New Design of Zero Cross Correlation Codes for Spectral Amplitude Coding in OCDMA systems. C. B. M. Rashidi, S. A. Aljunid, F. Ghani, M. S. Anuar, H.AI-Khafaji,
M.N.Junita, A.R.Arief
School of Computer and Communication Engineering, Universiti M a l a y s i a Pedis, No. 1 2 & 14, Jalan Satu, Taman Seberang Jaya Fasa 3, Kuala Pedis 02000, Pedis, Malaysia E-mail:
[email protected] [email protected]@unimap.edu.my.
[email protected],
[email protected],
[email protected]
Abstract- A new design code structure for Spectral Amplitude Coding with zero cross- correlation in Optical Code Division Multiple Access (OCDMA) has been proposed in this paper. The proposed code called Modified Zero Cross Correlation Code
The auto and cross correlation functions of the sequences are defined respectively by
(MZCC). MZCC code provides much easier code construction,
N -1
given any nmnber of users K and weights to have minimum code
(2)
L
length. MZCC code will be demonstrated using OptiSys 6.0. The results indicated that MZCC code is truly performs better in term of noise performance compared with existing Optical CDMA codes.
(3)
Keywords: Modified Zero Cross Correlation, Noise Performance, Optisys 6.0, In Phase Cross Correlation, Spectral Amplitide Coding.
Since an is a {O, I} binary sequence, the maximum value I.
INTRODUCTION
of Ii,a (r) in Equation (2) is for r = 0 and is equal to w.
One goal when designing OCDMA systems is to achieve desirable properties of the transmitted and received signals especially to reduce the impact of the MAl. MAl is the interference resulting from other users transmitting at the same time, which is the main effect limiting the effective noise performance for the overall system [1]. Various schemes have been investigated in order to increase the number of OCDMA's active users while at the same time reducing effect of the MAl [2]. Several code families have been developed for OCDMA such as Zero Cross Correlation codes [3], M-sequence codes [4], Optical Orthogonal codes [5], Prime codes [6] etc. However, these codes suffer from certain limitations such as the code either too long (e.g. Optical Orthogonal Codes and Prime Code), construction are complicated or cross correlation are not zero. The key to an effective OCDMA system is the choice of efficient address codes with low or almost zero correlation properties for encoding the source [7]. The proposed code structure does not have overlapping of bits '1' and does not cause zero cross correlation to interfere between users, thus suppressing Phase Induced Intensity Noise (PUN). PUN is strongly related to MAl due to the overlapping of spectra from different users [6]. This property ensures that each codeword can easily be distinguished from every other address sequence.
II.
(4)
Ii, a (0)
=
If Aam & Acm denote the maximum out of phase auto correlation and cross-correlation values respectively, then an optical code of length N and weight w can be written as (N,w, Aam, Acm> or (N, w, Ama,) where Amax = max {learn, Acm}. It may also be noted that for an optical code an with weight 'w'
A
amax
A (0) a
(5)
In practice it is desirable to have a large set of optical code for a given values of N, w, Aam and Acm. The codes described by Equation (1) can be also represented in vector form as: A=3j for i=O, I, . .N-l B=bi for i=O, 1, .. N-l
ai= '0' or 'l' , i= O, . . . N-l bi= '0' or 'I', i=O, . . . N-l
978-1-61284-264-6/11/$26.00 ©2011 IEEE
Aa(O)
=
Aa,b(O)
length N such that: (1)
(6)
Where A and B are vectors of length N with elements as defined by Equation (6). In term of the vectors A and B. Equation (2) and Equation (3) are written as
DEVELOPMENT OF MZCC CODE
Assume that, A = {an} and B = {bn} be the sequences of
W
AA
=
T
AB
= w
T
N
La..
T T Where A and B denote the transpose of vectors A and B respectively. A. Development of the code. Optical zero cross correlation codes are sets of optical sequences that require (7) In fiber optic CDMA system to allow receivers to distinguish each of the possible users, to reduce channel interference and to accommodate large number of users, optical zero cross correlation codes should have large values of w and the size K. However it is difficult to design such an optical orthogonal code which satisfied all the requirements, for example the condition expressed in Equation (7) is only achieved at the expanse of the smaller values of 'w' or larger values of code length or smaller values of code size K. Consider a set of K, Zero Cross Correlation codes of length N and weight w for K users. The set of codes can be represented by the K rows of the KxL matrix. whose elements aij are given by
a.j i=l, 2,... K, aij = '0' or 'l'
A
(A ) (A
More over for
A; to have rank K, (9)
N::::K
A
ff
l. The elements {aij} of
(13)
Where,
D;
in a KxK diagonal matrix with w as it diagonal
elements as shown below,
D;
w
0
. 0
0
w
... 0
= 0
... w
I
(14)
For w=1 and for K users, one of the code matrices must satisfy the above four condition as represented by Equation (10-13) and has the minimum possible length N in the KxK identity matrix Pk whose elements Pi j are given by,
P .. =lfori=j i=l,.. K,j=l,..K IJ
(15)
=
Similiarly the code matrix
j=1
lJ
i = 1,2
K
...
for K users and weight w=2
and satisfied the condition expressed by Equation (10-13), is
N
=w,
rAi� � �1
PK = O O lKK x
(10)
2. The weight of each code should be equal to w where,
La..
The KxK matrix Pk is called the Unit Code Matrix.
A; must have values "0" or "I"
a.j "0" or "I" for i=I,2.. K, j=I,2,.. N
"0" or
)
= 0 fori "* j w Thus, for to represent a valid set of K. Zero Cross Correlation co es of weight w, it must satisfy the following conditions.
=
This is given by,
0
A;
(12)
=w
4. The set of K code words represented by the K rows of the w code matrix must form an orthogonal set (Zero Cross K w w T must be a KxK K Correlation) that is K diagonal matrix with w as diagonal elements.
A;
The matrix is called the code matrix. Since the K codes represented by the K rows of the code matrix are unique and independent of each other. has rank K.
2
Note that Equation (11) and (12) are same since a.j "1".
(8)
j=1,2, . . . N
lJ
j=!
(11)
3. The auto-correlation of each code for r = 0 in Equation (7) must be equal to w. That is,
given by KxL matrix (15) (16)
or Noticed that, N = 2K
Following similar line of argument, the code matrix
(17)
A;
for
K users and weightw in KxwK matrix
Noticed that, the minimum length N to the code is given by, N =wK
Matrix A is the KxK unit code matrix of Pb where the elements Pkij of Pk are given by Equation (15). Thus, when the number of weight equal to w=2, Matrix A will be [Pk:PJKx2K whereas the number of code length are satisfied with for Equation (16). From Example 1 shows, the matrix A is unique and independent of each other, with unspecified number of users. Noticed that, the sub elements of matrix A are combination of 2 matrices KxK as given in Equation (15), which is number of weight is w=1. Since, number of weight are increasing w=2, Matrix A (KxL) will be coincided with n�,g f weight and cause
�
(19)
Thus, for a given number of users K, and a given weightw, a set of Zero Cross Correlation code of minimum length can be constructed as given by Equation (18). This procedure will be explained with the help of an example.
PERFORMANCE COMPARISON
III. A.
Code Length Comparison:
In optical CDMA systems using Spectral Amplitude Coding, the length of the code is an important parameter.
Example:
The methods of generating a family of zero cross correlation for given values of K andw consist of the following step: 1). First forms the KxK unit code matrix as defined in Equation (15). 2).From the unit code matrix, generate the Kx2K code matrix as defined by Equation (16). 3). The K rows of the code matrix give the K optical CDMA codes having zero In Phase Cross Correlation ([PCC) and weightw. This method will now be explained with the help of an example:Assume that, it is desired to generate a set of minimum length zero [PCC optical codes for 3 users having weight equal to 2. Let's, K=3 and w=2. Following the procedure outline in above section:
[ ]
1). The unit code matrix for this code is 1 00
�
= 01 0 001
KxK
and the code matrix for this code is
A;
=[� �
o 0
It is desirable to have smaller code length as this will required smaller bandwidth. Moreover, code with smaller length will require less number of filters at the encoder as well decoder [12]. This will reduce the complexity and cost of the system. For various numbers of users and code weight, Table 1 shows the code length for the MZCC, ZCC and OOC codes. It can be seen from the table that for any given number of users K and code weightw the MZCC code has the minimum length. Thus, systems using MZCC code will be better in term of power received at the receiver, complexity and bandwidth requirement. For the same, transmitted power, systems with MZCC code will, therefore, have better performance in the presence of noise.
B.
Code Weight Comparison
As has been discussed in Section II, the MZCC code proposed in this paper can be designed for any given number of users K and code weight w. However, this is not true with the ZCC code. In the case of ZCC code, the number of user K is related to the weight w of the code by the following relation [11] K=w+l (20) From Equation (20), it is seen that the variable w and K are not independent. Thus, it is not possible to obtain the ZCC code for any given number of users and code weight. For example for w=3, the code does not exist for two or three users.
IV.
..
� �
NETWORK SIMULATION
- - - -_ ......_ - -_ . ....._ - -_ ..... ---- ..... -----......-----......-----......----- . -......-----......-----......----- .
The performance of MZCC code was simulated using OptiSys version 6.0. A Simple simulation schematic block diagram was illustrated in Figure 1. Each chip has a spectral width of 0.8 nm. The tests were carried out at the rate of 1 Gbps for 10 km distance with the ITU-T G.652 standard single
mode
optical
fiber.
Attenuation
of
0.2
dB/km,
dispersion of 16.75 ps/nm-km and non linear effects such as four wave mixing and self phase modulation were activated with industrial specification to simulate as close as industry real environment. The dark current value is lOnA and the 22 thermal noise coefficient is 1.0 x 10- WlHz for each of the photo-detectors.
The
performance
of
the
system
was
characterized by referring to the BER. Figure 2 shows the system performance for MZCC, MFH, MDW, EDW and OOC codes. It is clearly depict that when the number of users are increase simultaneously, MZCC code will shown superior
Figure.1 Simulation Schematic Block Diagram
performance of noise in term of BER. The existing optical codes, shown that the BER of these codes will be higher thus the systems using these codes will degraded as the number of
users are increasing. Figure 3 shows the variation of BER
over the Distance for MZCC and ZCC codes. It can be seen
·
I . E-05
·
I . E-08
from the plots, when the increasing of distance it will increase the BER. Means, for a long distance, the more BER will affect the signal. Various factors which can be responsible for this,
for
instance,
longer
fiber
will
provide
a
larger
attenuation, thus increasing the Bit Error Rate. From Figure 3, 9 at distance 20km, MZCC code have better BER 10- as 7 opposed to BER for ZCC code is equal to 10- which is not error
rate
for
standard
optical
communication
I$$$i
1.E-11 II::
�
1.E-14
II
1.E-17 I.E-20
systems
�dl l l n VfSl ,, 11
11 , Ii
-+--l----i 1.E-23 .J--'4--'----i----+-----'-4...L..!....l...-+---'-
threshold.
o
20
40
--"'MFH W=5
Weight, (w)
MZCC
ZCC
OOC
N
N
N
2
3
6
12
13
3
4
12
20
40
4
5
20
30
85
5
6
30
42
156
60 80 100 Number of Active User (K) -+-EDWW=3
ooeW=4
Table 1: Code length (N) comparison between MZCC, ZCC and OOC
Users, (K)
II
--.- Mzee W=4
120
140
-0
MDWW=6
160
Figure 2: BER versus Number of Active Users (K) for MZCC with Existing Optical Codes.
I
10E-02 1.0E-04
-
1.0E-06
6
7
42
56
253
7
8
56
72
393
1.0E-l0
8
9
72
90
577
1.0E-12
9
10
90
110
811
10
11
110
156
1101
1.0E-08
ffi III
./
10E-14
/'
1.0E-16 1.0E-18 1.0E-20
¥
1.0E-22 1.0E-24
o
7'
/
7'
/'
,.-
.... ...
-- -
./
/1'
10
15 Distance (km)
-+-MZee
20
25
30
zee
Figure 3: BER versus Distance (km) for MZCC and ZCC codes.
V.
CONCLUSION
Several codes of OCDMA had been research for
REFERENCES [1]
Code
many years and codes with minimum cross correlation shown the numerous advantages including code efficient in term of BER performance, free from suffering of intensity noise even from incoherent source originating and easy code construction
effectively determined number of length given any number of
Coding
Optical
Code
Journal
of
Science and Network Security, Vol. 6, No Division Multiple Access
[3]
Wei Z. and Ghafouri-Shiraz H., "Codes for Spectral-amplitude coding
(OCDMA), DCSNS International 12,ISSN 1738-7906, pp. 180--184 Optical CDMA Systems," Journal of Lightwave Technology, vol. 20, no. 8, pp. 1284-1291, 2002 [4]
Kavehrad M. and Zaccarin D., "Optical Code Division- Multiplexed Systems Based on Spectral Encoding ofNoncoherent Sources", IEEE Journal of Lightwave Technology, vol. 13, no. 3 pp. 534-545, 1995.
[5]
S. A. Aljunid,M. Ismail,A. R. Ramli, Borhanuddin M. Ali Mohamad Khazani Abdullah, "A New Family of Optical Code Sequences For
users and weights thus it will improve the noise performance. MZCC code presented in this paper is simpler and effective.
Spectral-Amplitude
[2]
successfully developed in this paper. From the performance analysis we conclude that the proposed code structures can
For
Computer
existence for every natural number of weight and number of users. A MZCC code structure for OCDMA system has been
M.S. Anuar, S.A. Aljunid, N.M. Saad. (2006). Development of a New
Spectral-Amplitude-Coding Optical CDMA Systems", IEEE Photonics Technology Letters, Vol 16, No. 10, Oct 2004. [6]
Sun Shurong, Hongxi Yin, Ziyu Wang, Anshi Xu, "A New Family of 2 D Optical Orthogonal Codes and Analysis of Its Performance in Optical CDMA Access Networks", Journal of Lightwave Technology Vol 24, No.4,ApriI2006-11-14
[7] S.A. Aljunid, M. D. A. Samad, M. Othman, M. H. Hisham, A.H. Kasiman
and M. K. Abdullah, Development of Modified Double
Weight Code and its Implementation in Multi-Rate Transmissions. Networks, 2005, International Conference on Communication, 2005 13th IEEE International Conference, YoU, ISSN 1531-2216, pp.5 [8] M.S. Anuar, N.M. Saad, A. Mohammed, E.L. Balekir, "Development of a zero cross correlation code for spectral amplitude coding optical code division multiple access (OCDMA)," JCSNS International Journal of Computer Science and Network Security, vol. 6, no. 12, Dec. 2006. [9] M.S.Anuar, S.A. Aljunid, R.Badlishah, N.M.Saad, I.Andonovic Performance Analysis of Optical Zero Cross Correlation in OCDMA System",Journal of Applied Sciences 7 (23):3819-3822, 2007, ISSN 1812 5654.
