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INTERNATIONAL JOURNAL OF ELECTRONICS (IJECET), ISSN International Journal of Electronics and Communication Engineering & TechnologyAND – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue TECHNOLOGY (IJECET) 0976COMMUNICATION ENGINEERING &3, October- December (2012), © IAEME ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), pp. 112-121 IJECET © IAEME: www.iaeme.com/ijecet.asp Journal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEME www.jifactor.com NUMERICAL SUPPRESSION OF LINEAR EFFECTS IN AN OPTICAL CDMA TRANSMISSION Faîçal Baklouti1, Rabah Attia2 (UR-CSE, Polytechnic school of Tunis, EPT, BP 743-2078, La Marsa, Tunis Tunisia. Email: 1 baklouti.isimm@gmail.com, 2rabah.attia@enit.rnu.tn) ABSTRACT Fiber characteristics play a critical role in the propagation of short optical pulses. To implement a temporal Optical Code-Division-Multiple-Access (OCDMA) solution, it is necessary to take into account the linear and nonlinear effects resulting from the propagation inside the fiber. In this paper, we study the importance of these phenomena along with the performance of the network. This study is intended to improve the OCDMA technique by numerically suppressing the linear effects in a Single-Mode Fiber (SMF). For this goal, Fractional Step Method (FSM) is adapted to predict the deformation of Gaussian signals introduced by the support and to reconstitute them after propagation inside the SMF. To evaluate our study, these phenomena are analyzed starting from the case of a single Gaussian pulse, going through the case of perfectly-synchronized Gaussian signals for OCDMA transmission and ending with the case of asynchronous Gaussian signals. Keywords: FSM, Linear Effects, OCDMA, SMF I. INTRODUCTION OCDMA is an optical multiple access technique that allows communication resources (time and bandwidth) to be shared efficiently in order to improve the capacity of communication networks [1]. While the vast bandwidth of the optical fiber medium provides high-speed point-to-point data transmission, the CDMA scheme facilitates random access to the channel in a bursty traffic environment [2]. It allows multiple users to share a common optical channel simultaneously and asynchronously [3]. OCDMA is one class of system that has the advantages of being able to provide a graceful degradation in performance as the number of users increases, besides its great system capacity and high communication security [4]. In the context of OCDMA implementation on access networks, assuming the channel is ideal, the transmission chain is divided into two parts: transmission and reception. Fig. 1 shows a basic OCDMA network architecture. In a direct OCDMA transmission, user's data 112 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME are promptly multiplied by the assigned code [5]. The time bit of the data to be transmitted is divided into a number of intervals called time chips Tc, or chip intervals. The code is defined by its length F, which is the number of time chips, and its weight W, which is the number of chips, or pulses in the sequence. The distribution of these pulses in the chip intervals is related to the code family used [6]. Thus, the coded signal is transmitted through a channel assumed to be ideal (i.e., the optical fiber). In OCDMA access network implementations, two possible reception techniques can be employed [7], one with a Conventional Correlation Receiver (CCR) and the other with a Multi User Detection (MUD) [8]. In the last decade, most researches are interested in the amelioration of the reception technique using a signal distorted by the support effect. In this work we present an novel approach in order to eliminate this effect before detection. This paper is organized as follow: In section II, we study the impact of chromatic dispersion in CDMA transmission, next we describe our proposed model. In section III, we present our simulation result starting from the dispersion phenomenon in a Gaussian pulse, dealing with the case of perfectly synchronized Gaussian signal for OCDMA transmission and ending with the asynchronous case. Fig. 1: OCDMA network architecture II. PROPOSED MODEL Chromatic dispersion in a SMF is the most important linear phenomenon [9]. This phenomenon is due to material dispersion and waveguide dispersion. Material dispersion reflects the fact that the fiber is mainly composed of silica, which has an optical index (i.e., refractive index) that vary according to the wavelength. As a result, the pulse emitted in this fiber spreads out. Waveguide dispersion is caused by the fact that waves propagate in a waveguide and not in an unlimited environment, thus leading to a dependence in the effective index based on the wavelength. The effect of chromatic dispersion is that, as the power of chips decrease when detecting an OCDMA transmission chain, some chips will be detected as 1, when they are in fact nil [10]. This linear effect of the fiber causes the temporal signal to spread. Research has made it possible to model optical signal transmission and to estimate what may happen to this signal after propagation through the fiber [11]. Thus, we primarily focus on the reception of signals distorted by dispersion or by other effects (i.e. length of the 113 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME fiber, wavelength) in an attempt to estimate the desired user signal. The idea is to eliminate the linear effects introduced by the estimated spread in the fiber before data detection takes place. Fig. 2 shows the proposed model. For this goal, we introduce a class of optical fiber simulation methods, called Fractional Step Methods (FSM). These methods allow us to take into account the behaviour of the unsteady flow field and record certain phenomena that occur within the fiber, such as chromatic dispersion and non-linear effects, which have a significant impact on the performance of optical communication systems. Fig. 2: proposed model When a medium's refractive index depends on the frequency ω of the wave passing through it, this medium is called a dispersive medium. The relationship between wavelength λ and refractive index n of a medium is given by the following formula [12]: B1λ2 B λ2 B λ2 n 2 (λ ) = 1 + + 22 2 + 23 2 (1) λ2 − C12 λ − C 2 λ − C 3 B1,2,3 and C1,2,3 are the experimentally-determined Sellmeier coefficients. When a wave propagates in a dispersive medium, the different wave frequency components propagate at different speeds, creating a temporal spread of the wave. For a given wave, we define the phase speed at which each wave frequency spreads as: ω c vp = = (2) k n This is different from the group velocity, which is the speed at which the wave envelope spreads. The group velocity is also the speed at which energy or information is carried through the wave and is defined as: 1 c c vg = = = (3) dk / dω dn ng n−λ dλ The refractive index of the group νg is defined as follows: dn ng = n − λ (4) dλ 114 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME Thus, it is clear that the group velocity is a function of the wavelength. Therefore, a light signal travelling in a dispersive medium over a distance L in time t can be expressed as: L L Ln g t= = = (5) vg c c ng Since laser sources typically used are not strictly monochromatic but have a wide spectrum λ centered around a central wavelength λ0, the delay ∆t between two wavelengths separated by λ is: L dn g L d 2n (6) ∆t = ∆λ = ∆λ − λ 2 = LD∆λ c dλ λ = λ0 c dλ λ = λ0 1 dng λ d 2n The parameter D = =− is known as the dispersion parameter. If D is negative, c dλ c dλ2 the environment has a positive or normal dispersion; thus the signal is transmitted in a normal dispersion pattern and the high frequency components move slower than the low frequency components. If D is positive, the environment has an anomalous dispersion and the higher frequency components move faster over time. Finally, if D is equal to zero, the medium is non-dispersive and all frequency components of the signal move at the same speed through the fiber. In reality, we can approximate a pulse generated by a distributed feedback laser with a Gaussian signal. The incident pulse at z = 0 inside the fiber has the form: T2 U (0, T ) = exp(− ) (7) 2T02 where T stands for the time measured from a frame of reference that moves with the pulse of the group velocity and T0 is the time width at the intensity 1/e. β i is the ith order derivative of d nβ the propagation constant ( β n = n ). The amplitude envelope, A(z,T), of the field d ω ω =ω 0 during light propagation in a dispersive optical fiber without loss is governed by Schrödinger's non-linear equation, simplified as follows : ∂A 1 ∂2 A i = β2 2 2 (8) ∂z 2 ∂ T The Fractional Step Method very useful in such kind of study because it allows us to take into account the behaviour of the unsteady flow field and record certain phenomena that 115 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME occur within the fiber, such as the linear effects. Our developed programs are based on this method. We will describe here one part of our detection algorithm which is very interesting to understand our approach. Starting from the propagation equation : ∂A( z , T ) ^ = D A( z , T ) (9) ∂z with, ^ i ∂2 α D = − β2 − (10) 2 ∂T 2 2 when α is the parameter of absorption. We have : A( z , t ) = U n = A(ndz , t ) (11) with A (0 , t ) = U 0 = [ f (t 0 ), f (t1 ),..., f (t M −1 )] is the initial distribution of the field at z = 0. T Each step of the algorithm requires an iterative procedure to determine Un+1 from Un. Also for q +1 ^ each n, we calculate U n0 )1 = U n and until convergence is reached i.e.,U n +1 = exp dz D U n . ( + In what follows, we summarize the steps of the previous algorithm to determine a final signal after its propagation inside a SMF: 1) U 0 ← A(0, T ) = { f (t m )}m =0 (initialization of the field discretized in time) M −1 2) U fft ← fft (U 0 ) (when fft is the fast fourier transform). 3) For n=0,.., N-1 (number of steps on the longitudinal axis z) a) U n +1 ← U n ^ b) U fft ← exp(dz D). * fft (U n+1 ) c) U n +1 ← ifft (U fft ) (when ifft is the inverse fast fourier transform). So, to deduce the initial signal from a resulting signal spreading in a single mode fiber and distorted by the linear effects, we will repeat the same steps of the previews algorithm but ˆ ˆ with replacing the operator ( D ) by (- D ). III. SIMULATION RESULTS In this section, we present our simulation results. As will be shown from the following results, our detection programs prove to be very fast, powerful and efficient. We started our simulation by modulating a Gaussian pulse with width T0 = 1.8 ps and power P0 = 1 W. In these results we examine the effect of second-order dispersion on the propagation of a Gaussian signal in a SMF, ignoring the high-order dispersion parameter and assuming the non-linearity to be zero. To examine the effect of the wavelength on the signal transmission, 116 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME we superimposed the simulated pulse response for the case of a wavelength in which the attenuation in the fiber is minimal (λ = 1.55 µm) and the dispersion parameter D is equal to 3.5 ps/nm.km (case 1), with the case of a wavelength λ = 1.3 µm and D = 19 ps/nm.km (case 2). The light was spread over a distance z = 100 km. Fig. 3 shows the power profiles of the corresponding signals. As shown from these results, the initial pulse clearly spreads with the increase of the wavelength (i.e., as the dispersion parameter increases). Next, we examine the effect of the 2nd-order dispersion for different fiber lengths (z = 20 km and 100 km) for a transmission wavelength λ = 1.3 µm and a dispersion parameter D = 3.5 ps/nm.km. As Fig. 4 shows, pulse spreading becomes more significant as the fiber length increases. Fig. 3: 2nd-order dispersion phenomenon for the different wavelengths transmitted Fig. 4: 2nd-order dispersion phenomenon for different In addition to the dispersion phenomena, the absorption phenomenon can change the shape of the transmitted pulse by reducing its intensity. Fig. 5 (case 1) shows the effect of the 2nd-order dispersion without any absorption phenomenon, whereas the results in the same Figure (case 2) shows the effect of an absorption parameter α = 0.005. Although the contribution of the 2nd-order dispersion term is dominant in most optical communication systems, it is sometimes necessary to include higher-order terms proportional to β3. For 117 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME example, when the pulse propagates around the wavelength of zero dispersion, or for the case when the pulse is very short (T0 < 0.1 ps), the contribution of β3 becomes important. Fig. 6 shows the power profile of a Gaussian pulse emitted at λ = 1.55 µm (D = 19 ps/nm.km) in a fiber of length z = 100 km, under the influence of 2nd- and 3rd-order dispersion phenomenon (β3 = 0.1) without any absorption phenomenon. As shown from the previous results, for all the phenomena illustrated above, it was possible to recover the original Gaussian pulse without any error. Thus, starting from the pulse distorted by the linear effects, we were able to estimate the transmitted pulse as a function of the fiber parameters. Fig. 5: 2nd-order dispersion phenomenon with effect of absorption phenomenon Fig. 6: 2nd- and 3rd-order dispersion phenomenon without any absorption phenomenon For the case of a perfectly-synchronized Gaussian signal, we assume that all users transmit a digital signal (0 or 1) synchronously (i.e., without any delay). These signals are encoded and the multiplexed signal is sent through the fiber. Using a code equal to "2 2 0 0 3 0 2 1" and Tc = 10 ps, the transmitted signal will have the form shown in Fig. 7. This signal is then sent over a single-mode fiber (z = 200 km, λ = 1550 nm, D = 20 ps/nm.km, β3 = 0.1, α = 0.005). At the end of the fiber, the received signal is shown in Fig. 8. 118 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME We now focus on the signal recovered after propagation in the fiber where we estimate the transmitted signal. Several simulations were necessary in order to retrieve the original signal. We found that by choosing a step equal to 100 * Tc, the Bit Error Rate (BER) was constantly in the order of 10-4 times the power of the wave. Hence, it is possible to correct for the error and recover the input signal. Fig. 7: Gaussian CDMA signal before propagation in the fiber (synchronous case) Fig. 8: Gaussian CDMA signal after propagation in the fiber (synchronous case) For the case of an asynchronous Gaussian signal, we assume that all users transmit digital signals (0 or 1) asynchronously (i.e., at different times). We consider the case of three users: the first with a coded signal "1 0 0 0 1 0 1 0" with a zero delay, the second with a coded signal "1 1 0 0 1 0 0 1" with a delay of 0.5 * Tc (a more difficult case since the delay is about n * Tc where n is integer), and the third with a coded signal "0 1 0 0 1 0 1 0" with a delay of 0.3 * Tc. The overall transmitted signal is shown in Fig. 9. This signal is sent over the same fiber type as in the perfectly-synchronized case where the received signal is shown in Fig. 10. We applied our simulation method in the same manner and with the same parameters and the resulting signal matches exactly the original transmitted signal. 119 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME IV. CONCLUSION In this paper, we have investigated the different effects of optical fiber communications in CDMA based transmission. In addition, our results are very interesting for improving the implementation of an optical CDMA transmission chain. So, these programs can be integrated into an FPGA or a digital calculator, which would eliminate the linear effects of the propagation of a coded signal in a fiber prior to completing the decoding. Another advantage of our proposition is the cost reductions caused by cancelling such physical effects as the compensation fibers for chromatic dispersion. So, further research should be done to integrate other non-linear effects into our method, as well as applying our method to Multi-Mode Fibers (MMF) and other types of non-Gaussian signals. Fig. 9: Gaussian CDMA signal before propagation in the fiber (asynchronous case) Fig. 10: Gaussian CDMA signal after propagation in the fiber (asynchronous case) REFERENCES [1] Nelly M. Shafik (2012), "Performance of OFDM- CDMA System using Modified Space-Shift Keying Technique", International Journal of Information and Communication Technology Research, Volume 2 No. 2. 120 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME [2] C.M. Negi, Amit Pandey, Gireesh G. Soni, Saral K. Gupta and J. Kumar (2011), "Optical CDMA Networks Using Different Detection Techniques and Coding Schemes", International Journal of Future Generation Communication and Networking Vol. 4, No. 3. [3] P. Pallavi and P. Dutta (2010), "Multi-Carrier CDMA Overview with BPSK Modulation In Rayleigh Channel", Proceeding of 3rd IEEE International Conference on Computer Science and Information Technology (ICCSIT), vol. 4, pp. 464-469. [4] Shahab Etemad, Anjali Agarwal, Tom Banwell, Janet Jackel, Ron Menendez, and Paul Toliver (2007), "OCDM-based photonic layer 'security' scalable to 100 Gbits/s for existing WDM networks", Journal of Optical Networking 6, 948-967. [5] M. Abu Faisal, Mohima Hossain and Shaikh Enayet Ullah (2012), "Performance Evaluation of a Multi Antenna MC-CDMA System on Color Image Transmission under Implementation of Various Signal Detection Techniques", International Journal of Advanced Science and Technology Vol. 41. [6] L. K. Bansal and A. Trivedi (2011), "Performance Evaluation of Space-Time Turbo Code Concatenated With Block Code MC-CDMA Systems", International Journal of Computer Science and Information Security (IJCSIS), vol. 9(1), pp. 108-115. [7] S.Zahedi and Jawad A.Salehi (2000), "Analytical comparison of various fiber optic cdma receiver structures", IEEE Journal of Lightwave Technology, Dec., vol. 18, pp. 1718- 1727. [8] Anicet M’foubat, Iyad Dayoub, Jean Michel Rouvaen, Walaa Hamouda and Awad Mazen (2009), "A Novel Approach for the Interference Cancellation in DS-CDMA Optical Networks", IEEE/OSA Journal of Optical Communications and Networking, Aug, vol. 1, no. 3, pp. 204-212. [9] Y. Zouine, I. Dayoub, S. Haxha, and J. M. Rouvaen (2008), "Analyses of constraints on high speed optical code division multiplexing access (OCDMA) link parameters due to fiber optic chromatic dispersion", Opt. Commun., vol. 281, pp. 1030–1036. [10] S. P. Majumder and A. Azhari, (2004) "Performance limitations of an optical CDMA system impaired by fiber chromatic dispersion", In Proc. ICON, vol. 1, p. 137-141. [11] Apithy, H., Bouslimani Y. and Hamam H. (2004), "Overview and Advantages of the Split- Step Method", Proceedings of SCI 2004, Orlando, FL. [12] Beylkin, G. Coifman R. and Rokhlin V. (1991), "Fast Wavelet Trasforms and Numerical Analysis I"., Comm. on Pure and Applied Math., XLIV, pp 141-183.OT alphabetically. 121

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