Channel interference reduction using random Manchester codes forboth synchronous and asynchronous fiber-optic CDMA systems

26 JOURNAL OF LIGHTWAVE TBCHNOLOGY. VOL. 18, NO. I , JANUARY 2000

Channel Interference Reduction Using Random

Manchester Codes for Both Synchronous and

Asynchronous Fiber-optic CDMA Systems

Che-Li Lin and Jingshown Wu,

Senior Member, IEEE

Abstract-In this paper, we propose the random Manchester codes (RMC) to improve the bit error probability (BEP) per- formance in both synchronous and asynchronous fiber-optic code-division multiple-access (CDMA) systems. The spreading sequences used in the synchronous and asynchronous systems are modified prime sequence codes and optical orthogonal codes (OOC’s), respectively. Thermal noise, shot noise, and avalanche photodiode (APD) bulk and surface leakage currents are taken into consideration in the BEP analyzes. The results show that the proposed systems can support a larger number of simultaneous users than other systems with similar system complexity under the same bit-error probability constraint.

Index Terms-Code division multiple access (CDMA), optical fiber communication, optical hardlimiter, optical orthogonal codes, prime sequence codes.

1. INTRODUCTION

C

ODE ,divfsion multiple access JCDMAJ has been ap- plied In fiber-optic communications and reported in the literature [1]-[11]. The CDMA fiber-optic Communication system can provide a multiple access environment without using wavelength sensitive components, which are needed in the wavelength division multiple access network, and without employing very high-speed electronic data processing devices, which are necessary in the time division multiple access network. The extremely wide transmission bandwidth of single mode optical fibers is inherently suitable for this spread spectrum multiple access technique. Depending on the requirement of time synchronization, there are synchronous or asynchronous fiber-optic CDMA systems. Synchronous sys- tems, which are more complex because they need network-wide time synchronization, can accommodate much more users than asynchronous systems conditional on using the spreading sequence with same length.

The commonly used spreading sequences

in

synchronous and asynchronous fiber-optic CDMA systems are modified prime sequence codes 151, [ 6 ] and optical orthogonal codes (OOC’s) [I], [21, 1161, respectively. The modified prime se- quence codes are used io the synchronous systems because they can afford many more codes than OOC’s. OOC’s, however, have better autocorrelation and cross correlation properties

Manuscript received September 8, 1998; revised July 16, 1999. This work was suppolted by the National Science Council, R.O.C., under Grant NSC 88-221 5-E-002-035.

The authors are with the Department of Electrical Engineering, National Tniwan University, Taipei, Taiwan 106, R.O.C.

Publisher Item Identifier S 0733-8724(00)00386-8.

than the modified prime sequence codes

so

that they are suitable in the asynchronous systems. Because the fiber-optic CDMA systems are interference limited systems, the number of simultaneous users is much less than the number of the subscribers. Several schemes have been proposed to improve the system performance. For example, error control coding can be used to reduced the BEP [12]-[14]. The receiver with double hardlimiters has been recommended to improve the system performance for both synchronous and asynchronous fiber-optic CDMA systems [3],

[4].

Multi-attribute coding has been introduced to make the systems more bandwidth and broadcast efficient [91, [lo], 1171.

In this paper, we propose the random Manchester codes (RMCJ scheme which can improve the bit error probability (BEP) performance in both synchronous and asynchronous fiber-optic CDMA systems. Compared with the double optical hardlimiters system, the employment of the RMC scheme increases the system complexity little, but improves the per- formance significantly. In the BEP analyses, thermal noise, shot noise, and avalanche photodiode (APD) bulk and surface leakage currents are taken into consideration. The results show that this system can support a larger number of simultaneous users than other systems with similar system complexity under the same BEP constraint. In other words, under the same number of simultaneous users, the BEP is smaller.

The remainder of this paper is organized as follows. In Sec- tion 11, we describe the RMC scheme and the system architec- ture. The BEP analyzes for both synchronous and asynchronous systems are given in Section 111. Section IV presents the numer- ical results and comparisons with other systems. Some discus- sions are also given in this section. Finally, Section V concludes this paper.

11. SYSTEM DESCRIPTION

The Manchester encoding is often used in the baseband signal transmissions to simplify the synchronization of the receiver with the transmitter among other advantages [I 81. There are sev- eral ways to implement Manchester codes. For example, the bi- nary “1” can be represented by a pulse in the first half interval of the bit followed by absence of pulse in the second half in- terval. For binary “0,” the locations of presence and absence of the pulse are reversed. In the conventional fiber-optic

CDMA

systems, the arrangement of the optical pulses and chip times of a spreading sequence are shown in Fig. l(aJ or (b) [l],

[2].

In

LIN AND WU: CHANNEL IIVTERFERENCE REDUOTION USING RANDOM MANCHEBTER CODES 27 1 5 10 1 3 15 20 T, 25 28 30 32 (a)

&

I 5 I O 13 15 20

U

T, 25 28 30 32

r

!

”

20

L

T, 25 28

u

30 32 ” 1 5 I O 13 I5 (d)

Fig. 1. (a), (b) Arrangement of optical pulses and chip times of a spreading sequence for conventional schemes and (9, (d) the arrangement of optical pulses and chip times of a spreading sequence for the RMC scheme.

these cases, the optical pulses are at the fixed positions with re- spect to the chip time. In this paper, we apply the RMC scheme, in which the optical pulses are sent randomly in the f i s t half interval of the chip time or the second half interval of the chip time, in the spreading sequences. For example, the transmitter can transmit data bit “ I ” by sending the pattems of optical pulses either one as shown iri Fig. l(c) and (d) randomly, i.e., place the pulses in the first half (:hip intervals or the second half chip inter- vals for one spreadin8 sequence. The data bit

“ 0

is represented by absence of optical pulses.Then the total photon arrival rate at the input of the first optical hardlimiter, s ( t ) , is

k = l

The receiver structure is the same as the conventional fiber- optic CDMA receiver with double optical hardlimiters as shown in Fig. 2 [ 3 ] , [4]. The first optical hardlimiter placed before the optical correlator cuts down the interference higher than the possible level, and then the second optical hardlimiter further reduces the interfererice which is too small to be the desired signal. The two optical hardlimiters, however, cannot eliminate interferences completely. So the bit error is mainly due to the remained interferenca. Using the RMC scheme in the trans- mitter can improve the BEP performance in this double optical hardlimiter CDMA receiver. If all the transmitters choose the same half interval of the chip time to transmit “1,” the BEP performance is the same as that without the RMC scheme. But when the transmitters. randomly select the transmission inter-

vals, which is the usual case, the optical hardlimiter placed after

the optical correlator reduces interference much more effec- tively. An example is given in Fig. 3. Fig. 3(a) and (b) are the correlation pattem for the optical correlator in the receiver for desired data bits “1” and “0,’’ respectively. For the conventional double hardlimiter system without using the RMC scheme, if the desired received bit is “0,” and five other users send data

NeNiork Fabic

Oher Channels

Fig. 2. hardlimiters.

Block diagram of a fiber-optic CDMA receiver with double optical

I I I I I I I I I I I I I I I I I kl I I I I I l l T b I 5 10 15 T, 20 Zfi . . Tb 1 5 IO 15 T, 20 2:; T, T C ( e ) (0

Fig. 3. (a), (b) Correlation pattems for the optical correlator in the receiver for desired data bits “1” and “0,” respectively, (c) an example of the received bit pattem without the RMC scheme when the desired received data bit is ~ ~ 0 , ” (d) an example of the received bit pattem with the RMC scheme when the dasired received data bit is “0,” and ( e ) , (f) the optical pulses after Ihe Optical correlator in the last chip time for (c) and (d), respectively, where pX, is the threshold of the optical hardlimiters.

bit “1” as shown in Fig. 3(c), the optical pulse after the optical correlator at the last chip time is like that shown in Fig. 3(e). Therefore, the received bit will by mistaken as “1

.”

If the RMC scheme is applied to all the transmitters, the received bit pattem is probably like the one shown in Fig. 3(d). The optical pulse after the optical correlator at the last chip time is shown in Fig. 3(0. The second hardlimiter can remove the interference com- pletely and the decoding result is correct.

111. SYSTEM PERFORMANCES

A . Performance of Synchronous Fiber-optic CDMA System with RMC

In the synchronous fiber-optic CDMA system, the modified prime sequence codes are employed as the spreading sequences. It is assumed that each user is assigned a unique modified prime

28 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 18. NO. I. IANUARY 2000

sequence code of length p 2 . For example, the spreading se- quence of the kth user is (a;, a t ,

. . .

,

ai2-l), where a: E

{0, l} and the periodic spreading waveform can be written as

and

(tl,

t z , ,

. .

,

t p )

by T and

t ,

respectively, the probability

density function of

T

at

t

is derived as

m

d ( t )

=

a,kPT,(t

-

ZT‘)

(1)

Pr{T=

t }

= %=-cc

where where

a:+,> = a,” for all integers i ;

PTc (.)

unit-amplitude rectangular pulse of one chip P

time duration. Tr: ‘p =

N

- 1 - t,

*=1

defined by

PTe(t) 0 , otherwise. o < t < T c

At the input of first optical hardlimiter, the photon arrival rate of the kth user can he expressed as

j=-cc where P A S b: E { O , 1 ) Tb = p2Tc hit duration:

h(.)

PT,12( .)

photon arrival rate of the chip: data bit;

unit-amplitude rectangular pulses of duration Tb ;

unit-amplitude rectangular pulses of duration T&.

The last term in the above equation represents the effect of RMC, where S,” is a discrete random variable whose distrihu- tion IS as follows:

Pr{$

= 0 } =

Pr{s,k =

I}

= 1/2. ₍₄₎ where

N

is the number of simultaneous users.

pressed as

The two optical hardlimiters used in the receiver can he ex-

where

x input photon rate; g ( 2 ) output photon rate.

For modified prime sequence codes and a given prime numherp, the length of the spreading sequences is p 2 . There are p groups and each group contains p spreading sequences, where the code sequences which are time-shifted versions of one another he- long to the same group. Without loss of generality, the first user is destined as the desired user. We express the number of si- multaneous users which have a mark at the same position as the ith mark of the first user as

Ti:

i E {1, 2,

. .

.

,

p } and

Ti

t { O , 1,

. .

.

,

p ~ 1). Denoting the vectors ( T I ,

Tz,

. . .

,

T p )

ti

E {ti, mi”,

ti,

mi”

+

1: . . .

,

t i , max} (9)

I

i-1

I

0,

N

- p - ( p - i)(p - 1) -

t j

j=1

and the functions max{z,

U }

and min{z, y} are the maximum and minimum of z and y, respectively.

The number of users sending data bit “1” among t; users is denoted as ~ i : I G ~ E (0, 1,

. . .

,

ti}. Let

n (61, 6 2 ,

. . .

,

6), (12)

he the interference state pattern. Furthermore, we denote the number of users sending optical pulses in the first half interval of the chip time among K C users as K : : ni t { 0 , 1, . . .

,

I G ~ } ,

Also let

6’ ( K i , K k ,

. . .

,

n;) (13) and In’/ he the number of nonzero elements in 6‘.To simplify the notation of the following calculation, we denote n“ =

n-n‘.

Under the assumption that

Pr{b,k =

0) =

Pr{b;

= 1) = 1/2, the conditional probability density function of K ; is given as

P r

{

n; = Zi

ITi

=

t i }

=

(::)

.2-*‘. (14) And from the distribution of sf, we can have Pr(n: = l i l ~ ~ = li} _as

The accumulated APD output of the first user over the last chip time is denoted as

Y

and its conditional probability density function is as follows:

L W A N 0 W CHANNEL INTERFERENCE REDUCTION USING RANDOM MANCHESTER CODES

where the mean j+, 1 can be expressed as

py, 1 =

GT,[mlX,

+

Ib

/ e ]

+

T A

/ e ₍₁₇₎

where

G average API) gain; e electron charge;

& / e contribution of the APD hulk leakage current to the APD output..

I ,

APD surface leakage current;

m~ contribution of the desired signal and the multiple ac- cess interference (MAI);

p ,

p

1

2, otherwise

i f s : = 0

n

n2

= p o r $ = 1

n

nl = p

and the variance

mi,

can be expressed as 2

=

G2FeTc[mlXs

+ & / e ]

tT,I,/e+u,,,

2 where Fe is the excess noise factor given by

Fe = k,:wG

+

(2 - 1 / G ) ( 1 ~ kew) where

k,e AF’D effective ionization ratio;

U:,, variance of thermal noise expressed as

where

k s Boltzmann’s constant;

T,

receiver noise temperature; RL receiver load resistance.

Py (ylb: = 0, /A’/ = n1,

ld‘l

= n2) -

-

where the mean pLy, 0 can be expressed as

M ~ , O =

(:T,[maX,

+

&,/e]

+

TcIs/e.

ma

is the contributiori of the MA1 and can be derived as

p , i f n l = p

n

n 2 = p

o r n 1

<

p

n

n2 = p 0, otherwise

and the variance U;,

,,

can be expressed as

= G‘F,T,;moX,

+

& / e ] + T A / e +U:,$.

Then the BEP of the synchronous fiber-optic CDMA system with the double optical hardlimiters using the RMC scheme can be derived as

P,=Pr{b,’=O}.Pr{Y>Blb:=O}

[Pr

{Y

>

Bib:

= 0, A = 1 , A’ =

Z‘}

+

Pr

{

Y

<

B / b j

= 1, A =

I ,

A’ =

Z‘}]

. Pr

{A’ =

I’IK

=

I } .

P r { A =

ZIT

= t }

.

Pr{T = t } (26)

where

where erfc(,) stands for the complementary error function, de- tined as

and

Pr

{Y

<

016:

= 1, A = I , A’ = 1’)

2

The threshold level of the on-off keying (OOK) demodulator, 8, is set to a suboptimum value as [19]

= k , n “Y. 1 + & , I ‘ “ L O

(30) uy, 1

+

uy, n _{n , = p / 2 , m o = o}

B . Performance of Asynchronous Fiber-optic CDMA System with RMC

In the asynchronous fiber-optic CDMA system, we employ the OOC’s with autocorrelation and cross-correlation bounded by one as the spreading sequences [l], [2], [16]. It is assumed that each user is assigned a unique code sequence of OOC’s of length F and weight

K .

The number of available users, (D, is bounded by

where the symbol

1

.

1

denotes the greatest integer smaller than 2 . Again we destine the first user as the desired user.

The spreading sequence of the kth user is ( a i , a $ ,

. . .

,

a:), where a,“ E {0, 1). The periodic waveform can be written in the same form as ( l ) , where

at+F

= a: for all integers i . At the input of the first optical hardlimiter in the receiver. the photon amval rate of the ktb user can also be expressed as in (3) except that the photon arrival rate of the pulsed chip is K X 6 instead of PA,. To calculate the upper bound of the BEP. we consider the chip synchronous case among different users [2],

30 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. IX. NO. I . JANUARY 2000

[4]. Therefore, the total photon arrival rate at the input of the first optical hardlimiter,

s ( t ) ,

is

where

N number of simultaneous users;

Mk discrete random variable with the following distribu-

tion function:

(33)

i f z = 0, 1 , .

. .

,

F

~ 1 otherwise.

Pr{Mh = z } =

The input and output relation of the lwo optical hardlimiters is the same as (6) except that all pX,’s should be replaced by KX,’s.

We denote the number of hits which fall in the ith chip time of the first user from the optical pulses of the N - 1 other users as IC$. And define

K G ( K l , K 2 ,

. . .

,

K x j (34)

as the interference state pattern, and

I

is the total summation of ~ iFrom [2], we have .

for i = 0, 1,

. . .

,

N - 1. Furtheimore, the number of users sending optical pulses in the first half interval of the chip time among lii is denoted as K : , and

K’ G ( K i , K ; ,

.

. .

~ K X ) (36) is the state vector. Similarly, we have K”

=

K - K’.

Il

and

I ,

are the total summation of K: and K:, respectively. The accumu- lated APD output of the first user over the last chip time is also denoted as Y , and the threshold level of the OOK demodulator is 0. Then the BEP, Pe, can be expressed as

P e = i [ F r { Y > B l 6 ~ = 0 } + P r { Y < 0 ~ 6 ~ = 1 } ] where

.

P r { 1K’l

<

= i l } ’ pr{ lK”l =

KlIz

=

iz}

+

P r

{I’

<

Bib3 =

1, ln’l =

K ,

~ K ” I

<

K }

. Pr

{ I K ’ ~

=

Kill

= i l } P r

{ I K ” ~

<

KII2

= i z }

+

P r {Y

<

016:

= 1, 161‘

<

K ,

I K ” ~

<

K }

.

Pr {Id

<

KlIl = 2 1 ) ’ PI { / K ” I

<

Kllz = i 2 ) ₍₃₈₎ herethedistributionPy(y1b: = 1,

I K ‘ ~

= n l ,

IK”~

=

nz)

isthe same as that in (16). The expressions of mean and variance are also the same as those in (17) and (19). The expression of ml can be modified from (18) by replacing all p’s to

K’s.

Each user is equally likely to incur interference at any one of the

K

mark chips independent of all other users. The interfer- ence state pattem vector, K‘, obeys a multinomial distribution

[4], [SI. Therefore,

Pr {

IK’~

= nlll = i l } = NDP(K’)P(K’; H I , ) (39)

X‘EG,, lT’j=.L

where n = 0, 1,

...,

min(K,

i l l ,

and

H I ,

is the set of all the interference pattem vectors with total weight equal to

i l ,

GI,

is the set of representative interference vectors in

HI^

with elements in decreasing order, NDP ( K ’ ) is the number of distinct

permutations of the vector K’ _in

G I ,

_{and is expressed as}

K !

NDP(K‘) =

n

R ( K j ) ! (40) j where

R ( K j ) ! number of repetition times of an element ~j in the vector K’ and the product is taken over

j for which li) are distinct;

multinomial distribution for the interference pattem vector K‘ in 1{11 ;

P ( K ’ ;

H I ,

)

and expressed as

LIN A N 0 W U CHANNEL IUTERFERENCE REDUCTION USING RANDOM MANCHESTER CODES

~

31

TABLE 1 LINK PARAMETERS

"e Symbol Value

Laser waveIe~i@h a25

APD

n

0.6 qunntum efficiency APD gain G 100 APD effectiv,:

t

0.02 ionization ratio APD bulk 1, 0.1 nA leakage current APD surface 1, 10 nA leakage current

Data bit rate R6 30 Mbps

Receiver noise T, 300 K

temperature

Receiver load resistor RL 10300

Wnhout HL Double HCE - RMC 8 double H b

0 5 i n 15 20 25

Number of simunaneous users N

BEP Comparisons among three types of synchronous fiber-optic Fig. 4.

CDMA systems for p = !,.

0 10 20 30 40 50

Number Of simultaneous users N Fig. 5.

CDMA systems for p = i

REP comparisons among three types of synchronous fiber-optic

I

i o 6

1

I

- P=5, RMC 8 double HCs, Pw=-7OdBW

I

i o ' 1 0 8 .. .. ,

, A

0 i n 20 30 40 50

Number of SimUltmeoUs umrs N

REP comparisons between two typcs of synchronous fiber-optic Fig. 6.

CDMA systems.

where the distribution Py(ylbi = 0,

I K ~

= n l , 16'1 = n z ) is

the same as that in (22). The expressions of mean and variance are the same as those in (23) and (25). The expression of mo can also be obtained from

(24)

by replacing all p ' s to

K's.

0

is set to the suboptimum value in (30) with nil changing to K / 2 .

Iv.

NUMERICAL RESULTS AND DISCUSSIONS

We here compare the performance of three synchronous fiber-

1) without hardlimiter;

2)

with double hardlimiters;

3) with the proposed RMC scheme and double hardlimiters. These three systems have similar complexity. The values of some common parameters are given in Table I. The numerical results are depicted in Figs. 4 and 5 for p = 5 and p = 7, re- spectively. The received optical power for the proposed system is defined as follows:

optic CDMA systems:

P<,<T = (l/2)hfpXs/q (44)

where

the factor, 1/2 due to that the optical pulses are only trans- mitted in half of the chip time in the KMC scheme;

h

Plank's constant;

s

optical frequency;

7 APD quantum efficiency.

In fact, because fiber-optic CDMA networks are interfer- ence-limited systems, the values of PI,,, only affect the BEP when the number of simultaneous users, N , is smaller than or equal to p . Therefore, the following discussions only con-

c e n t r a t e on t h e situations when

N

is larger t h a n p . In these

two figures, we can see that the BEP of the proposed scheme is much smaller that of the systems without hardlimiter or with double hardlimiters. Fig. 6 replots the two curves: double hardlimiters for p = 7, and the proposed scheme for p = 5 . It is meaningful to compare these two curves because the lengths of the spreading sequences for p = 7 and p = 5 are 49 and 25, the

LIN AND WU: CHANNEL IUTERFERENCE REDUCTlON USING RANDOM MANCHESTER CODES 33

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-

Che-Li Lin was born in Taimi. Taiwan, R.O.C.. in degrees in electrical engineering from the National Taiwan University, Taipei, in 1995 and 1999, rcspec- tively.

Presently, he is working in the Computer and Communications Research Laboratories at Industrial Technology Research Institute, Hsinchu, Taiwan. His research interests include lightwave commu- nication, high-speed communication networks, mobile communication, and spread-spectrum communication.

Jingshown Wu (S'73-M78SM'99) received the B.S. and M.S. degrees in electrical engineering from National Taiwan University, Taipei, Taiwan, R.O.C., in 1970 and 1972, respectively, and the W.D. degree from Comell University, 1th;tca. NY, in 1978.

He joined Bell Laboratories, Holmdel. NJ, in 1978. where he worked on dieital network standards ~

and performance, and optical fiber communication systems. In 1984, he joined the Department of Elec- trical Engineering of Natioiidl Taiwan University as Professor and was the Chairman of the department from 1987 to 1989. He was also the Director of the Communication Research Center, College of Engineering of the University from 1992 to 1995. From 1995 to 1998, he was the Director of the Division of Engineering and Applied Science, National Science Council, R.O.C., on leave from the university. Currently, he is a Professor and Chairman of IEEE Taipei Section. He is interested in optical fiber communicatinns, communication electronics, and Computer communication networks.

Prof. Wu is a member of the Chinese Institute of Engineers, the Optical So- ciety of China, and the Institute of Chinese Electrical Engineers.