Histogram Based Clustering for Nonlinear Compensation in Long Reach Coherent Passive Optical Networks

Abstract

In order to meet the increasing capacity requirements, network operators are extending their optical infrastructure closer to the end-user while making more efficient use of the resources. In this context, long reach passive optical networks (LR-PONs) are attracting increasing attention.Coherent LR-PONs based on high speed digital signal processors represent a high potential alternative because, alongside with the inherent mixing gain and the possibility of amplitude and phase diversity formats, they pave the way to compensate linear impairments in a more efficient way than in traditional direct detection systems. The performance of coherent LR-PONs is then limited by the combined effect of noise and nonlinear distortion. The noise is particularly critical in single channel systems where, in addition to the the elevated fibre loss, the splitting losses should be considered. In such systems, Kerr induced self-phase modulation emerges as the main limitation to the maximum capacity. In this work, we propose a novel clustering algorithm, denominated histogram based clustering (HBC), that employs the spatial density of the points of a 2D histogram to identify the borders of high density areas to classify nonlinearly distorted noisy constellations. Simulation results reveal that for a 100 km long LR-PON with a 1:64 splitting ratio, at optimum power levels, HBC presents a Q-factor 0.57 dB higher than maximum likelihood and 0.21 dB higher than k-means. In terms of nonlinear tolerance, at a BER of 2×10 − 3 , our method achieves a gain of ∼2.5 dB and ∼1.25 dB over maximum likelihood and k-means, respectively. Numerical results also show that the proposed method can operate over blocks as small as 2500 symbols.

K-means clustering for mitigation of nonlinear phase noise in digital coherent optical systems using 16-QAM modulation format

“…Alternatively, some unsupervised classification algorithms, also known as clustering, have been studied. For example, in [19] and [20] expectation maximization and histogram-based-clustering are employed, respectively. Due to its low complexity in the test stage, K-means is another clustering algorithm that has been studied to compensate nonlinear distortion [21] [22].…”

Mitigation of nonlinear phase noise in coherent 16-QAM long-reach PONs by K-nearest neighbors-based classification

“…Machine learning algorithms can be roughly divided into supervised and unsupervised [13]. Unsupervised algorithms include clustering, as in [14] and [15], in which constellation symbols are classified utilizing histogram based clustering and expectation maximization, respectively. On the other hand, supervised algorithms require a training set in which both the data and their labels are previously known by the receiver.…”

Fiber-induced nonlinear limitation in 400-Gbps single-channel coherent optical interconnects

“…In this scenario, fiber-induced impairments can be considered as an upperbound limit to the transmission performance. In particular, the combination of the Kerr nonlinear effect, the chromatic dispersion (CD), and the transmission loss will ultimately limit the maximum achievable link range [8]. Given the high bandwidth and the multilevel nature of the transmitted signal, alongside with the adoption of polarization multiplexing, make difficult to predict and quantify the complex interplay among the different impairments.…”