![The Q-factor as a function of the degree of polarization of the noise for a back-to-back system. The red curve shows the result obtained using Eq. (6) and the circles show the experimental result when the Jones vectors of the signal and the polarized part of the noise are orthogonal. The blue curve and the squares show the corresponding results when the signal is co-polarized with the polarized part of the noise. [From Ref. 9, Y. Sun et al., Proc. OFC '03.]](https://www.researchgate.net/profile/Curtis-Menyuk/publication/228879418/figure/fig3/AS:670712809410584@1536921803964/The-Q-factor-as-a-function-of-the-degree-of-polarization-of-the-noise-for-a-back-to-back_Q320.jpg)
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Modeling Receivers in
OPTICAL COMMUNICATION
SYSTEMS With Polarization Effects
Modeling Receivers in
OPTICAL COMMUNICATION
SYSTEMS With Polarization Effects
John Zweck, Ivan T. Lima Jr., Yu Sun, Aurenice O. Lima,
Curtis R. Menyuk and Gary M. Carter
Recent experiments have demonstrated that the bit-error rate of an optical
fiber communication system can vary widely due to the random nature of
the polarization effects in the system. Using a newly developed receiver
model, we show that the bit-error rate depends not only on the optical
signal-to-noise ratio but also on the polarization states of the signal and
the noise. With the new model we obtained excellent agreement between
simulations and experiments for a long-haul transmission system.
November 2003 ■Optics & Photonics News
31
There is strong interest in under-
standing and quantifying how
polarization effects influence the
performance of optical fiber communica-
tion systems. The most widely used
performance measures are the optical
signal-to-noise ratio (OSNR), the
Q-factor and the bit-error rate. These
performance measures are progressively
more fundamental but also more diffi-
cult to measure. Their complex relation-
ship to each other, which is fully
understood only in special cases, is signif-
icantly complicated by polarization
effects. It is particularly difficult to char-
acterize the impact of polarization effects
on system performance since they are
inherently stochastic in nature because
of the random variations in the birefrin-
gence orientation and strength of optical
fibers. In our laboratory,we emulate
long-haul optical fiber communication
systems by propagating an optical signal
many times around a recirculating opti-
cal fiber loop. In these experiments,we
observed that the three performance
measures listed are not uniquely related
to each other and that they can each vary
widely depending on the particular real-
ization of the random polarization effects
in the loop. How can we explain these
performance variations? Given a set
of system parameters and a stochastic
model for the randomly varying birefrin-
gence, can we accurately relate the three
performance measures to each other and
calculate their probability density func-
tions? To answer these questions, we had
to develop accurate models of the trans-
mission line and the receiver that take
into account polarization effects.
In the context of this article, the most
important polarization effects are polar-
ization-mode dispersion (PMD), which is
caused by the rapidly and randomly vary-
ing birefringence in optical fiber,and
polarization-dependent loss (PDL),
which is present in polarization-sensitive
devices such as the couplers and isolators
in erbium-doped fiber amplifiers.
Polarization-mode dispersion causes fre-
quency-dependent random rotations of
the polarization state of the light as it
propagates through the fiber. As we will
explain, in combination with the gain
saturation effect in optical amplifiers,
PMD and PDL can cause random varia-
tions in the OSNR, and hence in the
Q-factor and the bit-error rate. To calcu-
late the variation in the OSNR, Wang and
Menyuk1developed a reduced transmis-
sion model for the polarization effects in
single-channel and wavelength-division
multiplexed systems.But to accurately
relate the OSNR to the Q-factor and to
the bit-error rate, we needed a model of
the receiver that takes into account the
polarization effects. Because none of the
existing receiver models could accurately
account for the effect of partially polar-
ized light, we were forced to develop our
own model.
The purpose of this article is to
describe the new receiver model we
developed. We will show how it helped us
to obtain excellent agreement between
theory and experiment, thereby leading
us to a deeper understanding of how the
performance of an optical fiber commu-
nication system is influenced by
polarization effects. One of the main
predictions of our model is that, even if
two random realizations of the polariza-
tion effects in a system produce the same
OSNR, they can nevertheless result in
very different bit-error rates. As we will
demonstrate, the reasons are that in the
transmission line the amplified sponta-
neous emission noise generated by the
optical amplifiers can become partially
polarized because of PDL, and that in
the receiver, both the Q-factor and the
bit-error rate depend not only on the
OSNR but also on the polarization state
of the noise.
Prior work on receiver modeling
To put our results in context, we begin
with a brief review of prior work on
receiver modeling for modern long-haul
optical fiber communication systems. In
these systems, the optical noise entering
the receiver dominates the electrical noise
generated in the receiver. The optical
noise is produced by erbium-doped
or Raman fiber amplifiers along the
transmission line and by an optical pre-
amplifier just prior to the receiver. The
performance of these systems is primar-
ily determined by the shape of the
noise-free or noise-averaged signal, the
statistics of the noise immediately prior
to the receiver, and how the optical filter,
square-law photodetector, and low-pass
OPTICAL COMMUNICATION SYSTEMS
1047-6938/03/11/0030/6-$0015.00 © Optical Society of America
electrical filter in the receiver shape the
signal and filter the noise to produce
the electrical current. Other important
parameters that affect the performance
are the sampling time and the decision
level used to differentiate between the
marks (ONEs) and spaces (ZEROs). The
bit-error rate is determined by the proba-
bility density functions (pdfs) of the
sampled electrical currents of the
marks and spaces. One can com-
pute the bit-error rate by use of
standard or biasing Monte Carlo
simulations to obtain histograms
of the currents in the marks and
spaces, where different samples
correspond to different realiza-
tions of the random variables in
the system. These variables could
include the noise added at each
frequency by each of the optical
amplifiers, the binary digit in each
bit slot, and the variables used to
specify the randomly varying bire-
fringence of the optical fiber.
However, since bit-error rates are
typically on the order of 10-9 or
less, it is not practical to compute
them by use of standard Monte
Carlo simulations. Even if we used
efficient biasing Monte Carlo
methods such as importance sam-
pling or the multicanonical Monte
Carlo technique of Berg and Neuhaus,
we would need on the order of 105sys-
tem realizations to accurately compute
the bit-error rate for a single set of system
parameters. Although this number of
realizations is feasible for validation
studies, it is too large for the parametric
studies required for system design and
performance evaluation.
For this reason, despite the recent
impressive successful use of biasing
Monte Carlo methods to calculate bit-
error rates, it is still necessary to use
reduced deterministic methods that are
as accurate as possible and that only
require the user to propagate data
through the system once or at most a few
times. One must validate these determin-
istic models and determine their range of
applicability by comparison to Monte
Carlo simulations and to experiments.
The simplest deterministic models con-
sider only the effect on the bit-error rate
of noise from optical amplifiers. These
However, because the numerical calcula-
tion of these pdfs is not straightforward,
it is often assumed that the electrical
currents in the marks and spaces are
Gaussian distributed, and so are charac-
terized by their means and variances.
In this situation, the bit-error rate is
given by
BER = erfc(Q/√2
–)/2, (1)
where the Q-factor is defined by
– –
I1– I0
Q= ——– . (2)
1+ 0
Here –
I0and –
I1are the means of the
low-pass filtered electrical current
at the sampling time for the spaces
and marks, respectively, and 0
and 1are the corresponding
standard deviations. In the case of
an integrate-and-dump receiver,
the Q-factor can be expressed in
terms of the electrical signal-to-
noise ratio, SNR = ( –
I1– –
I0)/ –
I0,
by the formula
SNR√—
2T—
Bopt
—
Q= —————–– , (3)
1 +√—
1+—
2SNR
——
where Tis the bit period and Bopt
is the bandwidth of the rectangular opti-
cal filter.2Although this method for
estimating the bit-error rate involves a
number of approximations, it has been
widely used because it enables the bit-
error rate to be obtained very easily from
the signal-to-noise ratio.
In the past few years, the modeling and
analysis of receivers have been reinvigo-
rated by the work of Peter Winzer. One of
Winzer’s contributions was to derive for-
mulae for the means and variances of the
marks and spaces for a receiver with arbi-
trary optical and electrical filters, under
the assumption that the optical noise
entering the receiver is unpolarized addi-
tive white Gaussian noise.4Although
these formulae are expressed in terms of
multidimensional integrals involving the
noise-free signal and the filters, it is easy
and fast to compute them numerically.5
Using Eqs. (1) and (2),the moments
of the electrical current can be used to
estimate the bit-error rate under the
appropriate inputs to the receiver model
are the shape of the noise-free signal and
the noise spectral density or, equivalently,
the OSNR.
In the early 1990s, Marcuse2and
Humblet and Azizo˜glu3showed that,for
a receiver that consists of a rectangular
bandpass optical filter,a square-law pho-
todetector and an integrate-and-dump
electric filter,the pdfs of the marks and
spaces are non-central 2-distributions.
The 2-distribution, which is the pdf of a
sum of squares of independent Gaussian
random variables with identical vari-
ances, arises here because the optical
noise is additive white Gaussian noise and
the photodetector squares the sum of the
signal and the noise. This analysis was
extended in various directions by Lee
and Shim, Bosco et al., Forestieri and
Holzlöhner et al. In particular, they
showed that, for arbitrary optical and
electrical filters, the pdfs of the marks and
spaces are generalized 2-distributions.
32
Optics & Photonics News ■November 2003
OPTICAL COMMUNICATION SYSTEMS
models ignore pattern dependences
caused by nonlinear pulse-to-pulse inter-
actions, nonlinear interactions between
the signal and the noise, and random
polarization effects. The behavior of such
a system is equivalent to that of a back-
to-back system consisting of a transmit-
ter, an optical pre-amplifier that adds
unpolarized white Gaussian noise to the
signal, and a receiver. In this situation,the
Voltage (a.u.)
spaces
0 1
10 0
10 -12
marks
pdf
Figure 1. Probability density functions of the marks and
spaces at the sampling time of the low-pass filtered
received electrical current for a back-to-back system. The
solid curves show the exact 2pdfs and the dashed curves
show the Gaussian approximations obtained using the
means and standard deviations of the exact pdfs.
November 2003 ■Optics & Photonics News
33
assumption that the current in each bit is
Gaussian-distributed rather than 2-dis-
tributed. It has been shown that, for sys-
tems with unpolarized additive white
Gaussian noise, over a wide range of sys-
tem parameters bit-error rates computed
using this approach are in good agree-
ment with those obtained using the exact
2pdfs. But as we see in Fig. 1,in the
tails, the Gaussian approximation under-
estimates the 2pdf in the spaces
and overestimates it in the marks.
Because of this fortuitous cancel-
lation of two errors, the minimum
bit-error rates agree with each
other to within an order of magni-
tude, although the optimal voltage
thresholds differ by almost a factor
of two in this case. Consequently,
receiver sensitivities that are calcu-
lated using the Gaussian approxi-
mations agree well with those
obtained using the 2pdfs.The
receiver sensitivity is most com-
monly defined as the power that
produces a bit-error rate of 10-9.
This result, which is a typical
example of a general phenome-
non,2is for a prototypical back-to-
back system. We used a 10 Gbit/s
return-to-zero raised cosine signal
with an optical signal-to-noise
ratio of 20 dB and an extinction
ratio in the spaces (ZEROs) of 20 dB. The
receiver filters were a 60 GHz Gaussian
optical filter and an 8 GHz low-pass fifth-
order electrical Bessel filter.
Winzer’s deterministic method can
also be used to calculate electrical eye
diagrams for realistic terrestrial transmis-
sion systems. In Fig. 2,we show eye
diagrams for a system similar to an
experimental loop in our laboratory that
we are using to emulate a long-haul ter-
restrial system with four channels spaced
200 GHz apart.6The main nonlinear
effects in this system are intrachannel
pulse-to-pulse interactions that result in
bit-pattern-dependent timing shifts and
distortions of the pulses. The eye diagram
in Fig. 2 (a) is computed using the deter-
ministic method at a transmission dis-
tance of 3,400 km. For this simulation,
we propagated the noise-free signal
through the system and added the appro-
priate amount of unpolarized additive
white Gaussian noise at the receiver.
Therefore, although we correctly mod-
eled nonlinear pulse-to-pulse interac-
tions, we did not model the nonlinear
interactions in the fiber between the sig-
nal and the noise. In Fig. 2 (b),we show
the corresponding result obtained from
a Monte Carlo simulation in which we
included the nonlinear interactions
between the signal and the noise. For a
wide range of system parameters, the
relative error in the Q-factors computed
using these two methods was less than
0.5 percent back-to-back and less than
5 percent for all distances less than
3,400 km. We did not include polariza-
tion effects in either simulation.
Polarization effects in receivers
Polarization effects cause random varia-
tions in both the OSNR and the polariza-
tion state of the noise in long-haul
systems.1,7 To understand why, suppose
for simplicity that within the bandwidth
of a channel the signal is polarized so
that its polarization state can be charac-
terized by its Stokes vector, which is a
unit-length vector s= (S1,S2,S3)/S0,
where S0,S1,S2,S3are Stokes parame-
ters. Suppose that in each PDL element,
the Stokes vector of the signal in a given
channel is closely aligned with the
Stokes vector that has the highest loss in
that element. Since the gain saturation
of the amplifiers keeps the total power
fixed, as the propagation distance
increases the signal in this channel will
gradually lose power to the other chan-
nels and to the noise, and its OSNR will
become lower than average.The degree
of alignment of the Stokes vector of the
signal with the high-loss Stokes vectors
of the PDL elements depends on the
realization of the PMD in the fibers.
Consequently,variations in the PMD
result in variations in the OSNR
and hence in the bit-error rate.
The average Stokes parameters
of the noise in a given bandwidth
can be decomposed as the sum of
a polarized part of the noise and
an unpolarized part. The polariza-
tion state of the noise can be char-
acterized by the Stokes vector of
the noise, which is a unit-length
vector determined by the polarized
part of the noise, and the degree of
polarization of the noise, which is
the power ratio of the polarized
part of the noise to the total noise.
If,in each PDL element, the Stokes
vector of the noise is closely
aligned with the Stokes vector with
lowest loss, then since the optical
amplifiers keep the total power
fixed, the noise within the band-
width of a given channel can
become partially polarized by
the time it reaches the receiver. Moreover,
the degree of polarization of the noise
and the angle between the Stokes vectors
of the signal and of the noise in a given
channel can vary widely depending on
the random realization of the PMD.
In the receiver, variations in the polar-
ization state of the noise result in varia-
tions in the Q-factor,even if the OSNR
is fixed. To explain and quantify this
effect, we derived a formula for the
Q-factor when the noise is partially
polarized.8We assumed that, within the
bandwidth of the optical filter, the signal
is polarized with Stokes vector sand
the noise is partially polarized additive
white Gaussian noise that is character-
ized by the noise spectral density NASE,
the degree of polarization of the noise
DOPn,and the Stokes vector of the
noise n.Generalizing Winzer’s results,
we derived formulae for the mean and
standard deviation of the low-pass elec-
trically filtered current in the receiver.
OPTICAL COMMUNICATION SYSTEMS
Time (ps)
Voltage (a.u.)
0 200
(a)
(b)
1
0
1
0
Figure 2. Eye diagrams for a terrestrial optical fiber trans-
mission system at a transmission distance of 3,400 km,
calculated (a) using Winzer’s deterministic method, with
unpolarized, white noise added at the receiver, and (b)
using a Monte Carlo simulation that accounts for nonlinear
interactions between the signal and the noise in the fiber.
In the derivation of these formulae, care
must be taken when the noise is partially
polarized, since the components of the
noise that are parallel and perpendicular
to the signal in Jones space may be corre-
lated with each other due to the com-
bined effect of PMD and PDL. We
showed that the mean of the current is
independent of the polarization state of
the noise. The variance of the
current at time tcan be expressed
as 2
i(t) = 2
S-ASE(t)+2
ASE -ASE ,
where 2
S-ASE(t) is the variance
caused by the beating of the sig-
nal with the noise in the receiver,
and 2
ASE -ASE is the variance
caused by the beating of the noise
with itself.
We proved that the variance
due to signal-noise beating
is of the form, 2
S-ASE(t)
=NASE S-ASE JS-ASE(t),where
S-ASE = 1
–
2(1 + DOPnsn), (4)
and where JS-ASE(t) is indepen-
dent of the noise and depends
only on the noise-free signal and
the receiver filter shapes.To
understand this formula, we
observe that, in the receiver, the
signal only beats with that por-
tion of the noise that is co-
polarized with it. For a fixed
noise spectral density, the signal-noise
beating variance is maximized when the
noise is totally polarized and is co-
polarized with the signal, i.e.,
S-ASE= 1, since in this case all the noise
beats with the signal. At the other
extreme, the signal-noise beating vari-
ance is minimized when the noise is
totally polarized and the Jones vectors
of the signal and the noise are orthogo-
nal,i.e.,S-ASE= 0, since in this case
there is no beating between the signal
and the noise. When the noise is unpo-
larized S-ASE= 0.5 is in the middle.
Similarly,the variance of the current
caused by noise-noise beating is of the
form 2
ASE -ASE =N2
ASE JASE -ASE /ASE -ASE,
where
1
ASE -ASE = ———— , (5)
1 + DOP2
n
and where JASE -ASE is independent of the
signal and noise and depends only on the
receiver filter shapes. The noise-noise
beating variance is maximized when the
noise is totally polarized, since in this
case all the noise beats with itself. The
minimum value, which is half the maxi-
mum value, occurs when the noise is
unpolarized. Putting all this together,
the formula for the Q-factor for systems
with partially polarized noise is
OSNR(ASE -ASE)1/2
Q=—————————————–.(6)
1+(1+2S -ASEASE -ASEOSNR)1/2
The only polarization-dependent par-
ameters in this formula are S -ASE and
ASE -ASE.The parameters and depend
on the receiver filter shapes and also
depends on the shape of the noise-free
optical signal.8The parameter is the
enhancement factor,which is equal to
the ratio of the noise-free current of the
marks at the sampling time to the average
optical power.5The enhancement factor
quantifies how much the combination of
the optical pulse shape and the receiver
enhances the electrical signal-to-noise
ratio relative to the optical signal-to-noise
ratio.Although the formula assumes that
there is no noise-free current in the
spaces, it can be extended to the case of
signals with a finite extinction ratio.
Comparison to experiments
To validate the formula and illustrate
the dependence of the Q-factor on the
degree of polarization of the noise, we
performed a back-to-back experiment
in which partially polarized noise
was added to a return-to-zero
signal.9We pro duced partially
polarized noise by combining
unpolarized noise from one
amplifier with polarized noise
generated by passing noise from a
second amplifier through a polar-
izer and a polarization controller.
The polarization controller was
used to vary the angle between
the Stokes vectors of the signal
and the noise. In addition, we
varied the degree of polarization
of the noise. In the experiment,
the electrical signal-to-noise ratio
was held fixed at 11 dB. In Fig. 3,
for each value of the degree of
polarization of the noise, we use
red circles and blue squares,
respectively, to plot the maxi-
mum and minimum measured
values of the Q-factor on a linear
scale. The red and blue curves
show the corresponding results
obtained using Eq. (6).As we
increase the degree of polarization of the
noise from 0 to 1, we observe an increase
in the range of the Q-factor. This result
illustrates the significant impact that
partially polarized noise can have on the
performance of an optical fiber trans-
mission system.
The real test of a receiver model is
to combine it with a transmission line
model to study the performance of a
realistic experimental optical fiber
communication system. As a first step
in this direction, we performed experi-
ments on a single-channel dispersion-
managed soliton recirculating loop
system in which we propagated
10 Gbit/s return-to-zero pulses over a
distance of 10,000 km.10 In this highly
nonlinear system, the balance between
dispersion and nonlinearity ensures that
the pulse shape evolves periodically,
with one period each round trip of the
34
Optics & Photonics News ■November 2003
OPTICAL COMMUNICATION SYSTEMS
DOPn
Q-factor
0 1
30
5
Figure 3. The Q-factor as a function of the degree of polar-
ization of the noise for a back-to-back system. The red curve
shows the result obtained using Eq. (6) and the circles show
the experimental result when the Jones vectors of the signal
and the polarized part of the noise are orthogonal. The blue
curve and the squares show the corresponding results when
the signal is co-polarized with the polarized part of the
noise. [From Ref. 9, Y. Sun et al., Proc. OFC ’03.]
November 2003 ■Optics & Photonics News
35
107 km loop.Consequently, for at least
the first 10,000 km there are essentially
no nonlinear interactions between the
different pulses, and system perfor-
mance is primarily determined by the
periodically stationary pulse shape, the
OSNR, and the polarization states of the
signal and the noise. With this system we
can therefore study polarization effects
independent of other effects. We
found that polarization effects in
recirculating loops can be very
different from those one would
expect in a straight-line system. In
particular, when we manually var-
ied the setting of a polarization
controller in the loop, we
observed variations in the bit-
error rate that are much larger
than would be expected for
a comparable straight-line system.
These large variations are due to
the periodicity of the PMD and
PDL in the loop system.
We have been developing and
evaluating experimental tech-
niques to make the polarization
effects in loops more closely
resemble those in a straight-line
system, and in particular to reduce
the large dependence of the bit-
error rate on polarization effects.
Inspired in part by the pioneering
work of Alan Willner’s group
at the University of Southern
California, we are using a lithium-
niobate polarization transformer
in the loop to break the periodic-
ity of the polarization effects. This
loop-synchronous polarization trans-
former imparts a different random rota-
tion to the light on each round trip of
the loop. To reduce the effect of polar-
ization-dependent gain in this single-
channel system, we used a second
polarization transformer at the trans-
mitter to scramble the polarization state
of the input signal. To study how much
the system performance is improved
with both polarization transformers,
we measured the distribution of the
Q-factor.With the loop-synchronous
polarization transformer, each sample of
the Q-factor corresponds to a different
set of random rotations for each round
trip of the loop. In Fig. 4, we show the
measured histogram with bars when
both polarization transformers were on
and the PDL per round trip of the loop
was 0.6 dB. The black solid curve shows
the corresponding theoretical result
obtained by using the new receiver
model, together with Wang and
Menyuk’s reduced transmission line
model.1This transmission model tracks
the evolution of the power and polariza-
tion states of the signal and noise, taking
into account the polarization effects and
the gain saturation of the amplifiers. We
have used these results to quantify the
extent to which the two polarization
transformers improve system perfor-
mance.10 Interestingly enough, the
Q-distributions in Fig. 4 are asym-
metric. Our simulations show that this
asymmetry occurs because the noise can
become partially polarized after many
round trips. For those samples for which
the signal is often closely aligned with
the low-loss axes of the PDL elements,
the OSNR is larger than average. But for
these same samples, the noise also tends
to be co-polarized with the signal.
Consequently,the signal-noise beating
variance is larger and the Q-factor is
lower than for a system with the same
OSNR but with unpolarized noise.
Therefore, the large-Qportion of the
Q-distribution with unpolarized noise is
missing, and the Q-distribution is asym-
metric. To confirm this,we performed a
simulation with the same OSNR sam-
ples but in which we assumed that the
noise was unpolarized at the
receiver.As expected, the result-
ing Q-distribution, shown with
the blue dashed curve, is much
more symmetric. This result illus-
trates the importance of using a
receiver model that accounts for
partially polarized noise when
modeling systems with PDL.
Conclusion
In optical fiber transmission sys-
tems with polarization-depen-
dent loss, random variations in
fiber birefringence can cause vari-
ations in the Q-factor and the bit-
error rate. By using transmission
and receiver models that account
for the polarization states of the
signal and the noise, we have
explained this variation and accu-
rately reproduced the statistics of
the performance of an experi-
mental system.
References
1. D. Wang and C. R. Menyuk, J. Lightwave
Technol. 19 (4), 487-94 (2001).
2. D. Marcuse, J. Lightwave Technol. 8(12),
1816-23 (1990).
3. P. A. Humblet and M. Azizo˜glu, J. Lightwave Technol. 9
(11), 1576-82 (1991).
4. P. J. Winzer et al., J. Lightwave Technol. 19 (9), 1263-
73 (2001).
5. I. T. Lima Jr. et al., IEEE Photon. Technol. Lett. 15 (4),
608-10 (2003).
6. H. Xu et al., “Quantitative experimental study of intra-
channel nonlinear timing jitter in a 10 Gb/s terrestrial
WDM return-to-zero system,” in Proc. OFC’ 03,
Atlanta, Ga., 2003, paper FE7.
7. Y. Sun et al., IEEE Photon. Technol. Lett. 13 (9), 966-8
(2001).
8. I. T. Lima Jr. et al., “An accurate formula for the
Q-factor of a fiber transmission system with partially
polarized noise,” in Proc. CLEO ‘03, Baltimore, Md.,
2003, paper CThJ2.
9. Y. Sun et al., “Effects of partially polarized noise in a
receiver,” in Proc. OFC ‘03, Atlanta, Ga., 2003, paper
MF82.
10. Y. Sun, et al., IEEE Photon Tecnol. Lett. 15 (8), 1067-9
(2003).
John Zweck (zweck@umbc.edu), Ivan T. Lima, Jr., Yu
Sun, Aurenice O. Lima, Curtis R. Menyuk and Gary
M. Carter are with the University of Maryland
Baltimore County Department of Computer Science
and Electrical Engineering, Baltimore, Md.
OPTICAL COMMUNICATION SYSTEMS
Q-factor
pdf
411
0.8
0
Figure 4. The probability density function of the Q-factor
for a dispersion-managed soliton recirculating loop at a
transmission distance of 10,000 km, where each sample of
the Q-factor was obtained using a different set of loop-syn-
chronous polarization transformations. The experimental
result is shown with red bars and the result obtained using
a receiver model that accounts for the polarization state of
the noise is shown with a black solid curve. The result
obtained using a receiver model that assumes that the
noise entering the receiver is unpolarized is shown with a
blue dashed curve. [From Ref. 10, Y. Sun et al., IEEE
Photon. Technol. Lett. 15(8), 1067-9 (2003).]
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