Low-Complexity Tracking of Laser and Nonlinear Phase Noise in WDM Optical Fiber Systems

Abstract

Abstract-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-tomoderate 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 16QAM, 64QAM and 256QAM with LLW up to 100kHz, and reasonable performance for LLW of 1MHz for 16QAM and 64QAM, at the moderate received SNR region. The performance in these cases is close to the information rate achieved by the above mentioned trellis processing.

Nonlinear Phase Noise Compensation in Experimental WDM Systems With 256QAM

“…We note that the BPS and the TMM receiver take advantage of the QPSK pilot symbols: the former by using the actual transmitted symbol when estimating the cost function in Eq. (3), and the latter by exploiting the fact that the prior distribution p(x k ) = 1 for the true symbol and p(x k ) = 0 for all other symbols at the pilot instances (details are given in [13]). …”

“…It has been shown that this model can also be used with reasonable accuracy for the NLPN in WDM systems [13], [14]. Since the NLPN and laser PN can be considered independent, their variances add-up and the system from the transmitter before pulse shaping to the receiver after equalization and before PN compensation can be modeled as…”

“…Under this model, well-developed techniques can be used to compensate the PN. In this work, we focus on the probabilistic method proposed in [13], and also the more popular BPS on a sliding window technique [15].…”

“…The last receiver we study is the algorithm from [13], which assumes a Wiener process for the NLPN and is tailored to estimate PN in such environments. The algorithm requires the values of ∆ 2 and the AWGN statistics σ 2 x and µ x .…”

“…The belief propagation algorithm is then applied, which is a popular method for estimating densities on a factor graph by message passing techniques (further details are given in [13]). Since the messages in the graph are modeled as mixtures of Tikhonov distributions, this receiver is referred to as the Tikhonov mixture model (TMM).…”