High-order Modulation Research Articles

FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects.

Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio.

High Spectral Efficiency and Low Error Rate MIMO-GFDM for Next-Generation Communication Systems

Multiple-input multiple-output (MIMO) technology with high order signal modulation method has been proposed recently as a scheme to achieve high throughput requirements of next-generation communication applications. However, the use of high-order modulation signals degrades the error rate performance. Generalized frequency division multiplexing (GFDM) has attracted enormous consideration for deploying in new communication scenarios due to its advantages in terms of out-of-band (OOB) emission, spectral efficiency (SE), and latency. Index modulation (IM) methods convey digital information by utilizing transmission entities with adjustable index parameters to provide flexible system design and offer attractive advantages such as energy and SE without increasing the computational complexity. The Multiple-Mode (MM) method permits multiple subcarriers to transmit multiple modes and employs the whole permutation of these modes to convey additional information bits. The proposed MIMO MM-GFDM-IM scheme improves the bit error rate and the spectral efficiency compared to the existing schemes. The proposed method can select the modulation order and the number of modes to achieve the design goals. Furthermore, a system with high modulation order can improve the spectral efficiency when the constellation point is fixed. This paper also proposes a practical and effective MM selection strategy and two low-complexity detectors.

Digital Sine Oscillators Based on Higher Order Sigma–Delta Modulation

In this paper, a new class of digital sine oscillators based on higher-order multibit sigma-delta modulation is presented. The samples of a given pure sine signal are quantized, resulting in a pulse-code modulated (PCM) sequence. A numeric condition for oscillation (NCO) based on the PCM signal is disclosed. If the NCO is fulfilled, a system constant <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> with a finite bit width can be derived and a hardware-efficient practical realization of a digital oscillator based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> -order sigma-delta modulation is possible. The oscillator output sequence is an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> -times differentiated version of the PCM signal and thus the PCM signal can be reconstructed by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> -subsequent accumulations. All signals are absolutely periodic and are represented by binary numbers with well-defined finite bit widths. Initial conditions for the registers of the oscillator are determined. An example for the generation of a high-purity PCM signal with 2048 samples per period is demonstrated. The noise spectrum of this signal is white and the ratio between the mean noise amplitude and the signal amplitude is about one over one billion. The resulting oscillator requires a third order sigma-delta modulator. The chip size is estimated for the oscillator being integrated in a commonly used CMOS technology.

Towards InAs/InP Quantum-Dash Laser-Based Ultra-High Capacity Heterogeneous Optical Networks: A Review

The unprecedented increase in internet traffic witnessed in the last few years has pushed the community to explore heterogeneous optical networks, including free-space-optics (FSO) communication, radio-over-fiber (RoF), wireless (WL), and their convergent hybrid technologies. This stems from the possibility of seamless integration with the existing fiber-optic backhaul networks while providing much-needed flexibility and scalability. Moreover, efficient optical transceivers, particularly light sources in the form of semiconductor laser diodes, are key in meeting the future demands of the next generation green optical access networks. In this respect, InAs/InP Quantum-dash (Qdash) nanostructure-based lasers have shown tremendous progress in the past few years with applications spanning from a wavelength division multiplexed (WDM) optical communication to recently, millimeter-wave (MMW) over fiber networks. This waveguide-based laser diode (LD) has demonstrated a rule-changing broad multi-wavelength lasing emission, thanks to the inherent and wavelength-tunable wide gain profile offered by the Qdash active-gain region covering S- to U-band regions. Moreover, exploiting mode-locking and optical injection locking assisting techniques, highly coherent InAs/InP Qdash comb laser source at 1550 nm and 1610 nm have been respectively realized, thus opening a new paradigm for their potential applications in green optical and 5G access networks. In this work, progress on utilizing InAs/InP Qdash LD, supporting several sub-carriers, in energy-efficient ~1550 nm and ~1610 nm WDM heterogeneous optical networks with single-mode-fibers (SMF) has been highlighted, exhibiting aggregate data rates of 11 – 12 Tb/s by employing a single device, and accommodating PAM4 and higher-order 32-QAM modulation schemes. Moreover, the recent deployment of this LD in the RoF domain, targeting MMW frequency band, for convergent fiber-wireless networks, is also summarized, with demonstrated 25 to >100 GHz MMW beat-tone frequency generates and transmission of up to 24 Gb/s.

Blind High-Order Modulation Recognition for Beyond 5G OSTBC-OFDM Systems via Projected Constellation Vector Learning Network

The blind modulation recognition (BMR) of high-order modulation types is a pressing task and needs to be raised in the calendar for the Beyond 5G (B5G) OSTBC-OFDM (Orthogonal Space-Time Block Coded-Orthogonal Frequency Division Multiplexing) system. In this letter, a BMR algorithm based on a project constellation vector which employs a temporal convolutional network (PCV-TCNet) is proposed to recognize 13 modulation formats, such as high-order 1024QAM and 2048QAM. Without any prior information, a zero-forcing blind equalization algorithm is leveraged to reconstruct the impaired signal. Furthermore, the learning content of PCV-TCNet is PCV features, which are transformed by the constellation diagram of the reconstructed signal. In addition, PCV-TCNet utilizes causal and dilated convolutions to accelerate the BMR process. The simulation results verify the proposed PCV-TCNet for recognizing the high-order modulation types in the B5G OSTBC-OFDM system and demonstrate its preferable recognition performance with the lowest complexity to existing methods.

Predistortion-Based Linearization for 5G and Beyond Millimeter-Wave Transceiver Systems: A Comprehensive Survey

The next-generation (5G/6G) wireless communication aims to leapfrog the currently occupied sub-6 GHz spectrum to the wideband millimeter-wave (MMW) spectrum. However, MMW spectrums with high-order modulation schemes drive the power amplifier (PA) at significant back-off, causing severe nonlinear distortions, thus deteriorating the transceiver&#x2019;s (TRXs) modulation process. Typically, the TRX efficacy is quantified with standardized linearization matrices, which take advantage of different predistortion (PD) schemes to handle deep compression of the PA. In this regard, TRX baseband signals are mostly linearized in the digital domain, where digitally controlled linearization needs higher sampling rates due to increasing MMW bandwidths to compensate for intermodulation (IMD) products, resulting in increased system cost and power consumption. Alternately, the digitally controlled analog-based linearization, i.e., the hybridization of digital predistortion (DPD) and analog predistortion (APD), is highly productive and cost-effective for fulfilling the linearized energy-efficient design vision of MMW networks. Therefore, this paper puts an extensive spotlight on the progress in PD-based linearization for 5G and beyond communications. It first provides background information on the advancements of PD schemes through recent surveys, then classifies the general roadmap of PD waveform processing across the TRX system models as preliminary. After this, we present three prominent PD architectures and their design approaches with intrinsic performance metrics. Finally, we explore four case studies encompassing PD operation under certain nonlinear constraints of different communication schemes. We examine the suitability of PD-based linearization solutions, both existing and proposed till the first quarter of 2022, and identify the potential prospects in this domain.

Numerical study of self-focusing and filament formation of intense vortex beams in plasmas

We have studied the self-focusing and filamentation of vortex laser beams propagating in underdense plasmas with different values of the topological charge and initial laser powers. The self-focusing dynamics of vortex laser beams is closely related to the topological charge, which has attracted widespread attention. Based on the paraxial approximation of the Helmholtz equation, the steady-state solution of vortex beams propagating in underdense plasmas is deduced, and the expression for critical power of vortex laser beams is obtained. Furthermore, using the split-step Fourier method to solve the wave equation, we analyze the numerical images of vortex laser beams propagating in underdense plasma under different parameters. The simulation results show that the critical power for self-focusing is positively correlated with the topological charge of vortex laser beams. When the initial laser power is high enough, the vortex laser beam will first be focused into a thin ring, and then the modulation amplitude increases continuously, which eventually leads to the ring structure breaking into filaments. The number of filaments has an integer multiple relationship with the topological charge. In the process of filamentation, the radius and the maximum light intensity of vortex laser beam both change drastically. After the filamentation process is completed, the vortex laser beam continues to propagate with a new topological type. We further increase the incident laser power and find that the number of filaments of the vortex laser beam increases. The increased number of filaments is the value of its topological charge at each time. With the development of filament instability, higher-order modulation instability can be excited in the later stage, and the intensity of filaments will exhibit angular modulation. Our results show that in compared with the standard Gaussian beam, the propagation behavior of vortex laser beams in underdense plasmas is much more stable under the same power, wavelength and plasma parameters. The propagation characteristics of vortex laser beams are helpful to the theoretical and experimental study of stimulated backward Raman amplification of ultra-strong vortex beam in underdense plasmas.

Design and Feasibility Verification of 6G Wireless Communication Systems with State of the Art Technologies

Frequencies above 100 GHz are the promising frequency bands for 6G wireless communication systems because of the abundant unexplored and unused spectrum. The increasing global demand for ultra-high spectral efficiencies, data rates, speeds and bandwidths in next-generation wireless networks motivates the exploration of peak capabilities of massive MIMO (Multi–Input–Multi–Output) wireless access technology at THz bands (0.1–10 THz). The smaller wavelengths (order of microns) of these frequencies give an advantage of making high gain antennas with smaller physical dimensions and allows massive spatial multiplexing. This paper presents the design of ultra-massive MIMO (ultra-mMIMO) hybrid beamforming system for multi users and its feasibility to function at THz frequency bands. The functionality of the proposed system is verified at higher order modulation schemes to achieve higher spectral efficiencies using performance metrics that includes error vector magnitude, symbol constellations, and antenna array radiation beams. The performance results suggest to use a particular mMIMO antenna configuration based on number of independent data streams per user and strongly recommended to use higher number of data streams per user in order to achieve higher throughputs that satisfy the needs of 6G wireless systems. Also the performance of the proposed system at 0.14 THz is compared with mmWave systems that operate at 28 GHz and 73 GHz bands to justify the feasibility of the proposed work.

Quadrature Acoustic Frequency Combs Multiplexing for Massive Parallel Underwater Acoustic Communications

AbstractUnderwater acoustic (UWA) communication has been developing rapidly over the past decades for its crucial position in resource exploration, environmental monitoring, and scientific research. However, the transmission data rate of UWA communication is limited by the narrow bandwidth of the underwater acoustic channel. Here, the generation of quadrature acoustic frequency combs (AFCs) is first reported. Massive parallel channels achieved with multiplexing of AFCs for UWA communication are demonstrated. The generated AFCs have unique characteristics which have a stable and precise division in frequency and time domain simultaneously with carrier spacing of 1 Hz with the stability of 10−8. The different frequency spacing in combs leads to different teeth spacings in time, which is orthogonal and separable in the time domain. The orthogonality among AFCs provides a new dimension for multiplexing and can drastically increase channel efficiency. The underwater acoustic communication experiments demonstrate that it is drastically increasing the transmission rate to 45.33 kb s−1 and high spectral efficiency of 1.51 (channel s−1) Hz−1 without utilizing other modulation techniques by a single transducer. Since AFCs multiplexing is a completely independent degree of freedom that can be readily integrated with other high order modulation techniques, such as quadrature amplitude modulation and phase‐shift keying, in a single channel, AFCs multiplexing opens a new dimension for acoustic communication.

Improved multiplier-free Mueller-Müller Baud-rate timing error detector for optical IM/DD system

Baud rate clock recovery scheme that supports high order modulation formats is an essential part in digital signal processing for current short reach transmission. In this paper, we propose an improved multiplier-free Mueller-Müller timing error detector (MMTED) sampling at baud rate, which shows excellent performance with low complexity. Using the sign operation, the multiplier is eliminated. The further use of error signal to substitute the original data helps to reduce the jitter of the clock. 25 GBaud PAM-4/8 and 50 GBaud PAM-4 transmission are carried out to evaluate the TED performance. Compared to the sign MMTED, more than 12 dB timing jitter improvement is realized.

Sub-sampling generation of ultra-high baud rate PAM/QAM signals via high-order partial response narrowing

Ultra-high baud rate signal generation and detection is of great importance for future intra-data-center interconnect (intra-DCI). In this work, based on a single digital-to-analog convertor (DAC) with 120GSa/s sampling rate, we experimentally demonstrate sub-sampling generation of pulse amplitude modulation (PAM) signals by using high-order partial response narrowing (HPRN) scheme. High-order partial response is utilized to concentrate most of the signal energy into the Nyquist region of DAC sampling rate. A digital brick-wall filter is then employed to avoid spectral overlap by removing the out-of-band components in the frequency domain. The manually induced inter-symbol interference (ISI) can be eliminated by maximum likelihood sequence detection (MLSD) at the receiver. In the experiment, 210Gbaud on-off keying (OOK) signal can be successfully generated and transmitted over 500m standard single-mode fiber (SSMF) with bit-error rate (BER) below the 20% hard-decision forward error correction (HD-FEC) threshold of 1.5×10−2, achieving sub-sampling rate of 0.571. For high-order modulation formats, 217.5Gb/s (145Gbaud) PAM-3 BTB generation and 256Gb/s (128Gbaud) PAM-4 500m transmission are also realized, respectively. Furthermore, for coherent detection systems, 160Gbaud quadrature phase shift keying (QPSK) signal generation is demonstrated by applying HPRN on the in-phase and quadrature components separately, and using carrier phase recovery including pilot symbol group-based coarse estimation and shaped constellation-based blind phase search (BPS) algorithm. The results reveal that the HPRN scheme can extend the usage of DAC at the expense of higher optical signal-to-noise ratio (OSNR) for 200G high-speed optical links and beyond.

Experimental demonstration of underwater wireless optical OFDM communication system with a single SPAD receiver

Generally, only binary modulation formats, such as on–off keying (OOK) and pulse position modulation (PPM), can be detected by a single photon avalanche diode (SPAD). In this paper, we propose to use a single SPAD receiver to achieve underwater wireless optical communication (UWOC) with high-order modulation formats. The feasibility is theoretically analyzed, and firstly demonstrated in a proof-of-concept orthogonal frequency division multiplexing (OFDM) experiment. The proposed OFDM system using quadrature phase shift keying (QPSK) and 16 quadrature amplitude modulation (16-QAM) can work with less than 68 and 390 photons per symbol, and with receiver sensitivities below the forward error correction (FEC) limit as high as −84.5 dBm and −77.8 dBm, respectively. These extraordinarily sensitive results indicate that the proposed scheme is a promising solution to long-distance UWOC systems or internet of underwater things (IoUT).

Turbo DFE Assisted Time-Frequency Packing for Probabilistically Shaped Terabit Superchannels

We present a probabilistically shaped (PS) time-frequency-packing (TFP) wavelength-division multiplexing superchannel system employing higher order modulation (HoM) formats, with an objective to improve the spectral efficiency (SE). However, TFP systems suffer from inter-symbol interference (ISI) and/or inter-carrier interference (ICI). Additionally, the bandwidth limitations of the wavelength selective switches in the fiber link may cause severe ISI for the edge sub-channels (SCs) in a superchannel. Mitigation of such interferences is particularly challenging for HoM systems, since the implementation of the well-known turbo equalization schemes, such as the Bahl-Cocke-Jelinek-Raviv equalizer, is computationally challenging for larger constellations. In this paper, we investigate an expectation propagation based, computationally efficient, turbo decision feedback equalizer for ISI cancellation, in tandem with a parallel interference cancellation based ICI mitigation. By optimizing the parameters in the shaping and the packing dimensions, we show through our numerical results that the proposed PS-TFP superchannels enabling 1.8 Tbps data rates offer up to 1.05 dB packing gain over an unpacked system using the same modulation format, and a 1.15 dB shaping gain over an unshaped system that uses a lower modulation order to achieve the same SE.

A Performance Comparison Between Quantum Dash and Quantum Well Fabry-Pérot Lasers

We directly compare the performance of 1.55 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> Fabry-Pérot lasers using quantum well (QW) and quantum dash gain regions. Other than the gain medium the designs were identical, grown in the same growth system, and processed at the same time. The static laser performance (light-current and spectral) were similar for both gain materials but the intensity and phase noise characteristics of the dash based lasers were significantly better. This was attributed to the self mode-locking of the dash lasers that was not observed for the QW lasers. This reduction in noise allowed individual lasing lines from the Fabry-Pérot dash lasers to be used for data transmission using high order modulation schemes, with quadrature phase-shift keying (QPSK) demonstrated at a symbol rate of 32GBaud. This performance could not be achieved using the equivalent QW based laser.

New 2 2 Sigma Delta Modulators for Different Applications

This work presents the design of a new 2-2 programmable sigma delta modulator architecture, for different applications, this transformation design of the ΣΔ modulator low-pass, band-pass and high-pass or vice versa with loopbacks addition, which improved the linearity of the converter and reduced the quantization noise. In this work, the MASH structure enables the implementation of stable and high-order modulator. This makes low voltage and low power applications ideal. The simulation result for sigma delta modulator for biomedical applications exhibit a signal to noise ratio is 95 dB @ 250Hz bandwidth and a 75dB @ 200KHz ,85dB @1MHz for pass band modulator. The SNR is about 70dB for 5MHz bandwidth and for high pass application. This tool will allow a development contribution and characterize a system optimization set from the start while remaining at a high level of design that is suitable for electronic systems and models VHDL-AMS, RF, Biomedical.

Experimental investigation of VCSEL-based optical heterodyning with PAM 4 and envelop detection for 5G fronthaul systems

Vertical cavity surface-emitting lasers (VCSELs) are power-efficient optical sources for application in passive optical networks. Despite these sources having the potential of generating coherent high-frequency radio frequency signal, their application for high-order amplitude modulation formats is yet to be demonstrated experimentally. In this work, for the first time, we experimentally demonstrate a four-level pulse amplitude modulation (4-PAM) format on a photonically generated RF carrier signal using optical heterodyning of two independent VCSELs. Two low-power VCSELs were combined at an optical coupler and allowed to beat a PIN photodiode to generate a 10-GHz RF carrier. In the first demonstration, an 8.5 Gbps data signal was modulated on the photonically generated 10 GHz RF carrier. In the second demonstration, a 17-Gbps PAM-4 data signal was externally modulated onto the same VCSEL carrier, ultimately doubling the network bit rate. A simple digital signal processing (DSP) receiver was used as an alternative to costly receiver hardware to decode the transmitted PAM-4 data signal. A 24-km fiber transmission penalty of 7-dB was recorded when PAM-4 signal was photonically generated and transmitted. The penalty introduced by moving from binary transmission to PM-4 transmission was recorded to be 3-dB.

Combining neural networks for modulation recognition

This paper proposes a combined Convolutional Neural Network (CNN) scheme appropriate for automatic modulation recognition. The suggested network includes a deep network involving multiscale convolutions with an attention module for recognizing 24 modulation modes and a shallow one network for recognizing two modulation modes, aiming to reduce the misjudgment caused by the deeper network. We evaluate our proposed network on the DeepSig dataset achieving an accuracy of 98.7% that exceeds the performance of current state-of-the-art (SOTA) methods exploiting this dataset. The network achieved almost 100% accuracy on modulation modes of the order less than or equal to 64 and under high SNR. The accuracy attained by our method on high-order modulation modes exceeds the one of ResNet, which currently is the SOTA method.

Systematic Polar Coded Modulation for Informed Receivers

The problem of coding for informed receivers (IR) is considered, where a transmitter multicasts a bunch of messages to its associated receivers, each of which already has a subset of messages as side information. Which receiver has what side information is unknown to the transmitter. A family of polar codes for IR was proposed for binary-input channels in (Huang and Shieh, 2018), which was shown to provide excellent side information gain regardless of side information configuration and content. A trial extension of this scheme to high-order modulations, however, was unsatisfactory. In this paper, two families of systematic polar coded modulations for IR are proposed. In the first family, by building a connection between the message bits and modulated symbols under systematic polar codes, we leverage the bit assignments and labeling techniques such that receiver side information can be directly translated to a minimum distance gain. In the second family, a permutation operation is added before modulation such that the message bits can be properly reordered to further advance and balance the gains among different side information configurations. Simulations show that the proposed schemes provide large and balanced side information gains and significantly outperform the system directly adapted from (Huang and Shieh, 2018) onto high-order modulations.

Algorithm Parameters Selection Method With Deep Learning for EP MIMO Detector

Expectation Propagation (EP)-based Multiple-Input Multiple-Output (MIMO) detector achieves exceptional performance in high-dimensional systems with high-order modulations and flexible antenna configurations. However, based on our studies, the EP MIMO detector cannot achieve superior performance due to the empirical parameter selection, including initial variance and damping factors. According to the influence of the moment matching and parameter selection on the performance of the EP MIMO detector, we propose a modified EP MIMO detector (MEPD). To obtain the initial variance and damping factors which lead to better performance, we adopt a deep learning scheme, the iterative process of MEPD is unfolded to establish MEPNet for parameters training. The simulation results show that MEPD with off-line trained parameters outperforms the original one in various MIMO scenarios. Besides, the proposed MEPD with deep learning parameters selection is more robust than EPD in practical scenarios.

Partially Information Coupled Bit-Interleaved Polar Coded Modulation

In this paper, we propose partially information coupled bit-interleaved polar coded modulation (PIC-BIPCM), which is a class of spatially coupled polar coding schemes designed for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{Q}$ </tex-math></inline-formula> -ary modulations. Specifically, we consider PIC-BIPCM schemes respectively constructed with three BIPCM schemes: direct BIPCM, punctured BIPCM, and multi-kernel BIPCM. We analyze the error performance of the proposed PIC-BIPCM over the binary erasure channel (BEC) via density evolution. With the analysis as a guideline, we jointly design the positions of coupled bits and the modulation bit-mapper by taking into account the partial polarization of finite length polar codes as well as the unequal error protection of high order modulations. Simulation results demonstrate significant performance improvement of the proposed PIC-BIPCM over the uncoupled BIPCM on both BEC and AWGN channels.