blum1

8/13/2019 blum1

1/6

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
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

8/13/2019 blum1

2/6

MAet al.: PERFORMANCE ANALYSIS ON PHASE-ENCODED OCDMA COMMUNICATION SYSTEM 799

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

8/13/2019 blum1

3/6


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

8/13/2019 blum1

4/6


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.

8/13/2019 blum1

5/6


Fig. 5. 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

[1] J. A. Salehi, A. M. Winer, and J. P. Heritage, Coherent ultrashort lightpulse code-division multiple access communication systems, J. Light-wave Technol., vol. 8, pp. 478491, Mar. 1990.

[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.

8/13/2019 blum1

6/6


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.

blum1

Documents

Transcript of blum1