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 $\sim$ 110 km and $\sim$ 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 $\sim$ 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 $\sim$ 240 km and $\sim$ 90 km at SE of 10 and 14 bits/4D-sym, respectively.

中文翻译：

---

相干整形用于相干光OFDM系统中的光纤非线性缓解

在本文中，对网格整形技术进行了数值和实验研究，以提高光正交频分复用（OFDM）信号的性能。与其他星座整形技术不同，可以设计网格整形以同时减小一个OFDM符号中OFDM数据序列的相关值和平均功率。这意味着通过网格整形生成的光OFDM信号可以提高线性和非线性信道下的性能。为了与网格整形技术进行比较，我们还考虑了10和14位/ 4D符号的频谱效率（SE）下的最佳Maxwell–Boltzmann（MB）整形和统一信令技术。数值模拟表明，在线性加性高斯白噪声（AWGN）信道下，网格整形可以在均匀信令上提供一定的整形增益。光纤传输结果表明，具有网格整形的OFDM信号具有比具有MB整形和均匀信令的OFDM更高的有效信噪比（SNR）。这意味着网格整形技术具有减轻光纤非线性噪声的能力。考虑到光纤链路中的线性和非线性噪声，网格整形可以通过以下方式扩展传输距离：$ \ sim $ 110公里和 $ \ sim $ 在10比特/ 4D符号的SE上通过MB整形和统一信令传输200 km。SE为14位/ 4D符号时，网格整形提供的性能与MB整形相似，但$ \ sim $ 与统一信令相比，扩展范围达120公里。在四通道波分复用（WDM）光纤传输系统中，还通过实验研究了具有网格整形，MB整形和均匀信令的OFDM信号的性能。实验结果表明，网格整形还可以减轻发射机侧的削波效应引起的非线性失真。与MB整形相比，网格整形将传输范围扩大了$ \ sim $ 240公里和 $ \ sim $ SE分别为10 km和14 bit / 4D-sym时为90 km。