1
PIECEWISE LINEAR EQUALIZER FOR 56 GBIT/S
PAM-4 SIGNAL TRANSMISSION USING DML WITH
LARGE ADIABATIC CHIRP
Yan Fu
1,2
, Deming Kong
2
, Haiyun Xin
1,2
, Shi Jia
2
, Kuo Zhang
1
, Meihua Bi
3
,
Weisheng Hu
1
, Hao Hu
2*
1
State Key lab of Advanced Optical Communication Systems and Networks,
Shanghai Jiao Tong University, Shanghai, China
2
DTU Fotonik, Technical University of Denmark, Kgs. Lyngby, Denmark
3
School of Communication Engineering, Hangzhou Dianzi University, Hangzhou, Zhejiang, China
*huhao@fotonik.dtu.dk
Keywords: LINEAR EQUALIZER, DIRECTLY-MODULATED LASER, PULSE-AMPLITUDE
MODULATION, DIRECT DETECTION, ADIABATIC CHIRP
Abstract
Computationally efficient piecewise linear (PWL) equalizer is, for the first time, proposed to compensate amplitude-dependent
skews caused by DML chirp and chromatic dispersion. 56 Gbit/s PAM-4 signals in C-band are respectively enabled for 40 km
and 60 km transmission below the HD-FEC and SD-FEC.
1 Introduction
Pulse-amplitude modulation (PAM) based directly-modulated
laser and direct detection (DML-DD) system has been widely
studied for short reach optical communications due to its low
cost and simple configuration [1]. However, the directly-
modulated PAM signals can easily suffer from distortions after
transmission. Affected by the adiabatic chirp from the DML
working in a high output power region, different intensity
levels of the PAM signals are frequency shifted respectively,
thus resulting in a tilted eye diagram (i.e., amplitude-
dependent skews) due to chromatic dispersion from the
transmission fiber. Various solutions have been proposed to
address this issue, including Volterra series based nonlinear
equalizers [2] and neural network based equalizers [3].
However, the Volterra equalizer requires high-order
polynomials to approximate the nonlinear transmission
response and is computationally inefficient. Neural network-
based equalizer requires intense training with large amounts of
computing resources. Alternative solutions with lower
computational complexity incorporate with two steps
including skew estimation and skew compensation [4-5].
These solutions are based on amplitude classification, which
are not accurate enough for the nonlinear response with a small
number of classification thresholds.
We propose, for the first time, a computational efficient
piecewise linear (PWL) equalizer to rectify the amplitude-
dependent skews due to the interaction between DML chirp
and fiber chromatic dispersion. Enabled by the PWL equalizer,
a 56 Gbit/s PAM-4 signal using DML at high output power
region with an extinction ratio (ER) of 5.18 dB is transmitted
over 40 km below the hard-decision (HD-FEC) threshold; and
60 km below the soft-decision forward error correction (SD-
FEC) threshold.
2 Principle of PWL equalizer
The PWL equalizer is originally proposed for acoustic echo
cancellation where loudspeaker nonlinearities result in a
nonlinear acoustic echo that distorts the output signal [6]. The
equalizer performs well for memoryless nonlinearities, where
adiabatic chirp from DML applies [7]. The PWL equalizer
consists of three steps, including amplitude threshold
decomposition, linear multichannel equalization and linear
addition.
Fig. 1 Workflow of the PWL equalizer.
For the amplitude threshold decomposition, a received
symbol can be represented as a vector of segments defined by
a set of pre-defined thresholds. Fig. 1 shows an example of a
signal sequence that
has been segmented using a threshold set .
The signal is therefore partitioned for four intervals of
(-
∞,
-
1.5), [-1.5, 0), [0, 1.5) and [1.5, ∞). The third element
(2.3) in the sequence is split into four segments as
, where the values are obtained as
(the subtraction of the value and the
threshold),
,
, and
.
In general, continuous threshold decomposition is an operation
that maps real numbers into vectors using a set of predefined
thresholds values. Considering , and the strictly ordered
set of N thresholds
. (1)