Four-dimensional Modulation Research Articles

Probabilistic Shaping Four-Dimensional Modulation With Soft Decision for Self-Homodyne Coherent Detection Systems

Probabilistic Shaping Four-Dimensional Modulation With Soft Decision for Self-Homodyne Coherent Detection Systems

Geometrically Shaped Four-Dimensional Modulation Formats for 5–7 Bits/Symbol Designed by Autoencoder

Geometrically Shaped Four-Dimensional Modulation Formats for 5–7 Bits/Symbol Designed by Autoencoder

Nonlinearity-Tolerant Probabilistically-Shaped Four-Dimensional Modulation at Spectral Efficiency of 9 Bits/Four-Dimensional Symbol

Network traffic between data centers has grown rapidly in recent years. Therefore, an optical modulation format with high spectral efficiency is desired in inter-data center links at data rates of more than 400 Gb/s in each wavelength. In order to further improve the transmission performance in single-span inter-data center links, a nonlinearity-tolerant probabilistically-shaped 4D modulation format with a spectral efficiency of 9 bits/4D symbol is proposed. The proposed modulation format fills the gap between polarization-multiplexed 16- and 32-ary quadrature-amplitude modulation (PM-16QAM and PM-32QAM). In numerical simulations, we compare our proposed modulation format with probability-amplitude-shaped 64QAM (PAS-64QAM) and 512-set-partitioned 32QAM (512SP-32QAM) at a spectral efficiency of 9 bits/4D symbol in a single-span transmission link. The simulation results indicate that the proposed modulation format shows better linear and nonlinear performances than a 512SP-32QAM format. Compared with PAS-64QAM format, the proposed modulation format can provide similar transmission performance with improved fiber nonlinear tolerance.

Geometrically shaped multi-dimensional modulation formats designed by deep learning

Geometrically shaped multi-dimensional modulation formats are designed by a bit-wise autoencoder (AE), which is one of the deep learning applications. The optimized four-dimensional (4-D) modulation constellation diagrams in two-dimensional (2-D) projection have highly unique symmetrical constellations with clever labeling. In addition, the numerically evaluated BER performances show that the receiver sensitivities of the optimally shaped multi-dimensional modulation format are equivalent to or better than those of the conventional 4-D and 2-D formats with the same transmission capacity.

Quadrant Multiplexing-based Geometrically Shaped Four-Dimensional Modulation Format for Polarization Multiplexed Coherent Optical Communication System

We present in detail the recently proposed novel geometric shaping four-dimensional (GS-4D) modulation format based on quadrant multiplexing and evaluate the signal from various aspects. GS-4D achieves a generalized mutual information (GMI) gain of 1.6 bits/4D-sym compared to polarization-multiplexed 16-ary quadrature amplitude modulation (PM-16QAM) at low signal-to-noise ratio (SNR) regions. Set partitioning (SP) at the expense of one bit of spectral efficiency is proposed to exponentially reduce the amount of constellation points and increase the Euclidean distance. For fiber channels influenced by additive white Gaussian noise (AWGN) and phase noise, a further GS scheme with binary labeling is designed. The scheme takes bit error ratio (BER) as fitness, preserves the feature of this format while using mirror symmetry to reduce the complexity, and is implemented by an improved particle swarm optimization (PSO) algorithm. Results demonstrate that the proposed scheme has high optical SNR tolerance and low BER performance. Compared with the PM-16QAM, the GS-4D, GS-4D with SP and GS-4D with SP-PSO can provide 3.6 dB, 5.6 dB and 6.6 dB optical SNR gain, respectively. With the equal distance of transmission, the BER of GS-4D is decreased by around one order of magnitude compared with PM-16QAM, the BER of GS-4D with SP is lowered by around two orders of magnitude, and the BER of GS-4D with SP-PSO is reduced by around three orders of magnitude.

Geometrically-Shaped Multi-Dimensional Modulation Formats in Coherent Optical Transmission Systems

Shaping modulation formats in multi-dimensional (MD) space is an effective approach to harvest spectral efficiency gains in both the additive white Gaussian noise (AWGN) channel and the optical fiber channel. In the first part of this paper, existing MD geometrically-shaped modulations for fiber optical communications are reviewed. It is shown that large gains can be obtained by exploiting correlation in the dimensions or/and by increasing the cardinality of the modulation format. Practical limitations and challenges are also discussed together with efficient solutions. In the second part, we extend the recently proposed four-dimensional (4D) modulation format family based on the constraint of orthant-symmetry to high spectrum efficiencies up to 10 b/4D-sym by maximizing generalized mutual information for AWGN channel. Reach increases of up to 25% for a multi-span optical fiber transmission system are reported. Lastly, with the help of a recently introduced nonlinear interference (NLI) model, an optimization for designing nonlinear-tolerant 4D modulation formats is introduced for a single-span optical fiber system. Simulation results show that the proposed NLI model-based 4D modulation format could increase the effective SNRs by 0.25 dB with respect to the AWGN channel-optimal 4D modulation format.

Extending Fibre Nonlinear Interference Power Modelling to Account for General Dual-Polarisation 4D Modulation Formats.

In optical communications, four-dimensional (4D) modulation formats encode information onto the quadrature components of two arbitrary orthogonal states of polarisation of the optical field. Many analytical models available in the optical communication literature allow, within a first-order perturbation framework, the computation of the average power of the nonlinear interference (NLI) accumulated in coherent fibre-optic transmission systems. However, all such models only operate under the assumption of transmitted polarisation-multiplexed two-dimensional (PM-2D) modulation formats, which only represent a limited subset of the possible dual-polarisation 4D (DP-4D) formats. Namely, only those where data transmitted on each polarisation channel are mutually independent and identically distributed. This paper presents a step-by-step mathematical derivation of the extension of existing NLI models to the class of arbitrary DP-4D modulation formats. In particular, the methodology adopted follows the one of the popular enhanced Gaussian noise model, albeit dropping most assumptions on the geometry and statistic of the transmitted 4D modulation format. The resulting expressions show that, whilst in the PM-2D case the NLI power depends only on different statistical high-order moments of each polarisation component, for a general DP-4D constellation, several other cross-polarisation correlations also need to be taken into account.

Orthogonally Polarized Dual-Channel Directional Modulation Based on Crossed-Dipole Arrays

Directional modulation (DM) as a physical layer security technique has been studied based on the traditional antenna arrays; however, in most of the designs, only one signal is transmitted at one carrier frequency. In this paper, signal polarization information is exploited, and a new DM scheme is designed, which can transmit a pair of orthogonally polarized signals to the same direction at the same frequency simultaneously, resulting in doubled channel capacity. These two signals can also be considered as one composite signal using a four-dimensional (4-D) modulation scheme across the two polarization diversity channels. Moreover, compressive sensing (CS)-based formulations for designing sparse crossed-dipole arrays in this context are proposed to exploit the degrees of freedom in the spatial domain for further improved performance, as demonstrated by various design examples.

A Novel Four-Dimensional Modulation Format Based on Subset Selection

Coherent optical transmission systems have a four-dimensional (4-D) signal space (two quadratures in two polarizations), which can be used to create 4-D modulation formats that have better sensitivity than traditional two-dimensional modulation signal. In this paper, we propose an interesting four-dimensional modulation format based on subset selection for coherent optical fiber communications. We compare the proposed modulation format to the polarization multiplexed quadrature amplitude modulation(PM-QAM) and the set-partitioning M polarization-multiplexed QAM (M-SP-QAM). Simulation results show that for the same spectral efficiency, the proposed modulation format can get SNR gains of up to1dB compared with PM-MQAMs at 7% forward exchange control (FEC) threshold at a BER of 1e-3 in back-to-back system. After 800 km transmission distance, the signal-to-noise ratio (SNR) gain is 1.05dB. It is also shown that the mapping process of the proposed modulation format has lower latency and occupies less memory units compared with the commonly used look-up-tables mapping method.

Constellation basis decomposition based blind equalization processing of four-dimensional modulation

Blind equalization processing of four-dimensional (4D) signal is a key factor to 4D modulation based system, in order to solve this problem, we propose “constellation basis” decomposition based blind equalization processing scheme for (4D) modulation format. A 4D modulation based optical OFDM system is simulated to verify the performance of “constellation basis” decomposition scheme. Compared to the data aided equalization with least mean square algorithm, the proposed scheme shows a better performance in the case of 4D modulation format. And it is also demonstrated that the proposed scheme can simultaneously realize blind equalization compensation for system or channel impairments including chromatic dispersion, phase noise, I/Q imbalance, etc. Meanwhile, it allows for flexible spectrum efficiency transmission.

Nonlinearity-Tolerant Four-Dimensional 2A8PSK Family for 5–7 Bits/Symbol Spectral Efficiency

We describe in detail the recently proposed four-dimensional modulation format family based on 2-ary amplitude 8-ary phase-shift keying (2A8PSK), supporting spectral efficiencies of 5, 6, and 7 bits/symbol. These formats nicely fill the spectral efficiency gap between the dual-polarization (DP) quadrature PSK (QPSK) and DP 16-ary quadrature-amplitude modulation (16QAM), with excellent linear and nonlinear performance. Since these modulation formats just use different parity bit expressions in the same constellation, similar digital signal processing can be seamlessly used for different spectral efficiency. A series of nonlinear transmission simulation results shows that this modulation format family outperforms the conventional modulation formats at the corresponding spectral efficiency. We also investigate the adaptive equalizer for these modulation formats.

Four-Dimensional Modulation and Stokes Direct Detection of Polarization Division Multiplexed Intensities, Inter Polarization Phase and Inter Polarization Differential Phase

We propose and experimentally demonstrate modulation and Stokes space direct-detection (DD) of four orthogonal dimensions or degrees of freedom (DOF) of a single laser being the intensity on two orthogonal polarizations, the inter-polarization phase and the inter-polarization differential phase. At the transmitter, a dual-polarization in-phase quadrature-phase (DP-IQ) modulator driven by a 4-channel digital-to-analog converter is employed to imprint the transmitted data onto the aforementioned four DOF. Transmitted symbols for each polarization are drawn from multi-ring/multi-phase constellations, e.g., 2-ring/4-ary phase shift keying (PSK) or 2-ring/8PSK, resulting in a polarization division multiplexed (PDM) format with intensity, inter-polarization phase, and inter-polarization differential phase modulation (PDM-IM-IPM-IDPM). At the receiver, a novel DD front-end 1 1 A direct-detection front-end refers to a family of receivers that employ a self-beating mechanism in which the received signal beats with itself or its polarization tributaries beat with themselves. Unlike a coherent front-end, a direct-detection front-end does not incorporate a local oscillator (LO) laser.

Secure coherent optical multi-carrier system with four-dimensional modulation space and Stokes vector scrambling.

A secure enhanced coherent optical multi-carrier system based on Stokes vector scrambling is proposed and experimentally demonstrated. The optical signal with four-dimensional (4D) modulation space has been scrambled intra- and inter-subcarriers, where a multi-layer logistic map is adopted as the chaotic model. An experiment with 61.71-Gb/s encrypted multi-carrier signal is successfully demonstrated with the proposed method. The results indicate a promising solution for the physical secure optical communication.

Multi-dimensional permutation-modulation format for coherent optical communications

We introduce the multi-dimensional permutation-modulation format in coherent optical communication systems and analyze its performance, focusing on the power efficiency and the spectral efficiency. In the case of four-dimensional (4D) modulation, the polarization-switched quadrature phase-shift keying (PS-QPSK) modulation format and the polarization quadrature-amplitude modulation (POL-QAM) format can be classified into the permutation modulation format. Other than these well-known modulation formats, we find novel modulation formats trading-off between the power efficiency and the spectral efficiency. With the increase in the dimension, the spectral efficiency can more closely approach the channel capacity predicted from the Shannon's theory. We verify these theoretical characteristics through computer simulations of the symbol-error rate (SER) and bit-error rate (BER) performances. For example, the newly-found eight-dimensional (8D) permutation-modulation format can improve the spectral efficiency up to 2.75 bit/s/Hz/pol/channel, while the power penalty against QPSK is about 1 dB at BER=10(-3).

Bandwidth-Variable Transceivers based on Four-Dimensional Modulation Formats

In this invited contribution, we discuss technology options for bandwidth-variable transceivers which are key components for the realization of flexible software-defined optical networking. Bandwidth-variable transceivers enable the software-controlled adaptation of physical layer parameters such as transmitted bit rate, spectral efficiency and transparent reach according to the traffic demands at hand. In particular, we focus on recent advances in four-dimensional modulation formats and in modulation format transparent data-aided digital signal processing. It is argued that four-dimensional modulation formats present an attractive complement to conventional polarization-multiplexed formats in the context of bandwidth-variable transceivers, where they enable a smooth transition with respect to spectral efficiency while requiring marginal additional hardware effort. Results of numerical simulations and experiments supporting this statement are presented. For the cost-efficient hardware implementation of bandwidth-variable transceivers supporting several polarization-multiplexed and four-dimensional modulation formats, digital signal processing algorithms are required which operate format transparent and consume little hardware resources. We discuss data-aided signal processing as one possible option, in particular with respect to carrier frequency recovery and channel estimation in combination with frequency domain equalization.

Modulation network coding

In this study, we propose a four-dimensional modulation, referred to as modulation network coding (MNC), to address the problem of decoding a signal from multiple source node transmissions in mobile fast fading channels. The MNC scheme judiciously mixes a two-dimensional (2D) pilot symbol with a 2D information symbol, and makes use of a π/4 rotated M-pulse-amplitude modulation (PAM) constellation to guaranty an effective decoding of all the interfering symbols even in the case of a smaller channel Doppler spread compared with the period of the MNC symbol. In addition, because the MNC scheme makes use of an additional dimension introduced through orthogonal pulse waveform, the use of the pilot symbols does not reduce the effective information rate. The analytical and simulation results show that it is possible to achieve a low symbol error probability with a good signal-to-noise ratio when controlling a few parameters impacting the performance of the system such as the synchronisation in time and in frequency of the source nodes.

A comparison of modulation formats for passive optical networks

The sensitivity of the four-dimensional modulation format, polarization-switched quadrature phase shift keying (PS-QPSK), is compared with polarization division multiplexed QPSK (PDM-QPSK), binary phase shift keying (PDM-BPSK) and 8-ary quadrature amplitude modulation (PDM-8QAM) at a constant bitrate (12.5 Gbit/s) using a preamplified signal to improve receiver sensitivity. The sensitivity without preamplification is also obtained. PS-QPSK is found to maintain a sensitivity advantage over the reference formats in line with theory with an absolute sensitivity of -52.7 dBm (4.2 photons/bit), assuming hard decision FEC.

Cutoff rates for coordinate interleaved QAM over Rayleigh fading channels

Cutoff rates for (perfect) coordinate interleaving over flat Rayleigh fading channels are computed for some representative two-dimensional (2-D) and four-dimensional (4-D) quadrature amplitude modulation (QAM) schemes and compared to the standard symbol interleaved approaches. It is shown that for optimized coordinate interleaving [i.e., using optimum rotation parameters that maximize the cutoff rate for a given signal-to-noise ratio (SNR)], coding gains can be achieved vis-a-vis symbol interleaving that increases with the dimensionality of the signal constellation. Perfect coherent detection, as well as perfect channel state information are assumed.

Digital transmission with coherent four-dimensional modulation

This paper examines codes for four-dimensional (4-D) modulation and their performance for digital transmission. The signals are defined by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> points inside a sphere in four-dimensional Euclidian space. Three classes of 4-D codes are presented, and an algorithm is given which yields good 4-D codes of any length. Bounds on symbol error probability are plotted versus symbol-energy-to-noise-density ratio. The performance is shown to exceed that of amplitude- and-phase modulation in two independent two-dimensional channels.