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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 14, JULY 15, 2009 2667
SOA Intensity Noise Suppression in Spectrum
Sliced Systems: A Multicanonical Monte Carlo
Simulator of Extremely Low BER
Amirhossein Ghazisaeidi, Francesco Vacondio, Alberto Bononi, and Leslie Ann Rusch, Senior Member, IEEE
Abstract—We present a thorough numerical study of intensity
noise mitigation of spectrum sliced wavelength-division multi-
plexing (SS-WDM) systems employing a nonlinear semiconductor
optical amplifier (SOA) before the modulator. Our simulator of
the SS-WDM link, embedded inside a Multicanonical Monte Carlo
(MMC) platform, estimates the tails of the probability density
functions of the received signals down to probabilities smaller
than
10
16
. We introduce a new, simple, and efficient technique
to handle intersymbol interference (ISI) in MMC simulations.
We address the impact of optical postfiltering on SOA noise sup-
pression performance. While previous research experimentally
observed the SOA-induced noise cleaning in SS-WDM systems,
this is the first complete simulator able to correctly predict the
ensuing BER improvement. We measure the BER at different
bit-rates and validate predicted BERs with and without post
filtering.
Index Terms—ISI, modeling, multicanoncial Monte Carlo, noise
suppression, SS-WDM, SOA.
I. INTRODUCTION
INTENSITY noise suppression of spectrum-sliced wave-
length-division multiplexing (SS-WDM) systems by
semiconductor optical amplifiers (SOAs) operating in deep
saturation has been the subject of several studies in recent years
[1]–[12]. Compared to other noise suppression techniques
[13]–[15], SOA-based noise suppression is interesting due to
its efficiency and ease of implementation, as well as its potential
for a solution in integrated optics. It has also been utilized in 2R
regenerators for long-haul transmission systems [16], [17], and
to reduce the mode partition noise of semiconductor lasers [18].
While SOA-based intensity noise mitigation has been studied
extensively both experimentally and theoretically, no general-
purpose design tool exists to optimize the bit error rate (BER)
performance for a desired SOA-based system. For example, for
a given SOA technology and modulation format what postfil-
tering bandwidth yields the lowest BER? Does this change with
a more complex modulation format? What SOA design param-
eters have the greatest impact on the noise mitigation perfor-
Manuscript received May 29, 2008; revised September 29, 2008. Current
version published July 01, 2009. This work was supported by the 2007-2009
Quebec-Italy Executive Program for Scientific Development, Project 13.
A. Ghazisaeidi, F. Vacondio, and L. A. Rusch are with the ECE Department,
COPL, Université, Laval, Quebec, QC, CA (e-mail: rusch@gel.ulaval.ca).
A. Bononi is with the Dipartimento di Ingegneria dell’Informazione, Univer-
sita di Parma, 43100 Parma, Italy.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2009.2014787
mance? The major contribution of this paper is to provide a tool
to answer such questions.
The exact form of the photon statistics at the output of a
nonlinear amplifier is extremely complicated to derive [19]. In
the case of saturated SOAs two approximate approaches exist:
1) characterizing the noise spectra at the SOA output whether
the source is coherent [20] or incoherent [4], and 2) analytical
approximations of the probability density function (PDF) of the
output intensity when the source is coherent [21]. In the first
approach the noise spectrum at the SOA output is calculated for
continuous-wave (CW) input light. This method is useful in that
it determines the suppression bandwidth, and provides an esti-
mate of the relative intensity noise (RIN) reduction. However,
it does not provide the indispensable knowledge of the PDF of
the output intensity for a complete statistical analysis.
In [21], a PDF is obtained when the source is coherent using
perturbation theory; the ASE field added to the coherent signal
is treated as a perturbation. Analytical expressions for the PDF
are derived using path-integral methods. However, the perturba-
tion approach to find the PDF cannot be extended to incoherent
sources whose optical field is a zero mean process. In summary,
to date we can find the RIN spectrum of the photodetected sig-
nals when the source is CW, either coherent or incoherent; or we
can find the PDF of the SOA output light intensity (and, hence,
find the BER) when the SOA input is coherent CW. In either
case the analysis is limited to continuous-wave only. The im-
pact of modulation, for example through the induced patterning
effects in the amplifier [22], is not captured. Our simulator fills
these gaps.
Our interest in noise statistics is applied in particular to
noise suppression properties of a SOA on incoherent light
in SS-WDM systems. In those systems, as demonstrated by
McCoy, et al. [10], [11], optically filtering the received signal
by a channel selecting filter (CSF) at the receiver side results
in significant neutralization of the intensity noise suppression.
Although the phase-to-intensity conversion due to optical
filtering signals with noisy phase is treated in [23] for coherent
sources, no quantitative analysis of the postfiltering in the case
of SS-WDM exists in the literature. Our simulator includes not
just the SOA, but the complete SS-WDM system in order to
capture this important phenomenon.
Given the insurmountable hurdles discussed for an analyt-
ical attack, numerical techniques are favored to study the statis-
tical properties of nonlinearly amplified spectrum slices. Since a
SOA is a nonlinear element with memory, standard semi-analyt-
ical methods for additive Gaussian noise [24] are not applicable;
we must resort to Monte Carlo (MC) simulations. Numerical
0733-8724/$25.00 © 2009 IEEE
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2668 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 14, JULY 15, 2009
Fig. 1. SS-WDM link equipped with a premodulator noise suppressing SOA. MZM: Mach–Zehnder modulator,
Y
: sampled received voltage.
PDF estimation of links including nonlinear amplifiers, how-
ever, requires prohibitive computation time. It is well-known
that in estimating the probability of an event by MC simula-
tion, if is the (unknown) desired probability and is its esti-
mate, and if samples are generated in an MC simulation, we
have , where stands for expec-
tation, i.e., the relative estimation error is given by .
If the target event is the bit error rate, generating
samples results in 33% relative error in estimating a
[25]. As an example, at 2.5 Gb/s, and using a fourth-order
Runge–Kutta method to solve the Agrawal SOA equations [26]
(the lowest-complexity dynamic SOA model) MC simulations
might require days to estimate a BER . Even worse, the
more accurate space-resolved SOA model used in this paper,
to achieve an accurate match to experimental results, requires a
simulation time two orders of magnitude larger than that of the
simple Agrawal SOA model.
To overcome this huge computational burden, we use the
Multicanonical Monte Carlo (MMC) simulation method [27].
The application of MMC in optical communication has been
discussed by several authors [28]–[34]. In particular, MMC was
used to study the statistical properties of a coherent laser pulse
amplified by a saturated SOA [35], [36]. Our contribution to the
extension of these MMC methods is twofold: an extension to
incoherent light and modeling of intersymbol interference.
We present a statistical characterization of SOA-based noise
suppression and BER estimation in SS-WDM systems using an
incoherent source, which is, to the authors’ knowledge, new in
the literature. We model incoherent light, in the time domain,
as a signal whose complex envelope is a zero-mean Gaussian
process [37]. This process is filtered optically in our numerical
simulations; the level of coherence of the output light depends
on the spectral characteristics of the filter.
We present a general MMC platform. We introduce a new,
simple and efficient technique to handle the intersymbol inter-
ference (ISI) in MMC simulations. We believe our simulator
can be used to study the performance of a large variety of op-
tical links employing nonlinear amplifiers, especially various
SOA-based regenerators. The organization of the paper is as fol-
lows. In Section II, we discuss the theory of SOA-based noise
suppression. In Section III, we describe the simulator. In Sec-
tion IV, we give the numerical and experimental results, and in
Section V, we conclude. We give details of the MMC algorithm
in the Appendix.
II. SOA NOISE SUPPRESSION MECHANISM
Fig. 1 shows an SS-WDM link equipped with a premodu-
lator noise-suppressing SOA. The optical field after the slicing
filter is a band-limited, complex Gaussian random process. The
source intensity at each instant has a negative exponential distri-
bution, resulting in 0 dB of source relative intensity noise. Such
a large intensity noise introduces a BER floor that severely limits
the performance of SS-WDM. A SOA operating in saturation
placed before the modulator offers considerable intensity noise
mitigation due to self gain modulation [11], [14], [20].
The propagation equation of the optical field inside a trav-
eling-wave SOA in the moving frame is [20]
(1)
where is the optical field, is position along the longitu-
dinal axis of the SOA waveguide, is time in the moving frame,
is the SOA material gain, is the SOA loss coef-
ficient, is the linewidth enhancement factor, and is a
random process modeling the spontaneous emission inside the
SOA waveguide. The material gain is given by
(2)
where is the carrier density, is the confinement factor,
is the differential gain, and is the transparency carrier
density. The loss coefficient is
(3)
where and are the carrier independent loss coefficients
[38]. Using (2) in (3), we get
(4)
where and .
The spontaneous emission is modeled by the well-known
Langevin force terms [35], and can be written as
(5)
where is the central optical frequency, and , and
are independent zero-mean white Gaussian noise
random processes. The dynamic gain equation is [20]
(6)
where is the SOA carrier lifetime, and is the SOA satu-
ration power. The parameters of the SOA we used in this work
are listed in Table I.
According to (6), at each and , the SOA gain inversely fol-
lows fluctuations of the optical intensity; if the light intensity
increases, the gain decreases, and the increased intensity expe-
riences decreased gain in subsequent instants. Similarly, a de-
crease in the light intensity allows the gain to recover; thus, a
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GHAZISAEIDI et al.: SOA INTENSITY NOISE SUPPRESSION IN SPECTRUM SLICED SYSTEMS 2669
Fig. 2. MMC platform. RVG: random vector generator, SUT: system under test.
TABLE I
SOA PARAMETERS USED IN SIMULATIONS
decreased intensity experiences a greater gain. This self gain
modulation mechanism reduces the relative intensity noise of
the SOA output compared to its value at the input. However, the
dependence in (6) indicates the SOA gain cannot respond
to light fluctuations faster than the carrier recombination rate
. The RIN spectrum of amplified CW light has a high-pass
response (i.e., a DC dip) as fluctuations slower than the SOA
active region response time are suppressed, while those above
the suppression bandwidth remain.
The preceding discussion qualitatively explains the physical
origin of SOA-based noise suppression. The detailed quantita-
tive treatment is given in [4] and [20], where expressions for
noise spectra are calculated for the CW coherent and incoherent
sources respectively. In the following sections we use (1)–(6),
and parameters given in Table I, to form a space-resolved model
for the SOA. The SOA model is a part of a larger one for the
the SS-WDM link of Fig. 1, which will be simulated inside an
MMC platform to estimate the PDF of the sampled output signal
(see Fig. 1).
III. SYSTEM SIMULATOR
In this section, we give a top-down description of the sim-
ulator. In the next subsection we discuss the MMC platform,
while a description of the MMC algorithm is given in the Ap-
pendix. In Section III-B, we discuss the model of the optical
link, and in Section III-C, we discuss the SOA model.
A. MMC Platform
MMC simulation method [27] is an adaptive importance sam-
pling that requires minimal a priori knowledge of the system
under test (SUT). It consists of a predetermined number of cy-
cles, the first of which is a short MC simulation of the SUT.
Learning from the histogram of the output samples of the SUT
at the end of each cycle, MMC forces the SUT to produce, in
a controlled way, rare outputs more frequently than their true
probability of occurrence. The goal is that at each cycle a new
segment of the PDF tail of the SUT output is estimated. In this
subsection we give a behavioral description of our MMC plat-
form. The algorithmic details are given in the Appendix.
Fig. 2 illustrates the block-diagram of the MMC platform.
The MMC simulation consists of MMC cycles. At each
cycle random vectors are serially generated by the random
vector generator (RVG) unit. A random input vector is denoted
by . The action of the SUT on the input vector is abstractly
shown by a mapping from the -dimensional input space of
random vectors to the one-dimensional output space of the test
statistic . In this paper, SUT is the SS-WDM link equipped
with the SOA, whose corresponding is described in the
next subsection. The test statistic is the sampled voltage at the
receiver. The input vector has the following form:
(7)
is a vector of independent, identically distributed, continuous
random variables called the noise vector. is a nonnegative
integer between 0 and , where is the SUT memory in
terms of number of bit intervals. The binary representation of
is the bit pattern loaded in the SUT.
The noise vector is written as
(8)
The noise vector consists of two subvectors, , and, , and
one scalar . Subvector contains random variables used to
synthesize the input spectrum sliced random process. Subvector
is passed to the SOA model inside the SUT to simulate the
spontaneous emission events in the SOA. It contains samples
of the real and imaginary parts of [see (1) and (5) and
Section III-C] at all sampled space-time points. The scalar
represents the receiver thermal noise voltage.
At the first MMC cycle, the elements of are independent
Gaussian random variables with zero mean and unit variance.1
is distributed uniformly among integers between 0 and
. At each cycle, after all samples are generated and passed to
the SUT, the histogram of outputs is formed. The histogram cal-
culated in cycle is denoted by . The PDF estimate of is
updated and denoted by . At each cycle, the PDF warper unit
uses the latest PDF update, calculated at the end of the previous
1More precisely, element
C
is not actually zero mean, but rather its mean is
selected to match measurements.
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2670 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 14, JULY 15, 2009
Fig. 3. Model of the SS-WDM link of Fig. 1 as a SUT inside the MMC platform of Fig. 2; BPG, bit pattern generator, MOD, modulator, SF, slicing filter, CSF,
channel selecting filter, PD, photodetector, EF, electrical filter; 4th BT stands for fourth-order (lowpass) Bessel Thompson. Gain blocks are explained in the text.
cycle, to warp the PDF of the random input vectors such that
the corresponding output values are a driven toward rare events.
The first MMC cycle is an MC simulation of the SUT. In sub-
sequent cycles, the joint PDF of the spectrum sliced light, SOA
amplified spontaneous emission (ASE), the receiver noise, and
the bit pattern, represented respectively through , and ,
is warped and the PDF of is estimated down to very low prob-
abilities. At the last cycle, the latest PDF update, ,
is output and the simulator stops.
To estimate the BER, conditional PDFs of marks,
, and spaces, , are separately
estimated, and the area under the crossing tails is computed to
yield the BER. The details of all the subsystems of the MMC
platform of Fig. 2 are explained in the Appendix. The SUT is
discussed in the next subsection.
B. System Model
The block-diagram of the SUT is shown in Fig. 3. This block
diagram corresponds to the SS-WDM link of Fig. 1. At the input,
the random vector is decomposed into its subcomponents:
, and . The gain parameter is used to set the average
input power to the SOA, since all filters in the simulator are
normalized such that the vector of the impulse response has unit
norm. , and are used to adjust the noise and received
signal power, respectively.
We model the thermal light source as having a lowpass equiv-
alent optical field that is a complex Gaussian random process
[11]. Experimentally, the BBS used had a 33.580 nm 3 dB band-
width, as directly measured by the optical spectrum analyzer.
In our SS-WDM experiment we filtered this BBS source using
a 0.24 nm optical slicing filter (SF). Experimentally the BBS
spectrum is flat over the narrow band of the slicing filter; thus,
we model the output optical field of the BBS in the time do-
main by a white complex Gaussian noise, and filter it by our
simulator’s digital version of the SF. The output light will be
partially coherent, with temporal coherence determined by the
SF.
To synthesize the slicing filter, we measured the optical spec-
trum from the setup in Fig. 1, and then used the Remez exchange
method, implemented in MATLAB, to extract the tap weights
of an equivalent FIR filter, , whose frequency response
Fig. 4. Measured and simulated spectrum slices at the SOA input and output.
matches the measured optical spectrum after the slicing filter
(see Fig. 1). The spectrum-sliced optical field is then obtained
by filtering a complex white Gaussian noise by . Fig. 4
shows the measured and simulated optical spectra at the SOA
input and output.
Fig. 4 shows measured and simulated PSDs of optical fields
both at the input and output of the SOA. The excellent cor-
respondence of the measurement and simulation of the output
light over the band of interest confirms that we have well mod-
eled the coherency introduced by filtering, and validates our use
of ideal, incoherent light as an input to the MMC simulator.
The SOA model is discussed in the next subsection. As il-
lustrated in Fig. 4, we have chosen such that the measured
and simulated spectrum slices match over a 30 dB range, which
is sufficiently accurate for the simulations of this paper. The
FIR filter had 10 taps. Matching over wider bandwidths can be
achieved, if needed, at the expense of increasing the number of
taps. The binary pattern generator (BPG) subsystem accepts the
integer , and outputs a vector , which is the binary repre-
sentation of . The modulator (MOD) subsystem shapes and
upsamples bits , and adjusts the extinction ratio of the modu-
lating waveform, for instance to match the experimental values,
and finally multiplies the modulating waveform by the output
vector of the SOA model.
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GHAZISAEIDI et al.: SOA INTENSITY NOISE SUPPRESSION IN SPECTRUM SLICED SYSTEMS 2671
Fig. 5. Input-output definition of the SOA spatially resolved model.
The optical channel selecting filter (CSF) is modeled simi-
larly to the SF, and the impulse response of its digital equivalent
is . The equivalent FIR filters synthesized by the Remez
method have flat group delay. We verified that SF and CSF
filters used experimentally also have flat group delay over
their passbands. The photodetector (PD) is an ideal square-law
element, and the electrical filter (EF) is obtained as the bi-
linear implementation of an analog fourth-order low-pass
Bessel–Thompson filter [39].
C. SOA Model
Our SOA model is based on the method suggested in [35],
where authors treat the propagation equation for the optical
power as a stochastic differential equation in , and apply
second-order Runge–Kutta to solve it. We adapted the propaga-
tion solver of [35] to the optical field, added carrier dependent
and independent loss coefficients (essential for satisfactory fit
to experiments), and complemented it with an efficient solver
of the dynamic gain equation. Here we discuss how the SOA
model fits, as a subsystem, into the simulator.
The behavioral block diagram of the SOA model, as a
subsystem in Fig. 3, is depicted in Fig. 5. We denote by
the memory of the link in terms of number of bits. Optical
and electrical filters and dispersive elements contribute to
system memory. A premodulator SOA does not contribute to
the memory while a postmodulator SOA with a carrier lifetime
comparable to the modulation bandwidth enhances the memory
through the patterning effect.
We suppose each bit is upsampled times. To calculate the
SUT output at each instant, the past time samples (called
the memory window) of the input waveform are needed. Since
all waveforms are in the complex lowpass equivalent form, the
length of is . In the spatially-resolved SOA model
that is used, the SOA cavity is divided into sections.
The spontaneous emission generated in each section over the
memory window contributes to the SOA output. Subvector
contains samples of spontaneous emission events affecting the
SUT output and it has elements; the factor 2 exists
because in (5) is a complex quantity. Given that is a
single element, the dimension of the input random vector is
(9)
IV. RESULTS
In this section, we report our numerical and experimental re-
sults on statistical properties of the SS-WDM received signals
in the presence of a nonlinear SOA and the CSF. Fig. 6 shows
the experimental and simulated PDFs of the received voltage
of the SS-WDM when a premodulator SOA was employed and
the SOA input was a CW signal. The slicing filter (SF) was
0.24 nm wide, and CSF was identical to SF. The electrical filter
bandwidth was 1.87 GHz. The DC-coupled receiver was an Ag-
ilent sampling scope. The power to voltage conversion ratio was
0.75 V/W.
Fig. 6(a) is the PDF of the SOA output without electrical fil-
tering. This PDF in fact corresponds to the light intensity at the
SOA output; since the slice bandwidth was 30 GHz, and the
photodetector bandwidth was 50 GHz, the distortion induced by
the finite bandwidth PD was not significant. The receiver noise
standard deviation, when the optical input was turned off, was
8.8 V as read from the scope. Fig. 6(b) corresponds to when
a CSF is placed after SOA, but no electrical filtering is applied.
In Fig. 6(c) the internal electrical filter of the sampling scope
(bandwidth 1.87 GHz) is applied, but the CSF is removed. In
Fig. 6(d) both CSF and electrical filter are present.
We can see that in all receiver configurations the fit of MMC
and experiment is quite satisfactory. The major conclusions
from Fig. 6 are that 1) the link model is accurate enough to
generate valid statistics, and 2) the MMC platform provides
PDF estimation down to very low probabilities with reasonable
computation time.
In all cases, the average optical power input to SOA was
0 dBm, corresponding to deep saturation, and the bias current
was 495 mA. Optical attenuators at SOA output were used to
ensure the receiver electronics is not damaged. Adding optical
and electrical filters led to extra insertion losses. We did not sep-
arately characterized the insertion losses of optical and elec-
trical filters; instead, in each measurement, we recorded the
sampled waveforms together with the histogram, and calculated
the waveform mean voltage. Since the receiver noise had been
separately characterized, we could account for the losses in our
simulation. In each case, we manually set the histogram window
of the scope, and recorded their limit values. These numbers,
together with the length of the measured histogram, were used
to define the output bins in simulations. The MMC simulations
consisted of five cycles, and at each cycle random vec-
tors were generated. The SOA was divided into 50 sections,
and the simulation time-step was 4 ps. The slowest simulation
[Fig. 6(d)] took 1.5 h per MMC cycle.
To compute the BERs we need to estimate the conditional
PDFs of marks and spaces. We have to set the SUT memory in
the MMC simulator, and estimate PDFs of marks and spaces
separately. To find the system memory, we performed a set
of MMC simulations, with increasing values of the system
memory, and continued the simulations until the PDF estimates
converged. Fig. 7(a) shows the PDF estimates at the last cycle
in three separate MMC simulations with increasing , when
the SOA is placed before the modulator. The small mismatch
in the tails is due to the ISI introduced by the electrical filter.
Although not the focus of our paper, the case in which the SOA
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2672 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 14, JULY 15, 2009
Fig. 6. Measured (dots) and simulated PDFs of the received voltage in a SS-WDM link equipped with premodulator nonlinear SOA, (a) no electrical filter, no
CSF, (b) no electrical filter, with CSF, (c) electrical filter of bandwidth 1.87 GHz, no CSF, and (d) electrical filter at 1.87 GHz and CSF.
follows the modulator provides an interesting contrast in the
PDF of marks, as shown in Fig. 7(b). In the postmodulator case
much larger ISI is visible in the multimodal structure of the
“true” PDF, obtained by increasing the system memory up to
. Note that for the MMC routine is not able
to reproduce the second ISI-induced mark “rail” on the eye di-
agram, and, thus, a single-mode PDF is produced, much as in
Fig. 7(a). In the case of Fig. 7(b), the bit-rate was set to 2.5 Gb/s,
and the SOA carrier lifetime was set to one bit duration, i.e.,
400 ps. Note this is faster response than the SOA we character-
ized and used in our premodulator measurements with 170 ps
lifetime. The extinction ratio was set to 20 dB to exaggerate the
patterning effect. The conclusion of Fig. 7(b) is that our simula-
tion tool can capture a possible link memory enhancement due
to SOA nonlinear operation.
To predict the BER of our SS-WDM link equipped with
premodulator SOA-based noise suppression, we set the SUT
memory to . Fig. 8 shows the conditional PDFs on
both marks and spaces at a received power of dBm in
the following cases: (a) with neither SOA nor CSF (label
“SS-WDM”); (b) with noise cleaning SOA but without CSF
(label “SOA”); (c) with both SOA and CSF (label “SOA and
CSF”). In each case, the BER at optimal threshold is the area
under the crossing tails of the conditional PDFs. Both BER
improvement due to SOA noise cleaning, and BER degradation
due to postfiltering are visible in Fig. 8. In this example, the
BER degradation ensuing from postfiltering is not severe, due
to the rather low linewidth enhancement factor .
We next compare simulated BERs with measured BERs. The
measured conversion ratio of the Agilent 11982A PD was
320 V/W. The extinction ratio of the external Mach–Zehnder
modulator was used as a fitting parameter to match the floors
of SS-WDM BER curves; an 11.2 dB extinction ratio was used
in all simulations. For simulated BERs we swept the input
power, found the optimal threshold (intersection of conditional
PDFs), and calculated the BER from the conditional PDFs.
Both 1.25 Gb/s and 2.5 Gb/s BERs were investigated. Fig. 9
reports both measured and simulated BERs for the three cases
already illustrated in Fig. 8. The receiver and BERT noises
were characterized using the techniques discussed in [40].
We note the excellent match between MMC simulation and
experiments, clearly illustrating the performance estimation
accuracy of the MMC method when a reliable simulator of the
SUT is available.
Finally, we comment on possible extensions of the presented
work. The SOA model used in this study included neither SOA
ultrafast processes nor polarization effects. Neglecting ultrafast
dynamics is justified for SS-WDM, as the optical field input to
the SOA has a narrow linewidth (0.24 nm) set by the SF. The
signal variations at the SOA input are much slower than typical
time constants of carrier heating and spectral hole burning [41];
hence, we neglected these processes in our study. By replacing
the present SOA model with one of the well-known models that
include ultrafast dynamics, we could investigate these effects.
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GHAZISAEIDI et al.: SOA INTENSITY NOISE SUPPRESSION IN SPECTRUM SLICED SYSTEMS 2673
Fig. 7. Simulated PDF of marks corresponding to different values of system
memory. (a) The premodulator setup with the parameters coming from the ex-
periment. (b) The postmodulator setup with a hypothetical SOA slower than
what we used in the measurements.
Fig. 8. Simulated conditional PDFs of marks and spaces corresponding
to: SS-WDM (label “SS-WDM”), SS-WDM with premodulator SOA (label
“SOA”), and SS-WDM with premodulator SOA and CSF (label “SOA and
CSF”).
Similarly, neglectingpolarization effects was not critical for our
experimental validation. We used a polarization beam splitter
after the BBS, and controlled the polarization state of the light
Fig. 9. Measured and simulated BERs.
both at the input of the SOA, and at the MZM input using polar-
ization controllers. The measurements were recorded after ad-
justing the SOA input polarization for maximum gain. The im-
pact of cross polarization on the light statistics can be studied by
replacing the SOA model in our simulator with a one including
polarization effects, e.g., [42], and enlarging the input vector
space to produce random input vectors for TE, and TM polar-
ization states.
V. CONCLUSION
In this paper, we described a simulation tool to evaluate the
performance of optical links employing nonlinear SOAs. We
applied our simulator to study noise mitigation of SS-WDM
systems by a premodulator SOA. We modeled the broadband
source, slicing, channel selecting, and electrical filters all in time
domain. We used a spatially-resolved SOA model including dis-
tributed carrier dependent, and carrier independent loss mecha-
nisms and ASE. We completed the standard MMC simulation
algorithm with a fast and efficient pattern warping technique
to capture the ISI. We showed that both the statistics of the
CW slices, and the BERs at various bit-rates can be predicted
with our simulation tool. In particular, we are able to quantify
the impact of receiver optical filtering effect on system perfor-
mance. The simulator can be useful as a design tool to optimize
SS-WDM systems, as well as studying various SOA-based re-
generative systems.
APPENDIX
Our goal in this Appendix is to provide sufficient detail for
other researchers to make use of our simulation tool. We will
present in broad outlines the techniques we have exploited in
our simulator, without going into detailed development. In the
following, we first give a general description of the MMC tech-
nique, then we give details of various subsystems.
The SUT is represented by an abstract mapping from
an input space to an output space. The elements of the input
space are vectors with a known PDF , possibly with
an unknown normalization constant [27]. We are interested in
estimating, by simulation, the unknown probability mass func-
tion (PMF) of the SUT output, , over a prespecified set of
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2674 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 14, JULY 15, 2009
output space bins that extend down to the tail. The multicanon-
ical Monte Carlo (MMC) is an adaptive importance-sampling
technique aiming to solve this problem by adapting to a flat his-
togram of the output samples. All flat histogram methods share
the basic idea that given a limited number of output realizations,
the best one can do to estimate the probability of a series of
events is to evenly distribute the samples over those events. In
our case, the events are SUT output bins.
We suppose the output space is divided into bins in-
dexed by integer . The MMC cycle number is
denoted by , where is the number of
MMC cycles. The PMF estimate obtained at the end of the th
cycle is denoted by . The output PMF is initialized to
(10)
where is the number of samples generated per MMC cycle.
We denote the th input sample, generated within the th cycle
by . The corresponding output sample is ,
with . The normalized histogram of the set of
output samples over the prespecified output bins is denoted by
.
The strategy of MMC is to first perform a “short” MC simula-
tion, during which a set of input samples with
the known PDF is generated, the corresponding set of
output values is obtained, and a first estimate
of the PMF of the output random variable is formed. Then
the first cycle is finished. In the second cycle, the input samples
are generated such that their distribution fol-
lows the following warped PDF:
(11)
where is a nomalization factor, and the “bin” function returns
the bin index of output samples. Drawing input samples from
the input warped PDF in (11) forces output samples to fall more
on the tail than on the mode, so that will be flatter than
. Cycles continue until the output histogram is sufficiently
flat, that is, when the unwarped output PDF has been estimated
to sufficient precision in the tails to achieve the simulation goals
(e.g., down to a .). Then is output for
all bins and MMC simulation stops.
Having described the MMC algorithm we proceed to discuss
the various subsystems. Fig. 10 shows the details of the subsys-
tems of the MMC platform block diagram of Fig. 2. We have di-
vided the MMC platform into four basic subsystems, i.e., PDF
warper, random vector generator (RVG), histogram update, and
PDF update. We briefly discuss each subsystem here.
We start with the PDF warper subsystem, the most im-
portant subsystem of the MMC platform. The adaptation in
the MMC approach requires generation of realizations in the
multidimensional input space following the statistics of the
very irregular multidimensional warped PDF that is fixed for
the cycle, see (11). We refer to the warped PDF of the th cycle
by . The input realizations (or samples) are generated using
a Markov chain Monte Carlo (MCMC) technique known as
Fig. 10. Detailed block-diagram of the MMC platform. RVG: random vector
generator, NVG: noise vector generator, PNG: pattern number generator, SUT:
system under test, D represents unit delay.
Fig. 11. Flowchart of the PDF Warper.
U
[0
;
1]
is a uniform RV on [0,1].
Metropolis-Hastings. The idea is to propose input samples ac-
cording to their unwarped distribution , which is known,
regular and well-behaved, and then either reject or accept the
proposed samples (rejection means that the previous realization
is reused) per a specified, randomized criterion. Proposal of
new samples is done by RVG, and will be discussed later. The
resulting dependent sequence of samples from will
asymptotically have the desired warped PDF , provided
proper selection of the randomized rejection criterion. For an
entire cycle, a Metropolis-Hastings MCMC algorithm runs
within the (input) PDF warper. The flowchart of the PDF
warper is shown in Fig. 11.
Now we consider RVG. The RVG uses Markov chain Monte
Carlo (MCMC) techniques to facilitate the generation of sam-
ples by the RVG, as illustrated in the flowchart in Fig. 12. The
Metropolis-Hastings MCMC techniques were used in the PDF
warper as the warped distribution is not well behaved. The RVG
uses MCMC to instead favor generation of samples in restrained
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GHAZISAEIDI et al.: SOA INTENSITY NOISE SUPPRESSION IN SPECTRUM SLICED SYSTEMS 2675
Fig. 12. Flowchart of the RVG.
subsets of the input space. The simulator can, thus, explore a cer-
tain area of the output space in greater detail, instead of covering
the entire area in a more “willy-nilly” fashion. While the pro-
posed input vectors are now correlated, the net effect is to lead to
a better overall convergence of the MMC adaptation. Consider
first the PNG. PNG generates uniformly distributed over the
set of integers . With probability an inde-
pendent sample is generated (using ), while with
probability the sample is constrained to fall in a certain
neighborhood of the old sample [44]. We used of 0.1 in
our simulations. calls a standard random integer gen-
erator routine to generate the new proposal independent from
the past. On the other hand, given proposes
a new pattern through , where de-
notes modulo addition. The innovation is constrained to
permit only a limited number of bits to flip. is a zero-mean,
discrete, uniformly distributed random variable taking integer
values from to . In our simulations, we used ,
i.e., from pattern we go either to ,orto ,orto
.
Consider next the RNG which generates a vector of Gaussian
random variables. With probability a sample of
independent, identically distributed zero-mean, unit variance
Gaussian elements is generated (using ), while with
probability the sample is either constrained to fall in a
certain neighborhood of the old sample or is simply
recycled (using ). consists of inde-
pendent Markov chains. Each chain generates an innovation
that is uniformly distributed over . We used
in our simulations. Note that parameters ,
and were chosen by trial and error. With probability the
previous sample is reused with no innovation where
(12)
With probability , the innovation is added to the previous
sample to generate the . The RVG flowchart is given
in Fig. 12.
Having now described all the component parts, we give in
Fig. 13 the overall flowchart of the MMC algorithm and discuss
how the input warped pdf is generated after each cycle.
The histogram update subsystem collects accepted output
samples and calculates , over the output bins. We assume
represents the number of outputs found in the th
bin at the end of cycle , normalized by the total number of
iterations .
The PDF update subsystem uses and the latest output
PDF estimate to make a new estimate; is the new proba-
bility that the output will fall in the th bin. The probability of
the first bin is , and we then use [31], [27]
(13)
where
(14)
(15)
The resulting PMF is normalized to assure the total proba-
bility is one.2
Finally, we note that the PDF warper does not calculate (11)
directly to achieve warping. In fact the warping exploits the ratio
. This ratio reduces to
(16)
2
~
g
and
^
g
should not be confused with the SUT mapping
g
(
1
)
.
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2676 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 14, JULY 15, 2009
Fig. 13. Flowchart of the MMC.
so that the normalization constants for the warped PDF need
never be found—an extremely desirable characteristic of the
MMC algorithm for high-dimensional inputs such as ours.
REFERENCES
[1] Y. Katagiri, K. Suzuki, and K. Aida, “Intensity stabilisation of spec-
trum-sliced Gaussian radiation based on amplitude squeezing using
semiconductor optical amplifiers with gain saturation,” Electron. Lett.,
vol. 35, pp. 1362–1364, 1999.
[2] S. J. Kim, J. H. Han, J. S. Lee, and C. S. Park, “Intensity noise sup-
pression in spectrum-sliced incoherent light communication systems
using a gain-saturated semiconductor optical amplifier,” IEEE Photon.
Technol. Lett., vol. 11, pp. 1042–1044, 1999.
[3] M. Zhao, G. Morthier, R. Baets, and J. Dekoster, “Investigation of the
intensity noise reduction using a saturated semiconductor optical am-
plifier in spectrum sliced WDM systems,” CLEO, pp. 383–384, 2001.
[4] M. Zhao, G. Morthier, and R. Baets, “Analysis and optimization of in-
tensity noise reduction in spectrum-sliced WDM systems using a sat-
urated semiconductor optical amplifier,” IEEE Photon. Technol. Lett.,
vol. 14, pp. 390–392, 2002.
[5] T. Yamatoya and F. Koyama, “Noise suppression of spectrum-sliced
light using semiconductor optical amplifiers,” Electron. Commun. Jpn.
Part 2, vol. 86, pp. 28–35, 2003.
[6] T. Yamatoya and F. Koyama,“Optical preamplifier using optical mod-
ulation of amplified spontaneous emission in saturated semiconductor
optical amplifier,” J. Lightw. Technol., vol. 22, pp. 1290–1295, 2004.
[7] T.-Y. Kim, “Intensity noise suppression of 2.5 Gb/s spectrum-sliced
incoherent signal using a gain-saturated SOA injected by broadband
light,” OECC, pp. 46–47, 2004.
[8] D. Forsyth, “Spectrum-sliced broadband source intensity noise reduc-
tion using semiconductor optical amplifier nonlinear gain compres-
sion,” Proc. SPIE, vol. 5825, pp. 448–454, 2005.
[9] F. Koyama and H. Uenohara, “Noise suppression and optical ASE
modulation in saturated semiconductor optical amplifiers,” in Proc.
38th Asilomar Conf. Signals, Systems and Computers, 2004, vol. 1, pp.
198–202.
[10] A. D. McCoy, B. C. Thomsen, M. Ibsen, and D. J. Richardson,
“Filtering effects in a spectrum-sliced WDM system using SOA-based
noise reduction,” IEEE Photon. Technol. Lett., vol. 16, pp. 680–682,
2004.
[11] A. D. McCoy, P. Horak, B. C. Thomsen, M. Ibsen, and D. J.
Richardson, “Noise suppression of incoherent light using a gain-sat-
urated SOA: Implications for spectrum-sliced WDM systems,” J.
Lightw. Technol., vol. 23, pp. 2399–2409, 2005.
[12] A. D. McCoy, P. Horak, M. Ibsen, and D. J. Richardson, “Performance
comparison of spectrum-slicing techniques employing SOA-based
noise suppression at the transmitter or receiver,” IEEE Photon.
Technol. Lett., vol. 18, pp. 1494–1496, 2006.
[13] P. R. Morkel, R. I. Laming, H. O. Edwards, and D. N. Payne, “Elimi-
nation of excess photon noise from fiber super-radiant sources,” CLEO
90, pp. 154–155, 1990.
[14] A. J. Keating, W. T. Holloway, and D. D. Sampson, “,” IEEE Photon.
Technol. Lett., vol. 7, pp. 1513–1515, 1995.
[15] J. Han, J. W. Ko, J. S. Lee, and S. Y. Shin, “0.1-nm narrow bandwidth
transmission of a 2.5-Gb/s spectrum-sliced incoherent light channel
using an all-optical bandwidth expansion technique at the receiver,”
1998, vol. 10, pp. 1501–1503.
[16] F. Ohman, S. Bischoff, B. Tromborg, and J. Mork, “Noise and regen-
eration in semiconductor waveguides with saturable gain and absorp-
tion,” IEEE J. Quant. Electron., vol. 40, pp. 245–255, 2004.
[17] T. Vivero, N. Calabretta, I. Tafur, Monroy, G. Carvalho, Kassar, F.
Ohman, K. Yvind, A. Gonzalez-Marcos, and J. Mork, “10 Gb/s-NRZ
optical 2R-regeneration in two-section SOA-EA chip,” LEOS, pp.
806–807, 2007.
[18] K. Sato and H. Toba, “Reduction of mode partition noise by using semi-
conductor optical amplifiers,” IEEE J. Sel. Topics Quant. Electron., vol.
7, pp. 328–333, 2001.
[19] E. Desurvire, Erbium-Doped Fiber Amplifiers, Principles and Appli-
cations. New York: Wiley-Interscience, 2002.
[20] M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semicon-
ductor optical amplifiers: Relation between semiclassical and quantum
descriptions,” IEEE J. Quant. Electron., vol. 34, pp. 869–878, 1998.
[21] F. Ohman, J. Mork, and B. Tromborg, “Output power PDF of a sat-
urated semiconductor optical amplifier: Second-order noise contribu-
tions by path integral method,” IEEE J. Quant. Electron., vol. 43, pp.
1188–1197, 2007.
[22] A. A. M. Saleh and I. M. I. Habbab, “Effects of semiconductor-op-
tical-amplifier nonlinearity on the performance of high-speed inten-
sity-modulation lightwave systems,” IEEE Trans. Commun., vol. 38,
pp. 839–846, 1990.
[23] G. J. Foschini, G. Vannucci, and L. J. Greenstein, “Envelope statis-
tics for filtered optical signals corrupted by phase noise,” IEEE Trans.
Commun., vol. 37, pp. 1293–1302, 1989.
[24] E. Forestieri, “Evaluating the error probability in lightwave systems
with chromatic dispersion, arbitrary pulse shape and pre- and postde-
tection filtering,” J. Lightw. Technol., vol. 18, pp. 1493–1503, 2000.
[25] M. C. Jeruchim, “Techniques for estimating the bit error rate in the
simulation of digital communication systems,” J. Sel. Areas. Commun.,
vol. SAC-2, pp. 153–170, 1984.
[26] G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral
broadening of optical pulses in semiconductor laser amplifiers,” IEEE
J. Quant. Electron., vol. 25, pp. 2297–2306, 1989.
[27] B. A. Berg, “Introduction to multicanonical monte carlo simulations,”
Fields Instrum. Commun., vol. 26, no. 1, pp. 1–24, 2000, (also available
at arXiv:cond-mat/9909236v1).
[28] D. Yevick, “Multicanonical communication system modeling-appli-
cation to PMD statistics,” IEEE Photon. Technol. Lett., vol. 14, pp.
1512–1514, 2002.
[29] D. Yevick and T. Lu, “Improved multicanonical algorithms,” J. Opt.
Soc. Amer. A, vol. 23, pp. 2912–2918, 2006.
[30] T. Lu, D. O. Yevick, L. Yan, B. Zhang, and A. E. Willner, “An exper-
imental approach to multicanonical sampling,” IEEE Photon. Technol.
Lett., vol. 16, pp. 1978–1980, 2004.
Authorized licensed use limited to: BIBLIOTHEQUE DE L'UNIVERSITE LAVAL. Downloaded on June 01,2010 at 20:43:19 UTC from IEEE Xplore. Restrictions apply.
GHAZISAEIDI et al.: SOA INTENSITY NOISE SUPPRESSION IN SPECTRUM SLICED SYSTEMS 2677
[31] R. Holzlohner and C. R. Menyuk, “Use of multicanonical Monte Carlo
simulations to obtain accurate bit error rates in optical communications
systems,” Opt. Lett., vol. 28, no. 20, pp. 1894–1896, Oct. 2003.
[32] A. O. Lima and C. R. Menyuk, “Error estimation in multicanonical
Monte Carlo simulations with applications to polarization-mode-dis-
persion emulators,” J. Lightw. Technol., vol. 23, pp. 3781–3789, 2005.
[33] W. Pellegrini, J. Zweck, C. R. Menyuk, and R. Holzlohner, “Computa-
tion of bit error ratios for a dense WDM system using the noise covari-
ance matrix and multicanonical Monte Carlo methods,” IEEE Photon.
Technol. Lett., vol. 17, pp. 1644–1646, 2005.
[34] Y. Yadin, M. Shtaif, and M. Orenstein, “Bit-error rate of optical DPSK
in fiber systems by multicanonical Monte Carlo simulations,” IEEE
Photon. Technol. Lett., vol. 17, pp. 1355–1357, 2005.
[35] A. Bilenca and G. Eisenstein, “Statistical noise properties of an op-
tical pulse propagating in a nonlinear semiconductor optical amplifier,”
IEEE J. Quant. Electron., vol. 41, pp. 36–44, 2005.
[36] A. Bilenca and G. Eisenstein, “Fokker-planck and langevin analyses
of noise accompanying the amplification of optical pulses in semicon-
ductor optical amplifiers,” J. Opt. Soc. Amer. B, vol. 22, pp. 1632–1639,
2005.
[37] J. W. Goodman, Statistical Optics. New York: Wiley, 1985.
[38] M. J. Connelly, “Wide-band steady-state numerical model and param-
eter extraction of a tensile-strained bulk semiconductor optical ampli-
fier,” IEEE J. Quant. Electron., vol. 43, pp. 47–56, 2007.
[39] M. C. Jeruchim, P. Balaban, and K. S. Shanmugan, Simulation of Com-
munication Systems, 2nd ed. Boston, MA: Kluwer, 2000.
[40] S. Ayotte, M. Rochette, J. Magne, L. A. Rusch, and S. LaRochelle, “Ex-
perimental verification and capacity prediction of FE-OCDMA using
superimposed FBG,” J. Lightw. Technol., vol. 23, pp. 724–731, 2005.
[41] A. Mecozzi and J. Mork, “Saturation effects in nondegenerate four-
wave mixing between short optical pulses in semiconductor laser am-
plifiers,” IEEE J. Sel. Topics Quant. Electron., vol. 3, pp. 1190–1207,
1997.
[42] H. J. S. Dorren, D. Lenstra, L. Yong, M. T. Hill, and G.-D. Khoe, “Non-
linear polarization rotation in semiconductor optical amplifiers: Theory
and application to all-optical flip-flop memories,” IEEE J. Quant. Elec-
tron., vol. 39, pp. 141–148, 2003.
[43] B. A. Berg and T. Neuhaus, “Multicanonical ensemble: A new ap-
proach to simulate first-order phase transitions,” Phys. Rev. Lett., vol.
68, p. 9, 1992.
[44] Y. Guan, R. Fleissner, P. Joyce, and S. M. Krone, “Markov chain monte
carlo in small worlds,” Statist. Comput., vol. 16, no. 2, pp. 193–202,
2006.
Amirhossein Ghazisaeidi received the M.A. degree
in communications systems and the B.S. degree in
electrical engineering from the Sharif University of
Technology, Tehran, Iran. He is currently pursuing
the Ph.D. degree in the ECE Department, Laval Uni-
versity, Quebec, Canada.
His research interests include optical-code-di-
vision multiple access and spectrum sliced WDM
using incoherent sources, dynamics, and noise prop-
erties of optical amplifiers, modeling optoelectronic
devices, and performance analysis of optical links.
Francesco Vacondio was born in Reggio Emilia,
Italy, in 1981. In October 2006, he received the
“Laurea Magistrale” degree (cum laude) in telecom-
munications engineering from the University of
Parma, Parma, Italy.
Since September 2005, he has been with the De-
partment of Electrical and Computer Engineering,
Universit Laval, Quebec, Canada, where his research
interests include semiconductor optical amplifiers,
phase modulated formats, and microwave photonics.
Alberto Bononi received the Laurea degree in elec-
tronics engineering (cum laude) from the University
of Pisa, Italy, in 1988, and the M.A. and Ph.D. de-
grees in electrical engineering from Princeton Uni-
versity, Princeton, NJ, 1992, and 1994, respectively.
Currently, he is an Associate Professor of telecom-
munications at the School of Engineering, Univer-
sità di Parma, Italy. He teaches courses in probability
theory and stochastic processes, telecommunications
networks, and optical communications. In 1990, he
was with the GEC-Marconi Hirst Research Centre,
Wembley, U.K., on a Marconi S.p.A. project on coherent optical systems. From
1994 to 1996, he was an Assistant Professor in the Electrical and Computer En-
gineering Department, State University of New York (SUNY), Buffalo, teaching
courses in electric circuits and optical networks. In the summers of 1997 and
1999, he was a Visiting Faculty at the Département de Genie Électrique, Uni-
versité Laval, QC, Canada, doing research on fiber amplifiers. His present re-
search interests include system design and performance analysis of high-speed
all-optical networks, nonlinear fiber transmission for WDM systems, linear and
nonlinear polarization mode dispersion, and transient gain dynamics in optical
amplifiers.
Leslie Ann Rusch (S’91–M’94–SM’00) received
the B.S.E.E. (honors) degree from the California
Institute of Technology, Pasadena, in 1980, and the
M.A. and Ph.D. degrees in electrical engineering
from Princeton University, Princeton, NJ, in 1992
and 1994, respectively.
In 1994, she joined the Department of Electrical
and Computer Engineering, Universit Laval, Qubec,
QC, Canada, where she is currently a Full Professor
performing research in wireless and optical commu-
nications. She spent two years as the manager of a
group researching new wireless technologies at Intel Corp. from 2001 to 2002.
Her research interests include optical-code-division multiple access and spec-
trum sliced WDM using incoherent sources for passive optical networks; semi-
conductor and erbium-doped optical amplifiers and their dynamics; radio over
fiber; and in wireless communications, high performance, reduced complexity
receivers for ultrawideband systems employing optical processing.
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