Four-dimensional Modulation Formats Research Articles

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

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.

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.

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.

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.

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.