Geometric shaping optimization of 64-APSK constellation in discrete nonlinear frequency division multiplexing systems

We experimentally demonstrated a geometric shaped (GS) 64-ary amplitude phase shift keying (64-APSK) eigenvalue transmission. The signal is modulated on the scatter coefficient of a single eigenvalue and linear minimum mean square error (LMMSE) estimator is used to reduce the noise. The channel response is estimated by transmitting a normally distributed 64-APSK constellation through a communication link. Based on the polar coordinates distribution of the received constellation, the diameter distributions for each circle can be obtained so that circles with larger noise can obtain larger judgment width. After optimization, the experimental results show that the Q-factor gain is 1.13 dB under 22 dB received optical signal to noise ratio (OSNR) configuration and 0.88 dB after 900 km transmission compared with normally distributed APSK configuration.