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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 12, DECEMBER 2005 2577
Study on the PMD Impairment of Optical Multilevel
DPSK Systems and its Mitigation Methods
Hosung Yoon, Member, IEEE, Na Young Kim, and Namkyoo Park, Member, IEEE
Abstract—We examine the polarization-mode dispersion
(PMD) impairment of optical multilevel differential phase-shift
keying systems, and also its mitigation method by comparing
the electrical equalization technique and the receiver bandwidth
optimization. Analysis has been carried out with 40-Gb/s systems
experiencing
ps of instantaneous differential group delay,
corresponding up to 240%/80% of bit/symbol transmission rate.
Results show considerable improvement in the PMD tolerance for
return-to-zero format for the optimized receiver bandwidth either
with or without the electrical equalization. For nonreturn-to-zero,
the bandwidth optimization alone does not significantly improve
the system’s PMD tolerances.
Index Terms—Adaptive equalizers, differential phase-shift
keying (DPSK), optical fiber communication, optical fiber
dispersion.
I. INTRODUCTION
S
YSTEM penalty associated with fiber dispersion forms
a critical barrier in realizing high data rate transmission
systems. Well-known resolutions for this type of system im-
pairment include the employment of the advanced modulation
format (at the transmitter end) and the optical–electrical equal-
ization technique (at the receiving end) [1].
A multilevel modulation, which encodes multiple bits on a
single symbol, is one of the attractive solutions to the above
problem that can be employed in the transmitter side. Among
various approaches, optical multilevel differential phase-shift
keying (DPSK) have received much attention with successful
experimental [2], [3] and theoretical [4], [5] demonstrations
of optical four-ary, differential quadrature PSK (DQPSK) and
eight-ary (D8PSK) systems.
Studied in depth with equal importance, on the receiver side,
post electrical equalization is also known to effectively reduce
the dispersion-induced penalty. Supporting the adaptation of
equalizer’s response for a time varying channel, they also fit ex-
cellently for the compensation of polarization-mode dispersion
(PMD) [6] – which has a statistical nature.
In this letter, we investigate the performance of the optical
multilevel DPSK systems under PMD effects, and study its mit-
Manuscript received May 20, 2005; revised July 20, 2005.
H. Yoon was with School of Electrical Engineering and Computer Science,
Seoul National University, Seoul 151-744, Korea. He is now with FTTH Devel-
opment Department, BcN Business Unit, KT, Daejeon 305-811, Korea (e-mail:
hsyoon@ieee.org).
N. Y. Kim is with Department of Electrical and Computer Engi-
neering, Queen’s University, Kingston, ON, K7L 3N6, Canada (e-mail:
nykim@ieee.org).
N. Park is with School of Electrical Engineering and Computer Science, Seoul
National University, Seoul 151-744, Korea (e-mail: nkpark@plaza.snu.ac.kr).
Digital Object Identifier 10.1109/LPT.2005.859158
Fig. 1. Structure of optical D8PSK receiver employing electrical equalizers.
igation method comparing approaches of receiver bandwidths
optimization [7] and electrical equalization.
II. S
YSTEM
MODEL
In our analysis, we assumed a generic optical multilevel
DPSK transmitter constructed with a phase modulator and a
chirp-free pulse carver [5]. Two of the most popular modu-
lation formats were tested: a nonreturn-to-zero (NRZ) with
constant power and ideal rectangular phase transitions and an
return-to-zero (RZ) with a duty cycle of 33%. For the transmis-
sion medium, only the first-order PMD with an instantaneous
differential group delay (DGD) and equal power splitting
between two principal states of polarizations was assumed. It
is worth noting that this reduced model provides a reasonably
good test-bed for the estimation of real PMD performance
including higher order effects [8]. To focus on/isolate the net
impairment due to the PMD, other fiber effects such as chro-
matic dispersion and nonlinearities were ignored in the current
analysis.
Among various optical D8PSK receiver schemes proposed
previously [4], [5], we tested a bilevel structure (Fig. 1) that is
known to exhibit the best chromatic dispersion tolerance as well
the lowest optical signal-to-noise ratio (OSNR) requirement [5].
An optical first-order Gaussian filter and an electrical fifth-order
Bessel filter (3-dB bandwidth
, ) were used. Amplified
spontaneous emission (ASE) noise from the optical preampli-
fier was included as additive white Gaussian noise while the
electrical noise from the photodiodes was ignored. The OSNR
was calculated with unpolarized ASE power within a reference
bandwidth of 0.1 nm.
For electrical equalizers to mitigate signal distortion, we con-
sidered two standard structures (Fig. 2): linear equalizer (LE)
and decision feedback equalizer (DFE). Their tap weights were
determined by using sgn-sgn least-mean-square algorithm [9].
1041-1135/$20.00 © 2005 IEEE
2578 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 12, DECEMBER 2005
Fig. 2. Generic structure of the electrical equalizer. According to the switch
position, it can be operated as either a DFE or an LE.
Here, we write the resulting tap weights in a vector form,
, where and are the
numbers of taps assigned for pre- and postcursor intersymbol
interference (ISI), respectively, [
taps in the feed-forward
filter (FFF),
in the feedback filter (FBF)] [9]. The equalized
decision variable
is expressed as the sum of outputs from the
FFF (
) and the FBF ( )
(1)
where
for an LE, and
for a DFE ( is the th
input to the equalizer, and
is the th symbol decision).
III. A
NALYSIS METHOD
For the precise estimation of the systems’ bit error rate
(BER), we employed a semianalytic technique based on the
Karhunen–Loève (KL) expansion formulated in the frequency
domain [10]. The method was modified for the optical multi-
level DPSK systems considering all tributaries of the receiver
hardware [5]. To include the ISI mainly due to three-symbol
patterns, we used a pseudorandom bit sequence with
in length [5]. Within the KL framework, the LE was modeled
as an analog electrical filter [11] with the following frequency
response, where
is the tap spacing
(2)
To analyze the DFE within the KL framework and meanwhile
to fully take into account the DFE’s nonlinear property, we di-
vided the DFE into two sections: linear FFF (FFF with
taps) and nonlinear decision-FBF (DFF with taps). The re-
sponse of the FFF was included in the KL expansion with the
same manner as the LE. On the other hand, the nonlinear DFF
was evaluated at the final error probability calculation stage, by
semianalytically adjusting the decision threshold by the amount
of feedback [9]. Noting that the equalized decision variable
is
the sum of the outputs from the FFF (
) and the FBF ( ),
we obtain the following expression for the error probability, with
given the original decision threshold
(3)
Fig. 3. Bandwidths optimization of unequalized optical D8PSK receivers
under a fixed DGD of 25 ps (
).
It is worth mentioning that it is observed that the current analysis
method with multiple tributaries showed excellent agreement
with the direct error count, using the Monte Carlo approach [5].
IV. R
ESULTS AND
DISCUSSION
By utilizing the method described in Section III, we carried
out numerical analysis to examine the optimal bandwidths that
minimize the PMD penalty for a 40-Gb/s optical D8PSK re-
ceiver without electrical equalizers [7]. Fig. 3 shows the OSNR
sensitivities (at
BER) plot for different sets of receiver
bandwidths (
, ), utilized in the search of the optimal band-
widths set. For this specific plot, we used a reference DGD
(DGD
) value of 25 ps ( ) for the receiver bandwidth
optimization.
It can clearly be seen that the bandwidth optimized receivers
(open circles in the figures) with nonzero DGD
signifi-
cantly improved OSNR sensitivity at the reference DGD value
more than the receivers optimized to back-to-back condition
(filled circles). For example, looking detail into the case of
RZ-D8PSK [Fig. 3(a)], when the receiver bandwidths were
optimized for back-to-back (equivalently, optimization made
for DGD
), 1.98 dB of the OSNR penalty was induced at
25 ps of DGD. However, reoptimizing the receiver bandwidths
with the DGD
value of 25 ps, the OSNR penalty at 25-ps
DGD was dropped to 0.61 dB (1.37 dB of penalty reduction).
For NRZ modulation with the same DGD
, we obtained
0.45 dB of penalty improvement against the back-to-back
optimized receiver.
In Fig. 4, we show the OSNR sensitivity plots as a func-
tion of the instantaneous DGD, obtained at different choice of
DGD
( , , , , )—used for the selection
of the optimum DGD
and corresponding receiver bandwidth
optimization. The system performance was investigated as the
DGD
value was changed to find the optimal DGD that
would provide the best (instantaneous) DGD tolerances overall.
For both of the transmission formats, the best system perfor-
mance was obtained at the DGD value of
. Specifically, for
RZ-D8PSK and NRZ-D8PSK, we obtained 32% and 17% more
DGD tolerances (at 2-dB OSNR penalty, compared to the re-
ceivers optimized with back-to-back condition) with negligible
offsets (
0.1 and 0.5 dB) in the system penalty for a wide range
of instantaneous DGD values.
YOON et al.: STUDY ON THE PMD IMPAIRMENT OF OPTICAL MULTILEVEL DPSK SYSTEMS 2579
Fig. 4. OSNR sensitivity according to the instantaneous DGD, for various sets
of receiver (bandwidths optimized at different reference DGD values).
Fig. 5. Comparison of the OSNR penalties as a function of instantaneous
DGD: equalized receivers versus bandwidth-optimized unequalized receiver.
The results are referenced to the OSNR sensitivities of the unequalized
receivers, optimized in the back-to-back condition.
Even better system performance was obtained with the elec-
trical equalization techniques. The electrical equalizers assumed
were five-tap LE (
), and four-tap DFE which con-
sists of three-tap FFF and one-tap DFF (
, ). Their
tap spacing
was set identical to the symbol period . Also
for the equalized receivers, their bandwidths were optimized to
provide maximum DGD tolerances. As can be seen in Fig. 5,
with the electrical equalization technique, up to 57.5 and 43.2 ps
of DGD tolerances were achieved for RZ- and NRZ-D8PSK
format, respectively. The sensitivity offset observed with un-
equalized NRZ-D8PSK receiver [Fig. 4(b)] was removed by the
application of electrical equalizers [Fig. 5(b)], actually showing
0.3-dB gain in the OSNR sensitivity overall. For the 40-Gb/s
DQPSK formats, similar DGD tolerance improvements were
observed exhibiting 36.3 and 29.0 ps for the equalized RZ and
NRZ systems, respectively (Fig. 5). It is worth mentioning that
we also tested equalizers with more taps or with fractionally
spaced taps. Improvement was observed in the regime of high
OSNR penalty or large DGD values, but within the range of
our interest (for the DGD range less than a symbol period and
modest OSNR penalty
2 dB), the observed enhancement was
not significant, in agreement with previous observations [12].
V. C
ONCLUSION
We examined the PMD tolerance of the optical multilevel
DPSK systems, and its improvement methods. RZ-D8PSK
systems showed greater PMD tolerance (
) than the
NRZ systems (
), without any mitigation effort. With the
application of receiver bandwidth optimization and electrical
equalization, the DGD tolerance window was increased by
(32%, 67%) for RZ format, and (17%, 60%) for NRZ-D8PSK
when compared to the receivers optimized at back-to-back.
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