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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 1, JANUARY 2007
207
Field Trial of 3-WDM × 10-OCDMA × 10.71-Gb/s
Asynchronous WDM/DPSK-OCDMA Using Hybrid
E/D Without FEC and Optical Thresholding
Xu Wang, Senior Member, IEEE, Naoya Wada, Member, IEEE, Tetsuya Miyazaki, Member, IEEE,
Gabriella Cincotti, Senior Member, IEEE, and Ken-ichi Kitayama, Fellow, IEEE
Abstract—A cost-effective hybrid wavelength division multiplexing (WDM), optical code division multiple access (OCDMA)
scheme by sharing a single multiport encoder in a central office
and using tunable decoders in an optical network unit has been
proposed and demonstrated in a field trial. A 111-km error-free
field transmission of asynchronous 3-WDM × 10-OCDMA ×
10.71 Gb/s/user has been achieved with differential phase-shift
keying for data modulation and balanced detection. Forwarderror-correction and optical-thresholding techniques were not
used in the experiment.
Index Terms—Beat noise, differential phase-shift key (DPSK),
fiber-optics communication, field trial, multiple-access interference (MAI), optical code division multiple access (OCDMA), wavelength division multiplexing (WDM).
I. I NTRODUCTION
T
HE OPTICAL code division multiple access (OCDMA)
technique is an attractive candidate for next-generation
broadband access networks. Fig. 1 illustrates a basic architecture and working principle of an OCDMA passive optical
network (PON) network. In the OCDMA-PON network, the
data are encoded into a pseudorandom optical code (OC) by the
OCDMA encoder at the transmitter, and multiple users share
the same transmission media by assigning different OCs to
different users. At the receiver, the OCDMA decoder recognizes the OCs by performing a matched filtering, where the
autocorrelation for the target OC produces high-level output,
while the cross correlation for undesired OC produces lowlevel output. Finally, the original data can be recovered after
electrical thresholding. Due to the all-optical processing for
encoding/decoding, the OCDMA has the unique features of
allowing a fully asynchronous transmission with low-latency
access, soft capacity on demand, protocol transparency, simplified network management, and increased flexibility of qualityof-service (QoS) control [1]–[3]. In addition, since the data are
Manuscript received June 30, 2006; revised September 10, 2006.
X. Wang, N. Wada, and T. Miyazaki are with the National Institute of Communication and Information Technology (NICT), Koganei, Tokyo 184-8795,
Japan (e-mail: [email protected]; [email protected]; [email protected]).
G. Cincotti is with the Department of Applied Electronics, University of
Roma Tre, I-00146 Rome, Italy (e-mail: [email protected]).
K. Kitayama is with the Department of Electrical, Electronic and Information
Engineering, Osaka University, Osaka 565-0871, Japan (e-mail: kitayama@
comm.eng.osaka-u.ac.jp).
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.2006.887186
encoded into pseudorandom OCs during transmission, it also
has the potential to enhance the confidentiality in the network
[4]–[6].
Recently, the coherent OCDMA technique, where encoding
and decoding are based on the phase and amplitude of optical
field instead of its intensity, is receiving much attention for
its overall superior performance over incoherent OCDMA and
the development of compact and reliable en/decoders (E/Ds)
[7]–[14]. In these coherent OCDMA systems, an ultrashort
optical pulse is either spectrally encoded time spread by a highresolution phase E/D [8] or spatial-light phase modulator (PM)
[9], [10] or directly time-spread encoded by a superstructured
fiber Bragg grating (SSFBG) [11]–[13] or multiport E/D with a
waveguide grating configuration [14], [15].
In a multiuser coherent OCDMA network, the major noise
sources are the signal-interference (SI) beat noise (coherent
noise) and the multiple-access interference (MAI) noise
(incoherent noise) [3]. Basically, in a coherent OCDMA
system with chip-rate detection, the SI beat noise dominates
the performance, while with the data-rate detection, the MAI
is dominating noise. Time gating [7]–[9], [16] and optical
thresholding (OT) [9], [10], [16]–[18] can be used to suppress
the MAI, enabling the data-rate detection. As for the SI noise
mitigation, most of the previous approaches use a synchronous
OCDMA, which operates under the best-case situation by a
proper timing coordination in the chip or slot level to carefully
avoid the overlaps between signal and interference [7]–[11],
[16]. Synchronous OCDMA can somewhat increase frequency
efficiency for transmission [16]; however, for practical access
network applications, the capability of asynchronous multiuser
access is of a key attribute. In an asynchronous OCDMA, signal
and interferers are received with a random overlap; therefore,
the system should be able to operate in the worst-case scenario
without any timing coordination to guarantee asynchronous
OCDMA. One effective solution is using an ultralong OC [13],
[18] and E/D with a very high power contrast ratio (PCR)
between auto-/cross correlation [14], [15] to suppress the interference level in an asynchronous environment. Another solution
is to use forward-error-correction (FEC) techniques to enhance
the noise tolerance of the system. Multiuser coherent OCDMA
at a data rate as high as 10 Gb/s has been successfully demonstrated [15], [18] by employing the SSFBG for ultralong OC
processing, supercontinuum generation-based OT [17], AWGtype E/D with high PCR, and FEC techniques. However, these
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Fig. 1. Working principle of OCDMA PON network.
Fig. 2. System models of (a) OOK-OCDMA with power detection and (b) DPSK-OCDMA with balanced detection.
are still not a cost-effective solution, which is the major concern
for practical applications. Besides, there have been few reports
on field trials of multiuser OCDMA transmission so far [19].
In this paper, for the first time, we demonstrate the field
trial of a cost-effective asynchronous wavelength division multiplexing (WDM)/OCDMA network using the multiport E/D
in the central office, tunable transversal-filter (TVF)-type decoder in optical network unit (ONU), and differential-phaseshift-keying (DPSK) data format. Asynchronous signals of
three wavelengths (400-GHz spacing) and 10-OCDMA users at
10.71 Gb/s/user have been successfully transmitted with a bit
error rate (BER) < 10−9 without using the OT and the FEC.
II. A DVANTAGES OF DPSK-OCDMA W ITH
B ALANCED D ETECTION
The most used modulation format for payload data in
OCDMA is ON – OFF keying (OOK) with power detection,
which is referred as OOK-OCDMA. Recently, the coherent
OCDMA with DPSK modulation format and balanced detection (DPSK-OCDMA) has been proposed and demonstrated
using 511-chip SSFBG E/D [6]. Fig. 2(a) and (b) shows the
theoretical models of the OOK- and DPSK-OCDMA, respectively. In the DPSK-OCDMA system, the data are encoded by
a DPSK encoder, the intensity modulator is replaced by a PM,
and the photodetector is replaced by a 1-bit delay interferometer
as a DPSK decoder followed by a balanced-detector. Fig. 3
illustrates the eye diagrams and noise distributions (probability
density function) of the different OCDMA schemes. Fig. 3(a)
shows those of the received signals in OOK-OCDMA with
fixed electrical threshold (Th) and optimal Th (Opt Th). Marks
“1” and “0” have an asymmetric noise distribution, as shown
in the figure. With the changing of the active users’ number, a
dynamic Th level setting is required in the receiver to achieve a
minimum BER by finding the Opt Th. However, both the realtime active users number estimates and dynamical threshold
setting are still practical issues in OCDMA receivers and will
result in additional cost. Fig. 3(b) shows the eyes and noise
WANG et al.: FIELD TRIAL OF 3-WDM × 10-OCDMA × 10.71-Gb/s ASYNCHRONOUS WDM/DPSK-OCDMA
209
Fig. 3. Comparison of eye diagrams and noise distributions of (a) OOK-OCDMA without OT, (b) OOK-OCDMA with OT, and (c) DPSK-OCDMA with fixed
threshold at 0.
Fig. 4. Performance comparisons (number of active users for a given BER versus interference level) between OOK-OCDMA and DPSK-OCDMA.
(a) Comparison between DPSK-OCDMA and OOK-OCDMA with fixed and optimal threshold (with BER = 6e−5 ). (b) Comparison between DPSK-OCDMA
and OOK-OCDMA with and without OT (with BER = 1e−9 ).
distribution in the OOK-OCDMA system with the OT. The performance could be significantly improved with the elimination
of the MAI noise by an ideal OT. However, the performance
of practical OT cannot be perfect. Supposing that the optical
signal-to-noise ratio (OSNR) of an optical signal changes from
OSNR1 (dB) to OSNR2 (dB) after going through an OT, the
OSNR improvement of the OT is OSNR2 − OSNR1 (dB). The
performance improvement of a system using the OT is highly
dependent on its OSNR improvement. This will be further
shown in the following numerical results. Fig. 3(c) shows those
in the DPSK-OCDMA. The noise has symmetric distributions
for marks “1” and “0” in this system. Therefore, minimum
BER could be easily achieved with a fixed Th at 0. Fig. 4
shows the numerical results for the comparison using these
models [3], [6]. Fig. 4(a) shows the number of active users
(K) that can be supported with BER ≤ 6 × 10−5 versus the
average interference level ζ, which is defined as the average
cross-to-autocorrelation ratio (in decibels) [3]. The three curves
from right to left are for DPSK-OCDMA, OOK-OCDMA
with Opt Th, and fixed Th, respectively. For a given value
of K, the DPSK-OCDMA can tolerate about 4 dB higher ξ
comparing to OOK-DPSK with Opt Th and 5–6 dB higher
comparing to OOK-DPSK with fixed Th. This is a significant
improvement for OCDMA because more active users could
be accommodated with a shorter OC length. For example, by
using a 511-chip OC (ξ ∼
= −27.1 dB), about six active users
(K = 6) could be supported at this BER for OOK-OCDMA
with fixed Th, K = 9 for OOK-OCDMA with Opt Th, and
K = 17 for DPSK-OCDMA. Fig. 4(b) shows K versus ζ with
BER ≤ 1 × 10−9 . From right to left, the thick curves are for
DPSK-OCDMA and OOK-OCDMA without OT (with Opt
Th), respectively, while the thin curves are for OOK-OCDMA
using ideal OT and an OT with 5-dB OSNR improvement,
respectively. The performance improvement of using the OT
in the OOK-OCDMA can be clearly seen, and it is dependent
on the OSNR improvement of OT in the practical system.
On the other hand, the performance of DPSK-OCDMA is close
to OOK-OCDMA with OT. Therefore, the DPSK-OCDMA
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Fig. 5. Proposed WDM/OCDMA network architecture.
is superior over the OOK-OCDMA with advantages of improved receiver sensitivity, better tolerance to beat noise and
MAI noise without OT, and no need for dynamic Th level
setting [6].
III. F IELD T RIAL OF M ULTIUSER WDM/DPSK-OCDMA
A. Consideration of a Cost-Effective WDM/OCDMA
The WDM technique is very successful in current fiberoptic communication networks. A prospective broadband access network with a high spectral efficiency will be a hybrid
WDM/OCDMA network [20]. Fig. 5 shows the architecture
of the proposed cost-effective WDM/OCDMA network, which
uses a large-scale multiport E/D in the central office and a lowcost E/D in the ONU. The multiport E/D [15], [21] has very
high PCR between auto- and cross-correlation signals, which
can significantly suppress the MAI and the beat noise with
a short OC [15]. The multiport E/D with a periodic spectral
response can process multiple OCs in multiple wavelength
bands with a single device as shown in the inset, and the cost
will be shared by all the subscribers. At the ONU side, fixed
SSFBG or TVF can be used as the low-cost E/D. The hybrid
of SSFBG and TVF-type E/D has already been verified for use
as OC E/D [22]. Here, we further used the multiport E/D as the
encoder and the tunable TVF-type E/D as the decoder to verify
that this hybrid can work properly as well. Fig. 6(a) shows the
waveforms of a generated 16-chip 200 Gchip/s OCs from the
16 × 16 multiport E/D (upper) and TVF-type E/D (lower).
The phase pattern of the represented OC is shown on the top of
the figure. The auto-/cross correlations of the hybrid of the multiport encoder/tunable TVF decoder (hybrid E/D) are shown in
Fig. 6(b). The measured PCRs are shown in Fig. 6(c), together
with those of multiports E/D for four different OCs. They are
in good agreement with each other, and the values range from
12 to 22 dB, which is one key to enable multiuser asynchronous
OCDMA by suppressing the noises.
On the other hand, the DPSK-OCDMA with a balanced
detection will be another key to enable multiuser asynchronous
OCDMA at 10 Gb/s without OT and FEC, due to its superior
noise tolerance over a conventional OOK-OCDMA.
B. Experiments
Fig. 7 shows the experimental setup of the field trial for
multiuser WDM/DPSK-OCDMA. The field trial was done in
an optical testbed of the Japan Gigabit Network II (JGNII)
[23]. JGNII is a nationwide open testbed network as shown in
Fig. 8(a); it is operated by the National Institute of Communication and Information Technology as an ultrahigh-speed testbed
network for R&D collaboration between industry, academia,
and government. The fiber used in this experiment is installed in
the field between our laboratory in Koganei City and Otemachi
of downtown Tokyo in a loop-back configuration, as shown in
Fig. 8(a). Fig. 8(b) shows several photos of the experimental
setup.
Three mode-lock laser diodes generated 3-WDM pulse signals with about 3.2-nm (400 GHz) channel spacing. The
∼1.8-ps optical pulses were generated at a repetition rate of
10.709 GHz with central wavelengths of 1550.2, 1553.4, and
1556.6 nm, respectively. Each signal was modulated by a
lithium niobate PM (LN-PM) separately with 231 − 1 pseudorandom bit sequence from independent data sources. The
signals were then multiplexed and sent to the port #1 of the 16 ×
16 ports E/D. Inset α in Fig. 7 shows the spectrum of this
multiplexed signal. Sixteen different OCs were generated at
WANG et al.: FIELD TRIAL OF 3-WDM × 10-OCDMA × 10.71-Gb/s ASYNCHRONOUS WDM/DPSK-OCDMA
Fig. 6.
Performance of multiport encoder with TVF decoder.
Fig. 7.
Experimental setup.
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Fig. 8. (a) JGNII and the configuration of the testbed used in the experiment. (b) Measured dispersion of the whole system. (c) Photos of experimental setup.
the 16 output ports and were then mixed in an asynchronous
manner with balanced power, random delay, random bit phase,
and random polarization states. Fixed fiber delay lines with
incremental differences of 10 m were used in each branch to
decorrelate the signals; variable optical attenuators were used
to balance the power. Tunable optical delay lines were placed
as well to investigate the system performance with different
phases of SI overlapping. In a practical PON environment, the
polarization states of the signals may be random. However,
for investigating the system performance in the worst sce-
nario where the interference becomes most serious, polarization
controllers (PCs) were placed to align the polarization states
of all the signals. Inset β in Fig. 7 shows the waveform of
the mixed signals of 3-WDM, 12-OCDMA users. This signal
was then launched into a 100-km-installed single-mode fiber
(SMF). Three spans of dispersion-compensating fiber with total
dispersions of around 430, 860, and 430 ps/nm, respectively,
have been used in the transmission line to compensate the
dispersion, as shown in Fig. 8(a). The dispersion of the system
is measured as shown in Fig. 8(b).
WANG et al.: FIELD TRIAL OF 3-WDM × 10-OCDMA × 10.71-Gb/s ASYNCHRONOUS WDM/DPSK-OCDMA
213
Fig. 9. Eye diagrams of (upper row) encoded, (middle row) decoded, and (lower row) electrical signals with 3 WDM and different number of active users in
each wavelength (K).
Fig. 10. BER performances.
After the transmission, the WDM × OCDMA signal was first
demultiplexed by the WDM DEMUX with 400-GHz channel
spacing and later transmitted through ∼11-km SMF before
reaching the 16-chip programmable TVF-type decoder. The
decoder was programmed to decode four different OCs that
correspond to the ones generated at encoder ports 4, 8, 12,
and 16. A fiber-based interferometer and a balanced detector
perform the DPSK detection. The bandwidth of the receiver
system is around 7.8 GHz, which performs the data-rate detection. Insets θ and ζ in Fig. 7 show the decoded signal and the
electrical signal after the balanced detector, respectively. The
data were finally tested by the BER tester with a clock signal
obtained from the clock-data-recovery circuit. Fig. 9 shows the
eye diagrams of the encoded (upper row), decoded (middle
row), and the electrical (lower row) signals with 3 WDM and
different number of active users in each wavelength (K).
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The measured BER performances are shown in Fig. 10.
Fig. 10(a) shows those for four different decoders with 3 WDM,
single, and 12 active OCDMA users (K = 1, 12) in the backto-back (B-to-B) case. Error free (BER < 10−9 ) has been
achieved for all the OCDMA users in 3-WDM channels. The
average power penalty for K = 12 to K = 1 is about 8 dB.
Fig. 10(b) shows a comparison of BERs between DPSKOCDMA and OOK-OCDMA with and without FEC for K =
12 [15]. The performance has been significantly improved
in DPSK-OCDMA compared to OOK without FEC. Even
compared to OOK with FEC, the sensitivity at BER = 10−9
was improved more than 2 dB. These results verify the previous statement that DPSK-OCDMA can accommodate more
active users than OOK-OCDMA without using FEC and OT.
Fig. 10(c) shows the BER performance degradation after a
field transmission. For K = 12, an error floor around 10−9 has
been observed in several cases due to impairments during the
111-km transmission and nonuniformity of the PCR [14], [15],
[21]. Fig. 10(d) shows that the error-free transmission has been
successfully achieved for all the four decoders with 3-WDM
and up to 10-OCDMA users in the field trail.
Finally, it is worth noting that all the measurements were
taken under the worst-case scenario by adjusting the tunable
optical delay lines and PCs to guarantee the asynchronous
operation [15], [18]. The threshold level was fixed to zero in
the measurement independent of K. Therefore, the dynamic
threshold level setting requirement could be relaxed in the
receiver as well. The four ports were randomly chosen for
good representativeness for all the others. The multiuser performances of other ports were tested to be within the spread
of the shown results. The spectral efficiency (η) is about 0.32
and 0.27 b/s/Hz for B-to-B and field transmission, respectively.
As a comparison, the authors in [7] and [8] have reported
WDM/OCDMA experiments with η = 1.6 and 0.125, respectively. However, they are synchronous approaches with stringent timing coordination combining with time gating [7], [8]
and polarization multiplexing [7]. For asynchronous OCDMA,
our result is the highest reported result so far.
IV. C ONCLUSION
The field trial of a cost-effective asynchronous WDM/DPSKOCDMA using hybrid E/D has been successfully demonstrated
with a frequency efficiency of 0.27 b/s/Hz in an asynchronous
environment. The total capacity is 3-WDM × 10-OCDMA ×
10.71 Gb/s, and the transmission distance is 111 km. The
nonuniformity of PCR is a limitation of the current device,
which can be mitigated in a larger scale device with better design and fabrication. Spectral efficient asynchronous OCDMA
could be expected by using a large-scale multiport E/D with
higher PCR, polarization multiplexing, and FEC.
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WANG et al.: FIELD TRIAL OF 3-WDM × 10-OCDMA × 10.71-Gb/s ASYNCHRONOUS WDM/DPSK-OCDMA
Xu Wang (S’91–M’98–SM’06) received the
B.S. degree in physics from Zhejiang University,
Hangzhou, China, in 1989, the M.S. degree in
electronics engineering from the University of
Electronics Science and Technology of China
(UESTC), Chengdu, China, in 1992, and the Ph.D.
degree in electronics engineering from the Chinese
University of Hong Kong (CUHK), Hong Kong,
in 2001.
From 1992 to 1997, he was a Lecturer with
the National Key Laboratory of Fiber Optic Broadband Transmission and Communication Networks of UESTC. From 2001
to 2002, he was a Postdoctoral Research Fellow with the Department of
Electronic Engineering of CUHK. From 2002 to 2004, he worked with
the Department of Electronic and Information Systems, Osaka University, Osaka, Japan, as Telecommunication Advancement Organization (TAO)
Research Fellow. In April 2004, he joined the Ultra-fast Photonic Network
Group, Information and Network Systems Department, National Institute of
Communication and Information Technology (NICT), Tokyo, Japan, as an
Expert Researcher. He is also an Adjunct Professor with two universities
in China. His research interests include fiber-optic communication networks,
optical code division multiplexing (OCDM), optical packet switching, semiconductor lasers, application of fiber gratings, and fiber-optic signal processing. He
has filed three patents and is the first author of more than 70 technical papers.
Dr. Wang received the Telecommunications Advancement Research Fellowship by the TAO of Japan in 2002 and 2003.
Naoya Wada (M’97) received the B.E., M.E., and
Dr.Eng. degrees in electronics from Hokkaido University, Sapporo, Japan, in 1991, 1993, and 1996,
respectively.
In 1996, he joined the Communications Research Laboratory (CRL), Ministry of Posts and
Telecommunications, Tokyo, Japan. He is currently a
Research Manager with the National Institute
of Communication and Information Technology
(NICT), Tokyo. His current research interests are in
the area of photonic networks and optical communication technologies such as optical packet switching (OPS), optical processing,
and OCDM.
Dr. Wada received the 1999 Young Engineer Award from the Institute
of Electronic and Communication Engineers of Japan and the 2005 Young
Researcher Award from Ministry of Education, Culture, Sports, Science, and
Technology. He is a member of IEEE Comsoc, IEEE LEOS, the Institute
of Electronics and Communications (IEICE), the Japan Society of Applied
Physics (JSAP), and the Optical Society of Japan (OSJ).
Tetsuya Miyazaki (M’03) received the B.S. degree
in physics from University of Tsukuba, Ibaraki,
Japan, in 1985 and the M.S. and Ph.D. degrees
in information processing from Tokyo Institute
of Technology, Tokyo, Japan, in 1987 and 1997,
respectively.
In 1987, he joined KDDI Research and Development (R&D) Laboratories, Saitama, Japan, where he
worked on coherent optical communications. From
1993 to 1996, he was with ATR Optical and Radio
Communications Research Laboratories, where he
worked on fiber amplifier for optical intersatellite links. From 1996 to 2002,
he was with KDDI R&D Laboratories, where he was engaged in WDM
optical networks. Since April 2002, he has been with the National Institute of
Communication and Information Technology (NICT), Tokyo, Japan, where he
has been involved in research on ultrafast photonic networks and multilevel
modulation techniques. In 2005, he was a Group Leader with the Photonic
Network Group.
Dr. Miyazaki is a member of the IEEE Lasers and Electro-Optics Society
(IEEE LEOS) and the Institute of Electronic, Information, and Communication
Engineers (IEICE) of Japan.
215
Gabriella Cincotti (M’00–A’03–M’03–SM’06) was
born in Naples, Italy, in 1966. She received the
Laurea (M.Sc.) degree (cum laude) in electronic engineering from “La Sapienza” University of Rome,
Rome, Italy, in April 1992.
From 1992 to 1994, she was a Project Engineer
with the microwave laboratory of ALENIA, Aeritalia
& Selenia S.p.A., Rome. In October 1994, she joined
the Department of Electronic Engineering of University “Roma Tre,” Rome, as an Assistant Professor. In
May 2005, she became an Associate Professor with
the Department of Applied Electronics. She has authored over 70 papers and
presentations in international journals and conferences.
Ms. Cincotti is a member of the IEEE Lasers and Electro-Optics Society
(LEOS), the National Inter-University Consortium for Telecommunications
(CNIT), and the Inter-University Research Centre for the Physical Agents
Pollution (CIRIAF).
Ken-ichi Kitayama (S’75–M’76–SM’89–F’03) received the B.E., M.E., and Dr.Eng. degrees in
communication engineering from Osaka University,
Osaka, Japan, in 1974, 1976, and 1981, respectively.
In 1976, he joined the NTT Laboratory. From
1982 to 1983, he was with University of California,
Berkeley, as a Research Fellow. In 1995, he joined
the Communications Research Laboratory (currently, NICT), Tokyo, Japan. Since 1999, he has
been the Professor with the Department of Electrical,
Electronic, and Information Engineering, Graduate
School of Engineering, Osaka University, Osaka. His research interests are in
photonic networks, optical signal processings, optical code-division-multipleaccess systems, and radio-on-fiber communications. He has published over
210 papers in refereed journals, written two book chapters, and translated one
book. He holds more than 30 patents.
Dr. Kitayama currently serves on the Editorial Boards of the IEEE
PHOTONICS TECHNOLOGY LETTERS, IEEE TRANSACTIONS ON
COMMUNICATIONS, Optical Switching, and Networking as an Associate
Editor. He received the 1980 Young Engineer Award from the Institute of
Electronic and Communication Engineers of Japan, the 1985 Paper Award on
Optics from the Japan Society of Applied Physics, and the 2004 Achievement
Award of the IEICE of Japan. He is a Fellow of the IEICE of Japan.