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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 272 http://sites.google.com/site/ijcsis/ 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. 273 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 3, 2010 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. 274 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 3, 2010 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=4 275 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 3, 2010 Figure.4: Direct recovery scheme Figure 5: Example of Schematic block diagram for 2 users 276 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 3, 2010 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. 277 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 3, 2010 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 278 http://sites.google.com/site/ijcsis/ 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. 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Fan., “Spread-spectrum fiber-optic local area network using optical processing,” J. Lightwave Technol,. vol. LT, no. 4, pp. 547–554, 1986. 279 http://sites.google.com/site/ijcsis/ ISSN 1947-5500