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

Abstract

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.