
Learning for Perturbation-Based Fiber Nonlinearity Compensation
Shenghang Luo(1), Sunish Kumar Orappanpara Soman(2), Lutz Lampe(1), Jeebak Mitra(3),
and Chuandong Li(3)
(1) Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver,
BC V6T 1Z4, Canada, shenghang@ece.ubc.ca,lampe@ece.ubc.ca
(2) School of Engineering, Ulster University, Newtownabbey, BT37 0QB, United Kingdom,
s.orappanpara soman@ulster.ac.uk
(3) Huawei Technologies Canada, Ottawa, ON K2K 3J1, Canada, jeebak.mitra@huawei.com,
chuandong.li@huawei.com
Abstract Several machine learning inspired methods for perturbation-based fiber nonlinearity (PB-
NLC) compensation have been presented in recent literature. We critically revisit acclaimed benefits of
those over non-learned methods. Numerical results suggest that learned linear processing of perturba-
tion triplets of PB-NLC is preferable over feedforward neural-network solutions. ©2022 The Author(s)
Introduction
The Kerr-induced fiber nonlinearity puts a cap
on the maximum achievable information capac-
ity in long-haul coherent optical transmission sys-
tems[1]–[3]. Over the last few years, the advances
in deep learning algorithms initiated the develop-
ment of several system-agnostic machine learn-
ing (ML) approaches to compensate for the fiber
Kerr nonlinearity effects. On this ground, learned
versions of the perturbation theory-based fiber
nonlinearity compensation (PB-NLC) technique
have widely been investigated and demonstrated
its effectiveness in estimating the complex nonlin-
ear distortion field with the perturbation triplets as
the input features[4]–[10].
Since the overall computational complexity of
the PB-NLC techniques has often been consid-
ered a limitation for practical implementation, one
direction of learned PB-NLC has been to lower
the complexity by, for example, reducing the input
feature vector size and pruning for neural network
(NN) based PB-NLC[5],[6],[9]. On the other hand,
the conventional (CONV) PB-NLC technique has
also notably been optimized in terms of nonlin-
earity compensation capability and overall com-
putational complexity. Nonlinearity compensation
performance improvements have been achieved
by using realistic pulse shapes and the inclu-
sion of the power profile in the coefficient com-
putation[11],[12]. Significant complexity reductions
have been obtained by coefficient quantization[13].
Furthermore, the introduction of a cyclic buffer
(CB) in the triplet computation stage permits fur-
ther complexity savings for both learned and non-
learned PB-NLC[10].
In this paper, we revisit the acclaimed
performance benefits of learned PB-NLC ap-
proaches[4],[5] over their non-learned counter-
parts. For this, we carefully evaluate the overall
computational complexity of existing learned and
non-learned PB-NLC techniques, considering the
available advancements for all of them. We note
that such a comparison has not been done in the
references proposing learned PB-NLC. As one
important finding, our results show that feedfor-
ward NN (FNN)-based PB-NLC has hardly ad-
vantages over non-learned PB-NLC. On the other
hand, the approach of learning PB-NLC coeffi-
cients from a least-squares (LS) optimization is
shown to outperform the best non-learned PB-
NLC variant and to provide the best performance-
complexity trade-off of all tested methods.
PB-NLC Techniques
In CONV PB-NLC, the nonlinear distortion field
is numerically calculated and subtracted from the
symbol of interest. However, the truncation of the
perturbation approximation at first-order in PB-
NLC leads to a power overestimation problem
and degrades the NLC performance. This can
be overcome using an additive-multiplicative PB-
NLC (CONV-AM PB-NLC) technique[15].
ML-based solutions utilizing the existing PB-
NLC distortion model have been investigated
in several literatures. In[4],[5], fully connected
FNNs with perturbation triplets as the input fea-
tures have been proposed to estimate the non-
linear distortion field instead of numerically com-
puting it. This technique is referred to as
FNN PB-NLC. NNs can also be used to predict
the distortions in the above-mentioned additive-
multiplicative model, which we refer to as FNN-
arXiv:2210.03440v1 [eess.SP] 7 Oct 2022