Average BER of coherent optical QPSK systems with
phase errors over M turbulence channels
Jiashun Hu (胡家顺)
1
, Zaichen Zhang (张在琛)
1,
*, Liang Wu (吴 亮)
1
, Jian Dang (党 建)
1
,
and Guanghao Zhu (朱广浩)
2
1
National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China
2
School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
*Corresponding author: zczhang@seu.edu.cn
Received July 8, 2018; accepted October 24, 2018; posted online November 27, 2018
The average bit-error-rate (BER) performance is studied for a coherent free-space optical communication system
employing differentially encoded quadrature phase-shift keying (QPSK) with the Mth-power phase estimation
method. A closed-form expression, considering the combined effects of the Málaga (M) turbulence fading, point-
ing errors, and phase estimation errors, is derived in terms of Meijer’s G function. Numerical and Monte Carlo
simulation results are presented to verify the derived expression.
OCIS codes: 010.1300, 010.1330, 060.1660, 060.2605.
doi: 10.3788/COL201816.120101.
Terrestrial free-space optical (FSO) communication is
a technology that transmits optical signals through
the atmosphere. In comparison with radio-frequency
(RF) systems, FSO solutions have lower cost, better secu-
rity, easier installation, and wider and license-free band-
width
[1,2]
. Recently, FSO communication systems have
earned much research attention
[3,4]
. Intensity modulation
with direct detection (IM/DD) is widely adopted in
commercial FSO communication systems because of its
simplicity. Compared to IM/DD, coherent detection
(CD) is more costly, uses a local oscillator (LO) laser at
the receiver, has higher receiver sensitivity, improved
spectral efficiency, and better background noise rejection,
and avoids using an adaptive threshold
[5,6]
. CD has been
well studied for FSO communications
[6–12]
.
However, FSO links may suffer from fading due to the
atmospheric turbulence and pointing errors. Many statis-
tical models have been proposed to describe the effect of
atmospheric turbulences. The Málaga (M) distribution is
a generalized statistical model, which unifies most of the
existing turbulence models, such as the lognormal, the
Gamma–Gamma, and the K models
[13]
. It matches well
with published simulation data over a wide range of tur-
bulence conditions (weak to strong)
[13]
. Pointing errors
originate from the misalignment between the transmitter
and receiver and can severely deteriorate the FSO link
performance. The performance of FSO links over M tur-
bulence channels with and without pointing errors has
been studied in IM/DD
[14]
, heterodyne detection
[10,15]
,
and mixed RF/FSO transmission systems
[16]
.
Besides the atmospheric turbulence and pointing errors,
phase noise is another severe impairment in coherent FSO
communication systems, since it impacts carrier synchro-
nization
[17]
. There are two main sources of phase noise in
FSO communication systems: wavefront distortion caused
by the atmospheric turbulence and spontaneous emission
of transmitting and LO lasers. The phase noise induced by
the turbulent atmosphere is proved to obey Gaussian
distribution
[18]
. Laser phase noise can be simplified as a
zero-mean Gaussian random variable in radio on FSO
(RoFSO) systems, and a closed-form expression for aver-
age bit-error-rate (BER) was derived for Gamma–Gamma
turbulence channels
[19]
. Fortunately, phase noise can be
mitigated by carrier synchronization at the receiver. Tra-
ditionally, a phase-locked loop (PLL) is used to recover
the carrier phase. The phase estimation error generated
by the PLL follows a Tikhonov distribution and is
considered in subcarrier phase-shift keying (PSK) FSO
systems under lognormal
[1]
and Gamma–Gamma turbu-
lence channels
[2,20]
. This type of phase error is also analyzed
in decode-and-forward (DF) relayed subcarrier FSO links
over M turbulence channels
[21]
and coherent FSO commu-
nication systems with heterodyne detection
[7,22]
. But, PLLs
are sensitive to the loop delay, and they exert stringent
laser linewidth (LW) requirements on coherent optical
systems
[17]
. Due to the recent development of high-speed
digital signal processing (DSP), simple and efficient
DSP algorithms can be employed to compensate time-
varying transmission impairments, including carrier syn-
chronization for optical fiber systems. The Mth-power
phase estimation method is a commonly used algorithm
for quadrature phase-shift keying (QPSK) (M ¼ 4)
[23]
.
The distribution of the phase estimation error related
to this method is approximately Gaussian, as it was de-
rived in Ref. [
24]. The error-rate performance of DSP-
based coherent optical fiber systems has been studied
[24]
.
However, to the authors’ best knowledge, no prior work
has studied the effect of Gaussian phase error on the
BER performance of the DSP-based coherent optical
QPSK systems over turbulence channels.
In this Letter, we investigate the average BER of differ-
entially encoded QPSK, considering the joint effects of the
M turbulence fading, pointing errors, and Gaussian phase
errors. We adopt the homodyne detection scheme, which
COL 16(12), 120101(2018) CHINESE OPTICS LETTERS December 10, 2018
1671-7694/2018/120101(5) 120101-1 © 2018 Chinese Optics Letters