SER estimation method for 56 GBaud PAM-4
transmission system
Aadil Raza
1
, Kangping Zhong
2,
*, Salman Ghafoor
3,
**, Saeed Iqbal
1
,
Muhammad Adeel
2
, Shahid Habib
1
, Muhammad Fasih Uddin Butt
1
, and Chao Lu
2
1
COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan
2
Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong, China
3
National University of Sciences and Technology (NUST), Islamabad, Pakistan
*Corresponding author: kangping.zhong@macom.com; **corresponding author: salman.ghafoor@seecs.edu.pk
Received February 6, 2018; accepted February 9, 2018; posted online March 26, 2018
In this Letter, we have proposed a generalized Gaussian probability density function (GGPDF)-based method to
estimate the symbol error ratio (SER) for pulse amplitude modulation (PAM-4) in an intensity modulation/
direct detection (IM/DD) system. Furthermore, a closed form expression of SER
GGD
for PAM-4 has been de-
rived. The performance of the proposed method is evaluated through simulation as well as experimental work.
The fitting of probability density functions of the received signal is applied via GGPDF and shape parameters P
1
and P
2
associated with different PAM-4 levels are determined. The optimum single value of shape parameter P is
then calculated to estimate the SER. The mathematical relationship of P with different received optical powers
and receiver bandwidths has been determined and verified. The proposed method is a fast and accurate method
to estimate SER of a PAM-4 system, which is more reliable and in agreement with the error counting method.
OCIS codes: 060.4510, 060.2330.
doi: 10.3788/COL201816.040604.
The ever-growing bandwidth requirement of data centers
and high speed optical interconnects has been driving re-
searchers to design efficient, short reach optical transmis-
sion systems to realize 400 Gbit/s or even higher speeds. In
the literature, many advanced modulation formats, such
as pulse amplitude modulation (PAM-N), carrier-less am-
plitude and phase modulation (CAP), and discrete multi-
tone (DMT), along with digital signal processing (DSP)
have been employed in intensity modulation/direct detec-
tion (IM/DD) systems instead of a coherent system to
achieve low cost short reach links over bandwidth limited
optical devices
[1–3]
. Although, all modulation format s have
shown good performance, but PAM-4 has been considered
as a strong candidate by the IEEE P802.3bs 400 GbE
task force due to the relaxed optical signal-to-noise-ratio
(OSNR) requirement and low implementation complex-
ity. The performance evaluation of a communication
system is based upon the bit error ratio (BER) using
the error counting method. However, this method requires
a large number of symbols to calculate BER. Different
analytical BER estimation methods have been proposed
for non-return-to-zero (NRZ)-based quadrature phase
shift keying (QPSK) systems with both linear and nonlin-
ear impairments
[4,5]
. In Ref. [6], the symbol error ratio
(SER) estimation method has been investigated for the
multilevel PAM-N signaling format, which is based upon
the Q factor metric. The Q factor depends upon statistical
moments, such as mean and standard deviation of the re-
ceived signal, which determine the probability density
function (PDF). Furthermore, the authors in Ref. [
6],
presumed additive-white-Gaussian noise (AWGN), which
provides an accurate SER
Q
estimation for a low
Q function and higher PAM-N format, such as PAM-8
and PAM-16. However, this accuracy deviates as the
Q function goes higher and the PAM-N order decre ases,
such as PAM-4 and PAM-2. The reason for such deviation
is the presence of noise at both the transmitter and
receiver sides, which is not exactly Gaussian and provides
inaccurate SER estimation. Therefore, it is required to de-
termine the accurate distribution of non-AWGN associ-
ated with the received signal. A detailed statistical
analysis of generalized Gaussian PDF (GGPDF) can be
applied on the noise distribution to manipulate the shape
parameters. In literature, different techniques have been
demonstrated for determining the shape parameter of
GGPDF
[7–9]
. In Ref. [10], a technique has been reported
to find the value of the shape parameter by equating
the SER
C
from error counting with the calculated
SER
GGD
for polarization-multiplexed QPSK (PM-QPSK).
These studies motivated us to investigate the PAM-4 sys-
tem to provide an accurate estimation of SER based on
shape parameter. To the best of the authors’ knowledge,
this has not been explored for a PAM-4-based system so
far and needs to be investigated in depth.
In this Letter, we proposed a method based on GGPDF
for accurately estimating SER for the PAM-4-based
IM/DD system. The shape parameter dependent GGPDF
fitting is applied to each level of the PAM-4 signal. The
shape parameter P
1
is used for both −3 and − 1 levels,
and shape parameter P
2
is used for both þ1 and þ3 levels.
Based on P
1
and P
2
values, a single value of shape
parameter P is determined to estimate SER. Our method
provides a faster way to accurately estimate SER for
PAM-4.
COL 16(4), 040604(2018) CHINESE OPTICS LETTERS April 10, 2018
1671-7694/2018/040604(5) 040604-1 © 2018 Chinese Optics Letters