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798 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 5, MAY 2002
Performance Analysis on Phase-Encoded OCDMACommunication System
Wenhua Ma, Student Member, IEEE, Chao Zuo, Hongtu Pu, and Jintong Lin
AbstractThe performance of an asynchronous phase-encodedoptical code-division multiple-access system is evaluated on thecondition that the impact of fiber channel is neglected. Phase-en-coded optical signal (pseudorandom optical signal with lowintensity) is analyzed in the view of stationary random process.The pseudorandom optical signal with low intensity is seen as asample function of a certain stationary random process whichis ergodic in strict sense. The analysis results reveal that thevariance of the corresponding random process is only inverselyproportional to the code length while the root-mean-square widthof the phase-encoded optical signal is proportional to the width ofinitial optical pulse and the code length . The numerical resultsdemonstrate that the better system performance can be achievedin case of larger code length and shorter initial optical pulse.
Index TermsOCDMA, phase-encoded, pseudorandom signal.
I. INTRODUCTION
THE OPTICAL code-division multiple-access (OCDMA)
communication system is currently a hot topic with many
scientists in the optical communication field. In the OCDMA
system, users can share all bandwidths simultaneously and
access the network asynchronously. Therefore, the OCDMA
system has higher utilization efficiency of bandwidth and
flexibility than other systems. Such advantages are expected in
the future of all optical networks. The OCDMA technique is a
possible solution for next-generation all optical networks.
In the OCDMA system, each user is assigned a unique
signature code which can distinguish itself from other users.
At transmitter end, when data bit is 0, the laser is kept silent;
when data bit is 1, the encoder impresses a signature code on
it and the data information is transmitted by the optical fiber. At
receiver end, the matched decoder can recover the desired in-
formation. The signals from undesired users are called multiple
access interference (MAI). In fact, though the fundamental
principle of different OCDMA systems is the same, there are
several different implementing schemes. Direct time spread
OCDMA usually employs optical orthogonal code or modified
prime code as signature codes. In order to accommodate
enough users, the code length is relatively longer. It leads tomuch shorter chip pulse and poses a challenge for light source.
The frequency hopping OCDMA system utilizes multiple fre-
quency points and mitigates the stringent requirements on light
source. However, the chip pulses with different frequencies
will travel in different velocities considering the actual optical
fiber channel characteristic, which will change the relative
positions among them. Consequently, the decoder cannot cor-
Manuscript received May 16, 2001; revised February 4, 2002.The authors are withthe BeijingUniversityof Postsand Telecommunications,
100876 Beijing, China.Publisher Item Identifier S 0733-8724(02)05123-X.
rectly recover the desired bit. Phase-encoded OCDMA, which
can realize all optical operation, does not impose stringent
requirements on light source. Phase-encoded OCDMA has
attracted the attention of experts on optical communication [1].
Several experiments on phase-encoded OCDMA were reported
recently. Tsuda et al. conducted such an experiment that a
10-Gb/s 810-fs return-to-zero signal is spectrally encoded,
transmitted over a 40-km dispersion shifted fiber, and decoded
using a photonic spectral encoder and decoder pair that uses
high resolution arrayed-waveguide gratings and phase filters
[2]. Grunnet-Jepsen proposed a novel encoder/decoder for
phase spectral encoded consisting of fiber Bragg gratings [3].
This paper is organized as follows. Section II describes thefundamental principle of phase-encoded system. Section III
thoroughly analyzes the properties of pseudorandom noise-like
signal with low intensity, which is the foundation of further
analysis for such a system. Section IV is a performance analysis
of the system, and Section V is the conclusion of this paper.
II. FUNDAMENTALPRINCIPLE OFPHASE-ENCODEDOCDMA
A. Principle Description
The schematic configuration of encoder for phase-encoded
OCDMA is shown in Fig. 1. The initial Gauss optical pulse
is first spectrally decomposed by diffraction grating and lens.
Phase mask panel (usually consisting of liquid crystal modu-lator) is arranged to append a random phase (0 or ) to different
spectral component [4], [5]. The second lens and diffraction
grating reassemble the signal. The output of such an apparatus
is pseudorandom optical signal with low intensity in temporal
domain. Then such noise-like optical signal is coupled into the
optical fiber network. At the receiver end, if the code sequence
is matched, the output of decoder is a recovered Gauss pulse.
Otherwise, only a noise-like optical signal with low intensity is
obtained.
For an initial Gauss optical pulse
(1)
Its spectral shape can be expressed as follows:
(2)
Assume the appendix phase to the spectrum by the phase
mask can be written as
,
otherwise.
(3)
0733-8724/02$17.00 2002 IEEE
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Fig. 1. Schematic configuration of encoder for phase-encoder OCDMA system.
In (3), is the code length and represents code sequence.
is the spectral range encoded by code sequence.
Therefore, the reassembled signal waveformcan be expressed
as
(4)
In (4), is inverse Fourier transform operation and
represents convolution operation.
B. Choice of Phase Code
It is clear that only the code with high random characteristic
can guarantee that encoded signal is more like a random noise.This is critical to the phase-encoded OCDMA system. For con-
venience of demonstration, here we mapthe signature code from
domain (1, 1) to domain (0, 1). In fact, the phase mask in the
receiver acts as a module 2 add operation to the phase of coded
optical signal. The module 2 add of two codes must be a se-
quence with high random characteristic, which can guarantee
that the phase-encoded signal is still a noise-like signal after it
passes through an unmatched decoder.
We can define phase code set as follows: assuming each
element in set is with high random characteristic, then
where represents module 2 add operation.
Then, the output of photocount in the receiver can be mathe-
matically written as
(5)
where represents conjugate operation and is a coefficient.
corresponds to , in which and are
the phase code of different users.
In this paper, we choose such a code set consisting of se-
quence and its time versions. It is well known that the code
length of sequence is . Therefore, the element number
of such a set is also .
III. THEORETICALANALYSIS OFPSEUDORANDOMOPTICAL
SIGNAL
For a phase-encoded optical signal (pseudorandom signal
with low intensity), though in fact it is a known signal, we
can approximately see it as a sample function of a certain
stationary random process which is ergodic in strict sense.
We also assume that the time duration of the phase-encoded
signal is long enough that the characteristic numbers of the
virtual stationary random process can be derived from the
phase-encoded signal itself. Under the above assumption, we
can employ a statistical method to conveniently study the
pseudorandom signal. In fact, for different phase codes in the
same code set, the characteristic numbers of the corresponding
random process may be slightly different. But if each code
is with high random characteristic and code length is long
enough, the slight difference in the characteristic numbers can
be neglected. In this paper, we ignore such a difference and
consider that for all codes, the characteristic numbers of the
corresponding random processes are the same. For the virtual
stationary random process, what we are most concerned about
is the one-dimensional (1-D) probability density function (pdf)
which can be obtained from a sample function.
If the initial optical pulse is Gaussian shape, then the phase-
encoded pseudorandom optical signal can be written as
(6)
In (6), and , when ,
where represents the integer part of ;
, when . is sampling function. The last
step of (6) is true only in case of .
For convenience of analysis in the following context, we have
(7)
(8)
The more important thing for us is to precisely weight the
width in temporal domain of the phase-encoded signal. We note
that the phase-encoded signal is theoretically infinite in tem-
poral domain. Because the amplitude of signal is negligible out-
side the first zero points of the function , we only
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800 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 5, MAY 2002
consider the part of whole signal within the first zero points.
Here, we assume the concept of root-mean-square (rms) width
, which is defined by
(9)
where
(10)
According to the (9), (10), and (6), we have
(11)
If the code is sequence, is equal to 0 or 2.Therefore, (11) can be approximated as
(12)
In order to derive the pdf of the virtual stationary random
process, we assume that the real part and the imaginary part
of the phase-encoded signal within the rms width following the
Gauss distribution whose variances are equal to and that
they are independent of each other (actually not). It is easy to
obtain the following equations:
(13)
(14)
In the above equations, represents the time average.
Because both and follow the Gauss distribution,
their variances and mean values are and 0, respectively.
According to the probability theory, should follow ex-
ponential distribution, which is given by
(15)
The total energy of Gauss optical pulse is . Note that
the energy of phase-encoded signal within the first zero pointsof function accounts for more than 90% of the
whole signal energy. Therefore, we have
(16)
(17)
In order to verify whether the above assumptions on the
phase-encoded signal are valid, we need to compare the pdf of
phase-encoded signal based on the theoretical analysis with its
practical version.
Fig. 2. Phase-encoded signal.
Fig. 3. Autocorrelation curve of the corresponding random process.
Fig. 4. Curve of cumulative probability versus normalized optical power.
Fig. 2 shows the phase-encoded signal. Fig. 3 is the autocor-
relation curve of the corresponding virtual stationary random
process. The sharp peak of autocorrelation demonstrates that
the phase-encoded signal is a noise-like signal. Fig. 4 shows the
practical and theoretical curves of cumulative distribution func-
tion (CDF). That the practical curve well matches its theoretical
version verifies that the assumptions and analysis are valid. In
Fig. 4, normalized optical power means the maximum power of
the phase-encoded signal in Fig. 2 is seen as 1.
IV. PERFORMANCEANALYSIS OFPHASE-ENCODEDOCDMA
SYSTEM
For the sake of simplicity, we assume each original optical
pulse has the same energy and neglect the impact of loss, dis-
persion, and nonlinear effects on the optical signal. The thermal
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noise and shot noise of receiver are also ignored. In the fol-
lowing, we also assume the rms width of the phase-encoded
signal is no more than the bit duration which is equal to 1000
ps.
For single undesired user case, the interference can be mod-
eled as a stationary random process whose 1-D pdf is exponen-
tial distribution. When multiple undesired users interfere with
the desired user, the total interference can be seen as the sum-mation of independent multiple random processes and be mod-
eled as a stationary random process whose 1-D pdf is given by
(18)
When the number of undesired users is relatively larger (
), according to the central limit theorem, we have
(19)
In (19), represents Gauss distribution.
We denote the photocounts detected by the receiver photo
detector as random variable . is the threshold of decoder.
Then, the bit-error probability of such a systemcan be expressedas
(20)
where
(21)
where and
(22)
In (22), is bit duration and represents duty cycle.
For the second term of (20), if , then
. Otherwise
(23)
in which .
In a practical optical communication system, the shot noise
and the thermal noise of the receiver cannot be neglected in
order to more precisely evaluate the system performance. How-
ever, in the presence of the multiple access noise, shot noise,
and thermal noise of the receiver, it is very difficult to precisely
calculate the bit-error probability from a very tedious integral
because theoretically the 1-D pdf of total noise, which is very
complex, is the convolution operation of the pdf of multiple
access noise, shot noise, and thermal noise. But it is very im-
portant to note that the OCDMA system is interference-limited,
like its counterpart in wireless communication, radio CDMA.
In other words, in the OCDMA system, the MAI is the domi-
nant noise factor, and the shot noise and thermal noise of the re-
ceiver are less important. In a usual case, the shot noise is mod-eled as a Poisson random process, and its expectation and vari-
ance are both denoted by . But here we assume Gauss model
for shot noise. Thermal noise of receiver is always modeled as
Gauss distribution . As for multiple access noise, we
assume (19). Therefore, in order to calculate the bit-error prob-
ability with less complex procedure, we assume Gaussian ap-
proximation in deriving the conditional pdf of random variable
, which is reasonable. So we can rewrite (21) by
(24)
where
(25)
(26)
Similarly, we also can rewrite (23) by
(27)
where
(28)
(29)
In (28), 1 represents the optical pulse energy.
Fig. 5 shows the curves of bit-error probability versus
threshold in case of different number of active users. Fig. 6
shows the curves of bit-error probability versus threshold
in case of different code length . Fig. 7 shows the curves
of bit-error probability versus threshold in case of different
initial optical pulsewidth . It is obvious that the optimal value
of the threshold is 1.
Fig. 8 shows the curves of bit-error probability versus the
number of simultaneous users when code length is equal
to 63 127 and 255, respectively. From Fig. 8 we learn that the
larger is the code length , the better is the system performance.
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802 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 5, MAY 2002
Fig. 5. Bit-error probability versus threshold in case of different .
Fig. 6. Bit-error probability versus threshold in case of different .
Fig. 7. Bit-error probability versus threshold in case of different .
Fig. 8. Bit-error probability versus the number of simultaneous users in caseof different .
Note that is inversely proportional to the code length .
When code length becomes larger, the interference of unde-
sired users to the desired user becomes smaller. Fig. 9 demon-
strates the curves of bit-error probability versus the number of
Fig. 9. Bit-error probability versus the number of simultaneous users in caseof different .
simultaneous users when is with different value in the
absence/presence of shot noise and thermal noise of receiver,
respectively. As we expect, the shot noise and thermal noise de-
grade the system performance. When is with smaller value,
that is to say, the initial optical pulse is with smaller width, the
system performance is better. Smaller duty cycle implies the
smaller probability of interference to the desired user.
V. CONCLUSION
This paper has analyzed the properties of the phase-encoded
optical signal (pseudorandom optical signal with low intensity)
in a view of random process. The phase-encoded optical signal
was seen as a sample function of a certain random process. The
variance of the corresponding random process is inversely pro-
portional to code length . The rms width of the phase-encoded
width is proportional to the width of initial Gauss optical pulse
and the code length . Neglecting the influence of the trans-
mission medium, we have evaluated the performance of asyn-
chronous phase-encoded OCDMA system and obtained the op-timal threshold of receivers. The numerical results revealed that
larger code length or shorter initial Gauss optical pulse is ben-
eficial to improving the system performance.
REFERENCES
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[2] H. Tsuda et al., Spectral encoding and decoding of 10 Gb/s fem-tosecond pulses using high resolution arrayed-waveguide grating,
Electron. Lett., vol. 35, pp. 11961187, July 1999.[3] A. Grunnet-Jepsen et al., Fiber Bragg grating based spectral en-
coder/decoder for lightwave CDMA, Electron. Lett., vol. 35, pp.
10961097, June 1999.[4] L. Wang and A. M. Weiner, Programmable spectral phase coding of an
amplified spontaneous emission light source,Opt. Commun., vol. 167,pp. 211224, Aug. 1999.
[5] H. P. Sardesai, C. C. Chang, and A. M. Weiner, A femtosecond code-division multiple-access communication system test bed, J. LightwaveTechnol., vol. 16, pp. 19531963, 1998.
Wenhua Ma(S01) was born in Henan, China, in 1975. He received the M. S.degree from the Wireless Communication Center, Beijing University of Postsand Telecommunications, Beijing, China, in 1999.
He is currently pursuing the Ph.D. degree from the same university. His re-search interests are in wireless communication, adaptive antenna, optical com-munication, optical CDMA, and all-optical networks.
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Chao Zuo was born in Shangdong, China, in 1972. He received the B.Sc degreein communications from Nanjing Institute of Communication Engineering in1994 and the M. Sc degree in optoelectronics from the National University ofDefense Technology in 1999.
He is currently pursuing the Ph.D. degree from the Beijing University ofPosts and Telecommunications, Beijing, China. Before beginning his Mastersstudies, he was a communications engineer for two years. He has worked on avariety of projects, including ring laser gyro, fiber hydrophone, and nonlinearoptics. He is now working on ultrafast all optical fiber communication systems.
Hongtu Puwas born in Beijing, China, in 1960. He received the B.Sc degree inlaser technology, the M.Sc degree in optics, and the Ph.D. degree in optics fromthe University of Electronic Science and Technology of China in 1983, 1991,and 1998, respectively.
He is now a Post Doctor Fellowat theOptical Communication Center, BeijingUniversityof Posts and Telecommunications, Beijing, China. He has studied thephotonics field for more than 16 years, especially high-speed signal measure-ment and nonlinear optics. At present, he is closely engaged with researchingand developing the components of wavelength-division multiplexing, includingfiber fusion coupler,optical filter, optical switch, and particularly multiple wave-length lasers.
Jintong Lin wasbornin Jiangsu, China,in 1946.He received thephysicsdegreefrom Peking University, the M.Sc degree in electronic engineering from BeijingUniversity of Posts and Telecommunications (BUPT), Beijing, China, and thePh.D. degree in electronic engineering from Southampton University, U.K.
Since 1978, he has been working on optical fiber systems, single-mode fiberlasers, and polarization effects in fiber devices. He took a professorship of op-tical communications at BUPT in 1993, and is now the President of BUPT. Hiscurrent research interests include fiber devices, ultrahigh-speed optical trans-mission systems, and communication networks.
Dr. Lin won the prize of Best Publication awarded by the World Communi-cation Year Committee of China in 1984, the Academic Achievement Prize ofBeijing in 1985, and the Electronics Divisional Board Premium for Best Elec-tronics Letters in 1986, awarded by the Institution of Electrical Engineers, U.K.