a method for monitoring the peak-to-average power ratio (PAPR), and also discusses the results of assessing the sensitivity of optical-OFDM systems to phase-frequency distortions. The results of a study of the noise immunity of an optical-OFDM system for frequency shift relative to the spacing of optical subcarriers are presented. A description of the factors causing interference and frequency-phase distortions caused by chromatic dispersion (CD) and polarization mode dispersion (PMD) on the performance of optical multiplexing systems with orthogonal frequency division is carried out. Monitoring the PAPR in OFDM systems is relevant, in particular, in the context of fiber optic communication problems that are caused by the nonlinearity of the optical fiber. It is shown that when directly deploying optical networks, the presence of frequency distortions and sensitivity to phase noise are the two main disadvantages of OFDM. Both frequency distortion and phase noise lead to interchannel interference (ICI). Due to the relatively large symbol length compared to a single carrier, OFDM is susceptible to both frequency distortion and phase noise. An additional cumulative distribution function is used for a visual description of PARP. The effect of the oversampling coefficient on the PARP value is determined. It is proposed to use the oversampled signal to obtain a more accurate PARP value. The results of the study show that the effect of phase noise on a signal in optical OFDM channels is due to the existing long symbol period compared to signal transmission on a single carrier. In addition, with an increase in the modulation order, optical OFDM becomes more sensitive to phase noise, which encourages an increase in the signal-to-noise ratio to counteract this. The results of the research showed that for coherent OFDM optical systems, the line width of the optical quantum generator is a critical parameter, especially when switching to high-order modulation. The paper discusses a diagram describing the process of convergence of radio and optical technologies in the context of the use of OFDM modulation. This technique allows for the correct choice of channel multiplexing strategy in optical OFDM telecommunications with multi-position signals.

CTRNet: An Automatic Modulation Recognition Based on Transformer-CNN Neural Network

Deep learning (DL) has brought new perspectives and methods to automatic modulation recognition (AMR), enabling AMR systems to operate more efficiently and reliably in modern wireless communication environments through its powerful feature learning and complex pattern recognition capabilities. However, convolutional neural networks (CNNs) and recurrent neural networks (RNNs), which are used for sequence recognition tasks, face two main challenges, respectively: the ineffective utilization of global information and slow processing speeds due to sequential operations. To address these issues, this paper introduces CTRNet, a novel automatic modulation recognition network that combines a CNN with Transformer. This combination leverages Transformer’s ability to adequately capture the long-distance dependencies between global sequences and its advantages in sequence modeling, along with the CNN’s capability to extract features from local feature regions of signals. During the data preprocessing stage, the original IQ-modulated signals undergo sliding-window processing. By selecting the appropriate window sizes and strides, multiple subsequences are formed, enabling the network to effectively handle complex modulation patterns. In the embedding module, token vectors are designed to integrate information from multiple samples within each window, enhancing the model’s understanding and modeling ability of global information. In the feedforward neural network, a more effective Bilinear layer is employed for processing to capture the higher-order relationship between input features, thereby enhancing the ability of the model to capture complex patterns. Experiments conducted on the RML2016.10A public dataset demonstrate that compared with the existing algorithms, the proposed algorithm not only exhibits significant advantages in terms of parameter efficiency but also achieves higher recognition accuracy under various signal-to-noise ratio (SNR) conditions. In particular, it performs relatively well in terms of accuracy, precision, recall, and F1-score, with clearer classification of higher-order modulations and notable overall accuracy improvement.

Dynamics of Airyprime beams with higher-order spectral phase modulation in the fractional Schrödinger equation

In this paper, the effects of spectral phase modulation on propagation characteristics of Airyprime beams modeled by fractional Schrödinger equation are studied, and the propagation dynamics of Airyprime beams are analyzed. It is found that the second and third-order spectral phase modulation significantly affect the beams dynamics. For the second-order spectral phase modulation, an increase in the Lévy index leads to a forward shift of the peak position, and the peak intensity increases for the positive spectral modulation coefficient, while the opposite tendency of the peak intensity is found for the negative spectral modulation coefficient. In addition, the appearance of multiple peaks depends on the positive modulation coefficient. For the third-order spectral phase modulation, the peak intensity increases under the larger spectral phase modulation coefficient with the backward shift of the maximum peak position, and an increase of the Lévy index results in the forward shift of the focusing position. The results show potential applications of Airyprime beams in various fields such as optical controlling and manipulation.

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.

Two-dimensional and high-order directional information modulations for secure communications based on programmable metasurface

Conventional wireless communication schemes indiscriminately transmit information into the whole space and pose inherent security risks. Recently, directional information modulation (DIM) has attracted enormous attention as a promising technology. DIM generates correct constellation symbols in the desired directions and distorts them in undesired directions, thus ensuring the security of the transmitted information. Although several DIM schemes have been reported, they suffer from defects of bulkiness, energy consumption, high cost, and inability to support two-dimensional (2D) and high-order modulations. Here, we propose a DIM scheme based on a 2-bit programmable metasurface (PM) that overcomes these defects. A fast and efficient discrete optimization algorithm is developed to optimize the digital coding sequences, and the correct constellation symbols can be generated and transmitted in multi-directional beams. As a proof-of-concept, three sets of constellation diagrams (8 phase shift keying (PSK), 16 quadrature amplitude modulation (QAM), and 64QAM) are realized in the multi-channel modes. This work provides an important route of employing DIM for ensuring physical-layer security and serves as a stepping stone toward endogenous secure 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.

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.

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.

Analysis and Design of Reactive Passive Mixers for High-Order Modulation IoT Cartesian Transmitters

Analysis and Design of Reactive Passive Mixers for High-Order Modulation IoT Cartesian Transmitters