# Theoretical and Simulation Approaches for Studying Compensation Strategies of Nonlinear Effects Digital Lightwave Links Using DWDM Technology

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2 J. Computer Sci., (11):887-89, 007 to analyze nonlinear effects. Generally, non return to zero (NRZ) and return-to- zero (RZ) are the leading coding used in light wave communication. Other form of signal may be used, the transmission bit rate and signal level are defined using Matlab/Simulink parameter. Different signal characteristics are tested with modified intensity and bit rate level. The important characteristics of optical laser are the optical spectrum, the temporal response defined by the rise time and the fall time and the waveform describing the oscillation mode of the laser. When the laser is modulated directly by the excitation courant, the carrier density is not clamped at the threshold value. The modulation of carrier density is accompanied by a modulation of the index of refraction and that to frequency modulation. A expression of the laser frequency chirp is defined by [1]. α1 dp ε λ (t) = + P(t) 4π P0 dt τp (1) where α is a phase amplitude coupling, ε is the gain suppression factor and τ p is the photon lifetime. So, optical laser is modeled by two filters and a delay time given by : p td = τn In( ) Is I I I () where τ n is the carrier lifetime, I p is the polarisation current and I s is the threshold current. Using differential equations describing laser behavior, the related transfer function can be written as. P( ω) T( ω ) = I( ω) A(1 εp 0)P0 () = e ε P0 + A τ P n (1 εp 0) P0 1 ε 0 + A τp(1 εp 0) P0 ω + + ω ( + ) τ τ (1 εp ) τ τ (1 εp ) n p 0 n p 0 Where A is the differential gain coefficient and ε is compression factor. This function can be written as : T(p) = p α + α p + β represented with second order filter. The laser chirping model is described by an additive functions to F 1 (t) and F (t) in Fig. 1. Student concentrates to find the dependence between physical models and simulated ones. They often study the effect of laser physical parameters on output signal characteristics when a high bit-rate, more then.5 Gbit/s, is transmitted. An example of Matlab/Simulink model of laser source is given in Fig.. Comparing output signals of laser with the experimental response shows the validity of this equivalent circuit model. (4) Optical fiber modeling: Only single mode SM fiber is considered. Its model should take into account the attenuation and dispersion effects. The base band transfer function of the single mode fiber, in the power domain, is given by []. + jωt( λ) H(f ) ( ). ( ).e d = σ λ α λ λ (5) where σ(λ) is the source spectrum versus wavelength, α (λ) is the fiber attenuation for length λ versus wavelength, T(λ) is the fiber group delay per unit length. dt( λ) λ = D( λ ) (6) df c D(λ) is the chromatic dispersion. If we take into account introduced Kerr and Raman nonlinear effects, the evolution equation of optical power is described by nonlinear equation of Schrödinger [4]. D ata O ptical driver Laser λ 1 P hotodetector analyse Receiver noise D ata O ptical driver Laser λ MUX N:1 Fiber parameters DeMUX 1:N P hotodetector analyse D ata O ptical driver Laser λ N P hotodetector analyse Fig. 1: Block diagram of digital light wave transmission system using DWDM technique 888

4 J. Computer Sci., (11):887-89, 007 Amplitude of data input signal (V) Amplitude of data output signal (V) Fig. : The time evolutions of signal channel powers at the input and output ends of SM optical fiber, Simulink model, Data input signal and temporal signal at fiber output (fiber length 0 Km, D = 1 ps/nm.km, attenuation 0. db Km 1 ) Amplitude of received signal Without filtering (V) Amplitude of received signal With filtering (V) Fig. 4: APD receiver performance, Simulink model, temporal signal at receiver output without filtering and temporal signal at receiver output with filtering To minimize system noise, we have to give solutions by using adaptive filter and amplifier placed after the photo detector. Different blocs are tested separately to evaluate there temporal and spectral responses. With the combination of all bloc functions composing the optical transmission system it is possible to evaluate the maximum transmission distance for 890 defined parameters. In the same way, the student can obtain the plots of the temporal response or the eye diagram at the receiver output. On the other side, we can imagine solutions allowing to reduce these non linear effect by the addition of bloc functions. The difficulty in this study is to find a good approach between physical parameters and electrical model. Sample results of simulation employing DWDM

5 J. Computer Sci., (11):887-89, 007 Amplitude of received signal (mw) Amplitude of received signal (mw) Fig. 5: Digital light wave system performance, Simulink model, temporal signal at receiver output(multiplexed optical signal N:) and Eye diagram (after demultiplexing) for.5 Gbit/s transmission over 100 Km SM fiber, D = 1 ps/nm. Km (station A) technique are discussed. A basic end-to-end single mode digital light wave system is analyzed for different transmitted capacity of 140 Mbit/s,.5, 10 and 40 Gbit/s Fig. 5 studies an example of digital light wave system composed of three stations and three transmitting (n = ) wavelengths. PERFORMANCE EVALUATION OF DWDM SYSTEMS WITH AND WITHOUT COMPENSATION The transmission penalty, due to dispersion induced self-phase modulation and cross-phase modulation, in wavelength division multiplexing systems has been evaluated following a matrix analysis. The transmission system is composed of fiber of length L, which is divided into N segments such that every segment is represented with a bloc function. Considering the input-output column vectors, the power fluctuation part of the signal of p-th segment in a WDM system can be put in the following form [6] : 1 1 M 1 S (p + 1) A s(p) A x(p) A x (p) S (p) S (p + 1) A x(p) A s (p) S (p) = k k k k S (p + 1) A x(p) A s (p)... A x(p) * k (8) S (p) M M M S (p + 1) M A x (p) A s (p) S (p) where, k = 1, M is a channel number in a M channels WDM system and p = 1,, N is a segment number. Also, A s k is the self-phase modulation (SPM), given by [6] and A x k while stands for the cross-phase modulation (XPM). 891

6 J. Computer Sci., (11):887-89, 007 λ1 10E-6 λ=λ1+0.5 λ=λ1+0.8 λ4=λ1+1.5 Mux EDFA L1(Km) D1, D, L1 L Lp(Km) D1, L1 D, L Channel selection, Filter and receiver 10E-7 10E-8 Input optical WDM signals channel (1) channel (M) channel (1) channel (M) channel (1) channel (M) received optical signals Fig. 6: Dispersion map for Standard Single mode fibre (SSMF) D 1 = 17 ps/nm. Km and Dispersion compensating fibre DCF, D = -85 ps/nm. Km, L 1 = 40 Km, L = 10 Km Probability of error 10E-9 10E-10 10E-11 10E-1 10E-1 10E Received Power (dbm) Fig. 8: (a and b) BER curve for the 1st channel (best) and 4th channel (worst) and 1st channel without compensation compensating fiber (DCF)+ (SSMF), and different spans of L(Km) are analysed to evaluate the importance of different compensation techniques. Figure 7 and 8 give examples of simulation results and show the importance place that take compensation techniques to reduce the distortions on the received signals. The response of the optical system describe as better realistic cases and experimental measurements of digital optical network. Fig. 7: eye diagram of output signal of a transmission optical system (of best channel) without compensation using only standard fibre SSMF and using compensating map of a transmission optical system composed on N = 4 segments, L 1 = L = 40, L = L 4 = 10 Km, D 1 = D = 17 ps/nm. Km (SSMF), D = D 4 = -100 ps/nm. Km (DCF) CONCLUSION With the increasing demand for low-cost broadband service, optimizing nonlinear effects on optical communication systems becomes a key to driving down the cost per bit per kilometer. For this purpose, computer simulation plays an important role in the design, analysis and evaluation of DWDM system performance. It allows students to develop more and more complex optical model by means of which optimum results can be provided and interpreted. When developing a model based on theoretical formulation, one can see the importance of taking into account or neglecting physical parameters. It is easy to study the influence of different parameters on quality of transmission (QoS) in terms of BER and eye diagram and that can simplify complex theoretical expressions. This method is there fore a tool that can be used by student to optimize fiber parameters according to a required performance. These flexible techniques have to develop theoretical functions and experimental results to describe as better existing optical system response or to In the simulation technique, each channel defined with A k s (p) term is represented with a bloc function, where dispersion parameters and fiber characteristics are introduced (Fig. 6). The dispersion map is used to reduce the impact of nonlinearities. Different solutions are used as standard single-mode fiber (SSMF)+(SSMF), dispersion optimize future solutions on optical networks and in the 89

7 J. Computer Sci., (11):887-89, 007 same time to approach to students physical phenomena affecting the capacity transmission of optical fibers. REFERENCES 1. Liu, M.M., Principe and Application of Optical Communications, Chicago, IL, R.D. Irwin.. Elrefaie, A.F., J.K. Townsend, M.B. Romeiser and K.S. Shanmugan, Computer simulation of digital lightwave links, IEEE J. Selected areas in Communicat., 6 (1): Pires, V.F., J. Fernando and A. Silvia, 00. Teaching Nonlinear Modeling, Simulation and control of electronic power converters using Matlab/Simulink, IEEE Transaction Educat., 45 (): Midwinter, J.E. and Y.L. Guo, Optoelecronics and Lightwave Technol., Wiley- Interscience Publication. 5. Yariv, Optical Electronics in modern communications, 5th Edn., Ed. Oxford University Press. 6. Pal, B., S.P. Majumdar and R. Gangopadhyay, Evaluation by matrix method heterodyne CPFSK transmission penality due to GVD, SPM and ASE noise, in Proc IEEE LEOS Conf. Florida, USA. 7. Yamazaki, S., T. Ono and T. Ogata, 199. Compensation for chromatic dispersion and nonlineair effect, IEEE J. Lightwave Technol., 11:

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