Trellis Shaping for Fiber Nonlinearity Mitigation in Coherent Optical OFDM Systems

In this article, trellis shaping technique is numerically and experimentally investigated to improve the performance of optical orthogonal frequency division multiplexing (OFDM) signal. Different from other constellation shaping techniques, trellis shaping can be designed to reduce the correlation value of OFDM data sequence and average power simultaneously in one OFDM symbol. It means that optical OFDM signals generated by trellis shaping can improve the performance under both linear and nonlinear channels. For comparison with trellis shaping technique, we also consider optimal Maxwell-Boltzmann (MB) shaping and uniform signaling techniques at spectral efficiency (SE) of 10 and 14 bits/4D-sym. Numerical simulations show that trellis shaping can provide certain shaping gain over uniform signaling under linear additive white Gaussian noise (AWGN) channel. The fiber transmission results indicate that OFDM signals with trellis shaping have higher effective signal-to-noise ratio (SNR) than those with MB shaping and uniform signaling. It means that trellis shaping technique has the ability to mitigate the fiber nonlinear noise. Considering both linear and nonlinear noise in the fiber link, trellis shaping can extend the transmission distance by ~ 110 km and ~ 200 km over MB shaping and uniform signaling at SE of 10 bits/4D-sym. At SE of 14 bits/4D-sym, trellis shaping provides similar performance as MB shaping but ~ 120-km extension reach in comparison with uniform signaling. The performances of OFDM signals with trellis shaping, MB shaping and uniform signaling are also experimentally investigated in a four-channel wavelength division multiplexing (WDM) fiber transmission systems. The experimental results show that trellis shaping can also mitigate the nonlinear distortions induced by the clipping effects at the transmitter side. Compared with MB shaping, trellis shaping extends the transmission reach by ~ 240 km and ~ 90 km at SE of 10 and 14 bits/4D-sym, respectively.