In this paper, the wavelength division multiplexed (WDM) fiber optic channel is considered. It is shown that for ideal distributed Raman amplification (IDRA), the Wiener process model is suitable for the non-linear phase noise due to cross phase modulation from neighboring channels. Based on this model, a phase noise tracking algorithm is presented. We approximate the distribution of the phase noise at each time instant by a mixture of Tikhonov distributions, and derive a closed form expression for the posterior probabilities of the input symbols. This reduces the complexity dramatically compared to previous trellis-based approaches, which require numerical integration. Further, the proposed method performs very well in low-to-moderate signal-to-noise ratio (SNR), where standard decision directed (DD) methods, especially for high-order modulation, fail. The proposed algorithm does not rely on averaging, and therefore does not experience high error floors at high SNR in severe phase noise scenarios. The laser linewidth (LLW) tolerance is thereby increased for the entire SNR region compared to previous DD methods. In IDRA WDM links, the algorithm is shown to effectively combat the combined effect of both laser phase noise and non-linear phase noise, which cannot be neglected in such scenarios. In a more practical lumped amplification scheme, we show near-optimal performance for 16 QAM, 64 QAM, and 256 QAM with LLW up to 100 kHz, and reasonable performance for LLW of 1 MHz for 16 QAM and 64 QAM, at the moderate received SNR region. The performance in these cases is close to the information rate achieved by the above mentioned trellis processing.
Bibliographical note(c) 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
- Cross phase modulation
- optical fiber communication
- Phase noise
- Wiener process