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New Codes for Spectral Amplitude Coding Optical CDMA Systems

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					                                                              (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                        Vol. 9, No. 3, 2010

      New Codes for Spectral Amplitude Coding Optical
                     CDMA Systems
 Hassan Yousif Ahmed, Communication & Networking                           Elmaleeh, M. A, Electronics Engineering Dept, Faculty of
               Engineering Department                                                   Engineering and Technology
   Computer Science College, King Khalid University                                         University of Gezira
            Abha, Kingdom of Saudi Arabia                                                    Wad Madni, Sudan
               hassanuofg@gmail.com                                                    maleeh_mowafug@yahoo.com
Hilal Adnan Fadhil, School of Computer and Communication                      S.A. Aljunid, School of Computer and Communication
Engineering, Universiti Malaysia Perlies, Malaysia                            Engineering, Universiti Malaysia Perlies, Malaysia



Abstract—: A new code structure with zero in-phase cross                   (TDMA) and Code Division Multiple Access (CDMA)
correlation for spectral amplitude coding optical code division            .TDMA is a technology that allows multiple users to access a
multiple access (SAC-OCDMA) system is proposed, and called zero            channel by allocating time slots to each user within each
vectors combinatorial (ZVC). This code is constructed in a simple          channel. WDMA is a technology allowing multiple users to
algebraic way using Euclidean vectors and combinatorial theories           access a channel by allocating wavelength or frequency for
based on the relationship between the number of users N and the
weight W. One of the important properties of this code is that the
                                                                           each user within each channel. TDMA and WDMA have a
maximum cross correlation (CC) is always zero, which means that            limited bandwidth for each user [1-4].
multi-user interference (MUI) and phase induced intensity noise            Optical CDMA is the latest multiple access technique and was
(PIIN) are reduced. Bit error rate (BER) performance is compared           proposed during the last twenty years after studies on the
with previous reported codes. Therefore, theoretically, we                 drawbacks of the previous multiple access techniques.
demonstrate the performance of ZVC code with the related                   CDMA was invented and used as the first technique for
equations. In addition, the structure of the encoder/decoder based         wireless communication. It provided the best results compared
on fiber Bragg gratings (FBGs) and the proposed system have been           to other wireless multiple access techniques. This fact
analyzed theoretically by taking into consideration the effects of         encouraged the researcher to study if the advantages of
some noises. The results characterizing BER with respect to the
total number of active users show that ZVC code offers a
                                                                           CDMA could also be utilized in optical communication
significantly improved performance over previous reported codes by         systems.
supporting large numbers of users at BER≥ 10-9. A comprehensive            Optical fiber offers a much larger transmission bandwidth and
simulation study has been carried out using a commercial optical           in CDMA every user is distinguished from the others by his
system simulator “VPI™”. Moreover, it was shown that the                   unique code, hence the user can use the whole bandwidth of
proposed code managed to reduce the hardware complexity and                the fiber optic media. The key advantage of using OCDMA is
eventually the cost.                                                       that, it can be encoded and decoded in an optical domain
                                                                           without converting the signal to electronic circuitry unless it is
Keywords: Zero Vectors Combinatorial (ZVC), MUI, (SAC-
                                                                           needed. In OCDMA, MUI [2] is the ultimate limit in system
OCDMA), BER, FBG.
                                                                           performance. MUI increases with the number of simultaneous
                                                                           users and severely limits the capacity of the system.
                                                                                In recent years, spectral amplitude coding (SAC) systems
                       I.    INTRODUCTION                                  gained more attention since the MUI could be completely
 In the recent years, interest in optical communication systems            eradicated by spectral coding existing in conventional systems.
has been rapidly growing due to the large bandwidth offered                Several codes families have been proposed for SAC-OCDMA
by fiber optic systems. The success of long-span fiber optic               systems, such as the Hadamard code, integer lattice, modified
communication systems has shifted the focus of optical                     quadratic congruence (MQC), modified frequency hopping
networks to shorter-span metropolitan and local area domains               (MFH), modified double code (MDW), and enhanced double
[1].                                                                       weight (EDW) [5-10]. Although MUI can be cancelled by a
There is no much difference between multiple access and                    balanced detection scheme, inherent problems of noise still
multiplexing techniques; in simple words, multiple access                  remain as phase induced intensity noise (PIIN) arising from
allows communication media to be shared between different                  the spontaneous emission from the broadband source. In
users. Multiple access techniques represent one of the most                particular, an intelligent design of the codeword is important
essential functions of access networks while multiplexing is               to reduce the effect of MUI and PIIN to total received power.
the combination of signals into a single transmission signal.              In OCDMA systems minimization of the cross correlation to a
The three basic multiple access techniques are Wave Division               small value is required, especially when the value goes to zero.
Multiple Access (WDMA), Time Division Multiple Access                      In addition, code with a zero-cross is not effected by the noise




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                                                                                                       ISSN 1947-5500
                                                              (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                        Vol. 9, No. 3, 2010
cancellation; so another advantage of reduced hardware
                                                                                                ⎛0 ⎞
complexity is considered.                                                                       ⎜ ⎟
 A series of new code families called zero vector                                          v3 = ⎜ 0 ⎟
combinatorial (ZVC), with zero in-phase cross correlation for                                                                                   (4)
                                                                                                ⎜1 ⎟
SAC-OCDMA systems, which is characterized by (L, N, W,                                          ⎝ ⎠
λc) with length L, number of users N, weight W (number of
marks) and cross correlation λc based on vector space using the            Let N be the number of users and L the code length. We can
parameters (W, N) have proposed. The advantages of the                     write the code in a matrix form corresponding to the code
proposed ZVC code family are: 1) any positive integer number               word of N users. We obtain an N×L matrix with two
of weights can be used; 2) large flexibility in choosing the               dimensions as shown in Fig. 1.
number of users (free cardinality); 3) simplicity of code
construction; 4) maximum cross correlation is zero.                                           Matrix (N users’ × L length)
   This paper is organized as follows. In section 2, code
construction and development of all theoretical studies will be
presented. Code comparison and its advantages compared with                     User1#            1        0         0        .         .       0
other OCDMA are reported in section 3. OCDMA system
design will be demonstrated in section 4. In section 5, the                     User2#            0        0         0        .                 1
performance analysis of the new proposed system. Results and
discussion will be drawn in section 6 and finally, the
                                                                                    .              .       .         1        .         .        .
conclusion in section 7.

                                                                                    .              .       .                  .         .        .
          II.     CODE CONSTRUCTION AND PROPERTIES
                                                                                UserN#            0        1         0        .         .       0
 Definition: The space of all M-tiples of real numbers forms
an M-dimensional vector space over R where R is a field of
real numbers that is denoted by RM [12]. An element y of RM                                   Figure 1: A general matrix of ZVC
can be written as a column vector as follows:
                                                                             In order to have zero cross correlation (ZCC), we must have
                      ⎛ y1 ⎞                                               one ‘’1’’ in each column. This means for ZCC any column is
                      ⎜ ⎟
                      ⎜y ⎟                                    (1)          an element of the standard basis of RW. Given the number of
                    y=⎜ 2 ⎟                                                users N and the weight W, we can generate all possibilities of
                       M
                      ⎜ ⎟                                                  ZVC having length L=N×W by getting the all permutations of
                      ⎜ yM ⎟
                      ⎝ ⎠                                                  the vectors v1, v2, …,vw with repetition of each vector W-times.
   Based on the above definition, considering the parameters
(W, N), let vi be a column vector where i is positive integer in a             A. Elimination of redundant patterns
set RW having “0s” at all rows (users) except row i whose
magnitude is “1”. The sequence v1, v2,...,vW is a basis of RW ,              Permutation has been done for all vectors to produce the
called the standard basis. For R3 (i.e., W=3), the columns                 code patterns for certain values of N and W. Permutation
vectors can be constructed as in (2), (3), and (4) according to i          process symmetric patterns appeared for the same weight and
position.                                                                  number of users i.e., swapping between the users’ locations,
                                                                           the first user becomes the second user or the last user and so
                                                                           forth, so we have to find way to remove the symmetric
                      ⎛1 ⎞                                                 patterns. Fig. 2 shows the flowchart step of ZVC codes.
                      ⎜ ⎟                                                  The code length L is given by:
                 v1 = ⎜ 0 ⎟                                  (2)
                      ⎜0 ⎟                                                           L =N×W                                           (5)
                      ⎝ ⎠                                                  Using Eq. (6), the code possibilities (C-poss) for given N and
                                                                           W can be calculated as follows:
                     ⎛0 ⎞                                                                         (W × N )!
                     ⎜ ⎟
                v2 = ⎜ 1 ⎟
                                                             (3)                                  (W !×W !)
                     ⎜0 ⎟                                                               C-poss=                                                 (6)
                     ⎝ ⎠                                                   where W represents the invert of W (i.e., the number of zeros).
                                                                           From Eq. (6) it can be seen that several identical patterns can
                                                                           be obtained for the same value of W and N.




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                                                                                                         ISSN 1947-5500
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                        Start                                                                   (W × N )!         ( 2×2 )!
                                                                                     C-poss =
                                                                                                (W !×W !)
                                                                                                        =
                                                                                                                  ( 2!×2!)
                                                                                                                       =6
                                                                        We obtain the code pattern possibilities as shown in (7), (8),
                                                                        (9), (10), (11), and (12).

                                                                                    ⎛
                                                                                   1100 ⎞
                                                                                    ⎜   ⎟
                                                                                    ⎜   ⎟
              Enter the weight W and                                                ⎜
                number of user N                                            Hz1 =
                                                                                    0011⎟
                                                                                    ⎜
                                                                                    ⎝
                                                                                        ⎟
                                                                                        ⎠                                                    (7)
                                                                                  ⎛      ⎞
                                                                                  ⎜ 0110 ⎟
                                                                                  ⎜      ⎟
                                                                                  ⎜
                                                                                  ⎜1001 ⎟⎟
                                                                            Hz = ⎝
                                                                               2
                                                                                         ⎠                                                   (8)
                                                                                     ⎛      ⎞
                                                                                    1010
                                                                                     ⎜      ⎟
                                                                                     ⎜      ⎟
             Compute the length L                                                    ⎜      ⎟
                                                                             Hz3 =
                                                                                     0101
                                                                                     ⎜
                                                                                     ⎝
                                                                                            ⎟
                                                                                            ⎠                                                (9)
                                                                                   ⎛     ⎞
                                                                                   ⎜ 0011⎟
                                                                                   ⎜     ⎟
                                                                                   ⎜
                                                                                   ⎜1100 ⎟
                                                                                         ⎟
                                                                             Hz = ⎝
                                                                               4
                                                                                         ⎠                                                  (10)
                                                                                     ⎛      ⎞
                                                                                     0101
                                                                                     ⎜      ⎟
                                                                                     ⎜      ⎟
                 Code patterns                                                       ⎜      ⎟
                  possibilities                                              Hz5 =
                                                                                    1010
                                                                                     ⎜
                                                                                     ⎝
                                                                                            ⎟
                                                                                            ⎠                                               (11)
                                                                                   ⎛      ⎞
                                                                                   ⎜1001 ⎟
                                                                                   ⎜      ⎟
                                                                                   ⎜
                                                                                   ⎜ 0110 ⎟
                                                                                          ⎟
                                                                             Hz = ⎝
                                                                               6
                                                                                          ⎠                                                 (12)

                                                                        From the above code pattern possibilities, we can observe that
                                            Elimination of              there is a symmetric pattern between (7) and (10), (8) and (12),
                       Any
                    redundant                 redundant                 (9) and (11). Fig. 3 represents the snapshot for these patterns
                                               patterns                 using C++ tools for two and four users when W=2 and 3
                                                                        respectively. In order to remove symmetric patterns Equation
                                                                        (6) can be re-written as in Eq. (13).
                                                                                            ( W × N )!

                                                                                     Nc =
                                                                                                ( )N
                                                                                             N! W!
                                                                                                                                (13)
                        All
                    possibilities                                       where Nc is the number of code patterns possible after
                                                                        modification. Using Eq. (13), consider the same example (N=2,
                                                                        W=2); the C-poss becomes:
                                                                                                ( W × N )!        ( 2× 2 ) !

                                                                                         Nc =
                                                                                                   ( )
                                                                                                N! W!
                                                                                                         N
                                                                                                          =
                                                                                                                   2 !( 2 ! )
                                                                                                                         =3
                                                                                                                                2
                        End
                                                                         Using Eq. (13), C-poss becomes 3 instead of 6, which means
                 Figure.2: A general matrix of ZVC                          we can rewrite the code patterns as Hz1, Hz2, and Hz3.
                                                                                   III.   CODE EVALUATION AND COMPARISON
Let us investigate the following example.
                                                                         In recent years, many codes have been proposed such as the
                               N=2                                      Hadamard code [5], integer lattice [6], MFH [7], MQC [8],
                               W=2                                      MDW code [9], and EDW [10] and zero cross correlation
                         L= N× W= 2×2= 4.                               (ZCC) [11]. All these codes suffer from various limitations
                         W = L-W= 4-2= 2                                one way or another; the code construction is complicated (e.g.,
                                                                        MFH, MQC and Integer lattice) or the cross correlation is not
                                                                        ideal (e.g., Hadamard). However, the code construction not
    Therefore, substituting the above values in (6) yields:             only depends on cross correlation properties, the length plays
                                                                        an important role we have to consider as well.



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                                                                     (IJCSIS) International Journal of Computer Science and Information Security,
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    TABLE 1: OCDMA CODES COMPARISON AND EVALUATION

                                                           Code
          Code Family        Existence       Weight                    λ               Code length
                                                           Size                                                                  SNR
                                                            p2                                                              Δv( p +1)         [7,8]
                                                                                           2
             MQC            Primes p>2         p+1                     1                  p +p                         BK[(K −1) / p + p + K]

                                                             q2                                                        Δv(Q + 1)           [7,8]
             MFH                               q+1                     1                  q2 +q                 BK [( K − 1) / Q + Q + K ]
                              All GF

                            Even integer                   w/2+1                    3n+8/3[sin(Nπ/3)]2                    2 ( W − 1) Δ v  [9]
             MDW                                n                      1                                                      λ
                                 n                                                                                      BK [( K + W − 2 ]
                                                                                                                                2  λ


           Hadamard                                         2m-1                                                           Δv
                                m ≥2           2m-1                   2m-2                 2m                                        [5]
                                                                                                                        BK ( K + 1 )
                                                           C=2m                                                                  2 2 2
                                                                                                                                ℜ Psr W
                                                                                                                                    2
                                                                                                                                  L
              ZCC              K=2m           2m -1                    0                  K×W              Psr e B ℜ
                                                                                                               L
                                                                                                                       [ (( K   −1 ) + W ) W   ]+     4 K b Tn B
                                                                                                                                                         RL

                                                                                                                                 [11]
                                                            any
                              Positive       Positive
              ZVC                                        number of     0                  W×N                            Refer to Eq (14)
                              integer        integer
                                                           users



                                                                                 Long length is a disadvantage since the code is subject to
                                                                                 either very wide band sources or narrow filter bandwidths are
                                                                                 required while short length limits the freedom of code
                                                                                 selection. Therefore, a tradeoff between the number of code
                                                                                 words and code lengths must be made as well as MUI because
                                                                                 it is a dominant source of the noise. ZVC code exists for
                                                                                 convenient lengths that are neither too long nor too short. In
                                                                                 MFH code, although the code length is shorter compared to
                                                                                 ZVC, the cross correlation is always equal to unity and this
                                                                                 contributes to phase induce intensity noise (PIIN), while in
                                                                                 ZVC the cross correlation always equals to zero, which
                                                                                 eliminates the effect of PIIN.
                                                                                 In Table .I ZVC shows flexibility in terms of choosing the
                                                                                 number of users and the weight due to the use of a novel
                                                                                 method in code construction that generates many possibilities
                                                                                 from a given number of users and weights.
                                   (a)


                                                                                               IV.   SYSTEM DESIGN AND DISCUSSION

                                                                                   In the OCDMA system, an intelligent design of the code
                                                                                 sequences is important to reduce the contribution of MUI to
                                                                                 total received power. In addition, the structure of the
                                                                                 transmitter/receiver side plays an important role that should be
                                                                                 addressed as well. In conventional SAC-OCDMA, the balance
                                                                                 detection scheme is used to differentiate between the wanted
                                                                                 and the unwanted code sequences. Consequently, a new
                                                                                 structure of the transmitter/receiver for ZVC is proposed
                                                                                 called direct recovery scheme (DRS). Fig. 4 shows our
                                                                                 proposed transmitter and receiver structures consisting of four
                                                                                 users. At the transmitter, the information signal is modulated
                                                                                 to produce a series of optical pulses then coupled to the fiber
                                                                                 media.
                                   (b)
Figure.3: Snapshot of ZVC code patterns (a) W=2, N=2, (b) W=3, N=4




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            Figure.4: Direct recovery scheme




Figure 5: Example of Schematic block diagram for 2 users




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At the receiver side, the received signals are split into equal                               VI.    RESULTS AND DISCUSSION
parts followed by the filter and the photodiode; finally the
signals are recovered by the intended users using error                        In this section we will analyze our proposed system based on
detectors and this significantly eliminated the effect of MUI                  ZVC code only because it is able to accommodate a large
since only the wanted signal would be filtered out.                            number of users. The eye pattern diagram for ZVC codes is
Fig. 5 shows the setup of the proof of principle simulation for                illustrated in Figs. 6-8, respectively. From the figure we have
the proposed scheme. The performances of ZVC code were                         found that in order to transmit data at high bit rates over
simulated by using the simulation software Virtual Photonic                    dispersive fiber, an intelligent design of code construction has
Instrument (VPI) version 7.1. A simple schematic block                         to be taken into consideration to reduce the chips overlapping.
diagram consists of four users as illustrated in Fig. 4. Each                  However, the transmission distance remains limited due to
chip has a spectral width of 0.8 nm (100GHz).                                  unavoidable attenuation in the fiber and the noise generated in
The tests were carried out at a data rate of 10Gb/s for 10, 50                 the detector.
and 70 km. distance with the ITU-T G.652 standard single
mode fiber (SMF). All the attenuation α (i.e., 16 ps/nm km)
and nonlinear effects such as four-wave mixing, the cross
phase modulation, and the group delay were activated and
specified according to the typical industry values to simulate
the real environment as close as possible. As shown in Figure
4 after transmission, we used an optical filter to filter out the
coded sequence.
The decoded signal was decoded by a photo-detector (PD)
followed by a 0.7 GHz low pass filter (LPF) and error
detector, respectively.
The transmitted power used was 0 dBm of the broadband
source. The noise generated at the receiver was set to be
random and totally uncorrelated. The dark current value was 5
nA and the thermal noise coefficient was 2.5×e-23 W/Hz for
each of the photo-detectors.
                   V.    PERFORMANCE ANALYSIS

The signal to noise ratio (SNR) of the ZVC was calculated by
using the same method described in [6] and is given by the
formulas (14). Since the value of the cross correlation is zero                Figure 6: Eye diagram of ZVC channels at 10Gb/s for 10 km.
we compensated this value in the SNR [6], taking into account
the effects of phase induced intensity noise, the photodiode
shot noise and the thermal.                                                    Using the parameters: W=4, data rate 10Gb/s for 10 km, the
                                                                               eyes diagram shown in Fig. 6 clearly illustrates that the ZVC
                                2
                               ℜ P2W2
                                  sr
                                   2
                                                                               code system gives a better performance, having a large eye
                                  L                                            opening for a practical BER equal to 10-29. In Fig. 6, the
SNR=   P eBℜ
        sr
           L
               [ (N −1)+ W] + PsrΔBVℜL2N [ (N −1)+ W2]+ 4KRbLnB
                               2 2

                               2
                                                            T     (14)         estimated BER for ZVC is 10-28, which is satisfactory in
                                                                               practical communication systems. From the figure we obtained
                                                                               a clear eye diagram using the parameters: W=4, data rate
where ℜ is the photodiode responsivity, Psr is the effective                   10Gb/s for 50 km. In Fig. 7, the estimated BER from the eye
power of a broadband source at the receiver, e is the electronic               diagram for ZVC is in the order of 10-10 ... 10-14, which is
charge, B is the electrical equivalent noise bandwidth of the                  satisfactory in practical communication systems for the
receiver, KB is the Boltzmann’s constant, Tn the absolute                      parameters: W=4, data rate 10Gb/s for 70 km. Moreover, from
receiver noise temperature, RL is the receiver load resistor, ΔV               the figures, we can observe that the vertical distance between
is the optical source bandwidth, W, N, L, are the code weights,                the top of the eye opening and maximum signal levels gives
the number of users, and the code length as being the                          the degree of distortion.
parameters of ZVC code. The bit error rate (BER) is computed                   The deterioration is caused by the higher optical attenuation in
from the SNR using Gaussian approximation as [7].                              the longer fiber span. The more the eye closes, the more
                                                                               difficult it is to distinguish between ones and zeros in the
                                                                               signal. The height of the eye opening at the specified sampling
        BER = Pe = 1 erfc (
                   2
                                        SNR
                                         8    )                   (15)         time shows the noise margin or immunity to noise.




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                                                                                                          ISSN 1947-5500
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                                                                                                                                                                        0
                                                                                                                                                         10

                                                                                                                                                                        -2
                                                                                                                                                         10

                                                                                                                                                                        -4
                                                                                                                                                         10




                                                                                                                       Bit Error Rate (BER)
                                                                                                                                                                        -6
                                                                                                                                                         10

                                                                                                                                                                        -8
                                                                                                                                                         10

                                                                                                                                                                        -10
                                                                                                                                                         10

                                                                                                                                                                        -12
                                                                                                                                                         10
                                                                                                                                                                                                                                              ZVC code (w=4)
                                                                                                                                                                        -14                                                                   MDW code (w=4)
                                                                                                                                                         10
                                                                                                                                                                                                                                              HADAMARD code
                                                                                                                                                                        -16
                                                                                                                                                                                                                                              MQC code (w=8)
                                                                                                                                                         10
                                                                                                                                                                              0        20       40       60   80      100   120    140            160    180   200
                                                                                                                                                                                                         Number of Simultaneous Users

                                      Figure 7: Eye diagram of ZVC channels at 10Gb/s for 50 km.                     Figure 10: BER versus number of active users when Psr = -10dBm at data rate
                                                                                                                     155Mb/s.

                                                                                                                         Using Eq. 14, Fig. 9 shows the relationship between the
                                                                                                                     number of users and the SNR, for ZVC, MQC, MDW, and
                                                                                                                     Hadamard codes, where they have been plotted for different
                                                                                                                     values of N (number of users) when Psr = -10dBm at a data
                                                                                                                     rate of 155Mb/s. This figure clearly depicts that ZVC code
                                                                                                                     results in a much better performance, i.e. (Higher SNR) than
                                                                                                                     MQC, MDW and Hadamrad codes.


                                                                                                                                                                             0
                                                                                                                                                                        10

                                                                                                                                                                                                                                                  MQC code W=14


                                                                                                                                                                             -5
                                                                                                                                                                        10
                                                                                                                                              B it error rate (B E R)




                                                                                                                                                                                                                                                 MFH code W=17

                                                                                                                                                                                            ZVC code W=8,


                                      Figure 8: Eye diagram of ZVC channels at 10Gb/s for 70 km.
                                                                                                                                                                             -10
                                                                                                                                                                        10



                                  6
                                 10                                                                                                                                                                  Bit rate:622Mb/s
                                                                                       ZVC code (w=4)                                                                        -15
                                                                                       MDW code (w=6)                                                                   10
                                  5                                                    HADAMARD code
                                 10
                                                                                       MQC code (w=12)
   Signal to Noise Ratio (SNR)




                                  4
                                 10                                                                                                                                              -40         -35          -30           -25         -20       -15        -10      -5   0
                                                                                                                                                                                                                Effective power from each user: Psr(dBm)

                                  3
                                 10
                                                                                                                     Figure 11: SNRs versus number of active users when Psr = -10dBm at data
                                                                                                                     rate 155Mb/s.

                                  2
                                 10

                                                                                                                     This is evident from the fact that by minimizing the cross
                                  1
                                 10                                                                                  correlation, the power of interference from other users is
                                                                                                                     reduced, while the Hadamard code has an increasing value of
                                  0
                                 10                                                                                  cross-correlation as the number of users increase. Note also
                                       0    20   40    60   80      100   120    140     160   180   200             that the calculated SNR for ZVC code is achieved for W=4
                                                       Number of Simultaneous Users
                                                                                                                     while for MQC, MDW and Hadamard codes, the calculated
Figure 9: SNRs versus number of active users when Psr = -10dBm at data rate                                          SNR are for W=12, W=6 and W=64, respectively.
155Mb/s.                                                                                                             Using Eq. 15, Figure 10 shows the relationship between the
                                                                                                                     number of users and the BER, for ZVC, MQC, MDW, and



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                                                                                                                                                                                                                     ISSN 1947-5500
                                                                          (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                                    Vol. 9, No. 3, 2010
Hadamard codes, where they have been plotted for different                              [5]  [5] M. Kavehrad, and D. Zaccarh., “Optical Code-Division-Multiplexed
                                                                                             Systems Based on Spectral Encoding of Noncoherent Sources,” Journal
values of N (number of users) when Psr = -10dBm at data rate                                 of Lightwave Technology,” vol. 13, no. 3, pp 534–545, 1995.
155Mb/s. This figure clearly illustrates that ZVC code results                          [6] [6] Ivan B. Djordjevic and Bane Vasic., ”Novel Combinatorial
in a much better performance, i.e. (lower BER) than MQC,                                     Constructions     of Optical Orthogonal Codes for Incoherent OCDMA
MDW and Hadamrad codes. This is evident from the fact that                                   Systems,” Journal of Lightwave Technology. vol. 21, no. 9, pp. 1869–
when the cross correlation is reduced, the power of                                          1875, 2003.
interference from other users is reduced, while Hadamard code                           [7] [7] Zou Wei, H. M. H. Shalaby, H. Ghafouri-Shiraz.,” Modified
                                                                                             Quadratic Congruence codes for Fiber Bragg-Grating-Based SAC-
has increasing value of cross-correlation as the number of                                   OCDMA,” Journal of Lightwave Technology. vol. 19, no. 9, pp. 1209-
users increase. Note also that the calculated BER for ZVC                                    1212, 2001.
code is achieved for W=4 while for MQC, MDW and                                         [8] [8] Z. Wei and H. Ghafouri-Shiraz., " Proposal of a novel Code for
Hadamard codes, the calculated SNR are for W=8, W=4 and                                      Spectra Amplitude-Coding Optical CDMA Systems,"IEEE Photonics
                                                                                             Technology Letters, vol. 14, no. 3, pp. 414-416, 2002.
W=64, respectively.
                                                                                        [9] [9] S.A.Aljunid, ,M.Ismail, A.R.Ramli, Borhanuddin M. Ali, and
 Fig. 11 shows the BER variations with Psr when the number                                   Mohamad            Khazani Abdullah., “A New Family of Optical Code
of active users is 30 while W=4, 14 and 17 at the data rate                                  Sequences for Spectral-Amplitude-Coding Optical CDMA Systems,”
622Mb/s by taking into account the effects of the intensity                                  IEEE Photonics Technology         Letters. vol. 16, no.10, pp. 2383–2385,
noise, thermal noise and shot noise for ZVC, MQC and MFH                                     2004.
codes respectively. It has shown that, the ZVC has a lower                              [10] [10] Mohamad Khazani Abdullah , Feras N. Hasoon , S.A. Aljunid ,
                                                                                             Sahbudin Shaari., “Performance of OCDMA systems with new spectral
BER than that MQC and MFH codes, this due to eliminate the                                   direct detection (SDD)technique using enhanced double weight (EDW)
MUI effects through reduction of spectral overlapping.                                       code,” ScienceDirect, Optics Communications. vol. 28, no. 8, pp. 4658–
                                                                                             4662, 2008.
                                                                                        [11] [11] S. Anuar, S. A. Aljunid, N.M.Saad and S.M. Hamzah, "New design
                           VII. CONCLUSION                                                   of Spectral-Amplitude Coding in Optical code Division Multiple Access
                                                                                             (OCDMA) with Zero Cross-Correlation," Optics Communication, vol.
                                                                                             282, pp. 2659-2664, 2009.
  In this paper, an algorithm of code construction with a zero                          [12] [12] Kelley, John L. (1975). General Topology. Springer-Verlag. ISBN
cross correlation for the SAC-OCDMA system, based on                                         0-387-90125-6. http://en.wikipedia.org/wiki/Euclidean_space.
combinatorial theory and vector space, is presented. The
properties and theoretical development of a new family have
been proved and discussed with the related equations. New
structures of both transmitter and receiver sides have been
designed using FBG groups. To conclude, the advantages of                                               Hassan Yousif Ahmed is an Assistant
the codes can be summarized as follows: 1) any positive                                                 Professor in Network and Communication
integer number of weights can be used; 2) large flexibility in                                          Engineering Department at the University of
choosing the number of users (free cardinality) over other                                              King Khalid, Abha, KSA. He holds a PhD
codes like MQC and MFH; 3) simplicity of code construction;                                             degree in Electrical and Electronics
4) maximum cross correlation is zero. The new structures of                                             Engineering from University Technology
transmitter and receiver have been analyzed using ZVC,                                  Petronas, Malaysia, 2010 in addition to Data Communication
taking into consideration the effect of noises such as thermal                          Diploma and membership of IEEE. His research interests are
noise and shot noise. The study showed that, compared with a                            on Computer Network, wireless communications networks,
former code such as Hadamard, MQC and MDW better                                        and optical communications.
performance could be achieved by eliminating the effect of
phase induced intensity noise.


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