Abstract

Kramers-Kronig (KK) receiver shows strong feasibility since the phase can be extracted from the detected intensity through the Hilbert transform (HT). To reduce the complexity and make the HT more suitable for the practical KK system, the HT can be approximated as the finite impulse response (FIR) filter, i.e., the HT-FIR filter. However, the finite Fourier series expansion of the HT-FIR filter suffers from oscillations around the discontinuities and further results in an unsatisfactory in-band flatness, which is the so-called Gibbs phenomenon. In the experiment and the simulation, we found that the performance of the KK system using the HT-FIR filter is strongly impaired due to the Gibbs phenomenon, by the roll-off factor of the shaping filter, frequency gap between the direct-current (DC) component and one edge of the signal spectrum, carrier-to-signal power ratio (CSPR), tap number of the HT-FIR filter, and the digital upsampling rate. We have systematically investigated the practical KK phase retrieval performance and the computational complexity considering the Gibbs phenomenon due to the adoption of the HT-FIR filter, rather than the HT used in the previous works without the Gibbs phenomenon. We conclude that there is an optimal upsampling rate when the HT-FIR filter is used, and the optimal upsampling rate is closely related to the five aspects mentioned above. We have carried out a transmission experiment using a 112-Gbit/s 16-QAM system over 1920-km with a Raman fiber amplifier to investigate the limit transmission performance of the practical KK receiver. The experimental results show that by using the 9-tap HT-FIR filter with a digital upsampling rate of 84-GHz (3-sps), the signals can be transmitted the same distance as the HT, up to 1440-km with a bit error ratio (BER) below the 20% soft-decision forward error correction threshold.

Investigation of the low-complexity Hilbert FIR filter enhanced 112-Gbit/s SSB 16-QAM transmission with parallelized Kramers-Kronig reception over 1440-km SSMF

Yuyang Liu, Yan Li, Jingwei Song, Ming Luo, Zhixue He, Chao Yang, Jianxin Lv, Jifang Qiu, Xiaobin Hong, Hongxiang Guo, and Jian Wu
Opt. Express 29(23) 38796-38810 (2021)

Impact of resampling interpolation FIR filter in the practical Kramers-Kronig receiver

Yuyang Liu, Anxu Zhang, Lipeng Feng, Kai Lv, Hao Liu, Guangnan Su, Xia Sheng, Yadong Gong, Xiaoli Huo, Junjie Li, Chengliang Zhang, Yan Li, and Jian Wu
Opt. Express 31(8) 13455-13471 (2023)

Transmission of a 112-Gbit/s 16-QAM over a 1440-km SSMF with parallel Kramers-Kronig receivers enabled by an overlap approach and bandwidth compensation

Yuyang Liu, Yan Li, Jingwei Song, Lei Yue, Honghang Zhou, Ming Luo, Zhixue He, Jifang Qiu, Yong Zuo, Wei Li, Xiaobin Hong, Hongxiang Guo, and Jian Wu
Opt. Express 29(6) 8117-8129 (2021)

Optimizing DC restoration in Kramers-Kronig optical single-sideband receivers

Tianyu Wang, Bill Corcoran, and Arthur Lowery
Opt. Express 30(2) 2825-2835 (2022)

Kramers-Kronig receiver operable without digital upsampling

Tianwai Bo and Hoon Kim
Opt. Express 26(11) 13810-13818 (2018)