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Scilab Open-Source Software for Fiber Optic Communication Systems Simulation Marek Jaworski Department of Transmission and Fiber Optics, National Institute of Telecommunications 1 Szachowa Str., 04-894 Warsaw, Poland E-mail:
[email protected] ABSTRACT Scilab toolbox for fiber optic communication systems simulation was developed, named SSS. The features of SSS simulator are presented by including examples of program code with short comments explaining the key instructions, followed by graphical presentation of simulation results. Scilab is an open-source alternative of Matlab and combined with SSS toolbox could be implemented in research and education. Keywords: Scilab, numerical simulations, optical communication systems, open-source. 1. INTRODUCTION To meet the constantly increasing traffic in optical networks due to growth of the Internet, spectral efficiency should be increased by using, e.g., an advanced modulation formats and reduced distance between channels. This results in increasing the power spectral density and interferences with an adjacent channels. Furthermore, dynamic links switching in the network is foreseen. All this makes the physical layer simulations an important task in network modeling, helping to optimize the transmission range of individual optical paths. There are several professional programs designed to simulate fiber optic systems, e.g., TransmissionMakerTM, OptiSystemTM, and OptSim ModeSYSTM. The programs are rather expensive, whereas there is no simpler, e.g., shareware software of this type. For this reason, we develop our own software, which was used as a support for research projects. In our opinion, such a software could also find applications in education. The simulator modules based on algorithms available in the literature [1-4] were developed and then verified by comparing the simulation results with obtained using commercial simulators. In the next few years many new modules was added, due to cope with the rapid development of optical telecommunication techniques. So far, simulations of physical layer optical network in our group were performed in a LabView programming environment. This involved many drawbacks. Firstly, LabView is a graphical programming language, primarily intended for control measuring equipment – not for simulation, and is developed to enhance measuring abilities. Secondly, LabView is an expensive program. Thirdly, graphical programming language used for simple calculations give a clear code that can be seen on one screen, but expanding the complexity of the algorithm leads to visualization problems, to this extent that software maintenance create more problems than main algorithm itself. The above-mentioned disadvantages of LabView was motivation to transferring prepared simulator modules to more universal and accessible software platform. To accomplish this task Scilab numerical calculation program was chosen. This is a free software (available at www.scilab.org), originally created in 1990 by the French National Institute for Computer Science and Control (INRIA), currently being developed and distributed on open-source license. Scilab, which is an open-source alternative of Matlab, is high-level programming language oriented on numerical calculations. 2. SIMULATOR DESCRIPTION The simulator called SSS (which stands for Fiber Systems Simulator in polish language) has modular, hierarchical structure, in which the modules correspond to specific elements of the simulated system (see Table 1). The general assumption was that the program code should contain up to several dozen of lines, to clearly visualize the whole analyzed system. The simulator was developed as an integral toolbox and all its features are automatically available when the SSS item is selected from the drop-down toolboxes list, visible in the main menu of the Scilab console. In the console appear available SSS module names after typing their initial letters (SSS is a unique suffix of all modules). Contextual help for each module is also generated. The help file can be generated automatically when developing the new module directly from the in-line code comments. The features of SSS simulator are presented below by including examples of program code with short comments explaining the key instructions, followed by graphical presentation of simulation results.
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Table 1. Selected developed modules. System elements − global constants generator Electrical components − delay line − phase shifter − phase modulator − mixer Electrical filters − low pass filter (Bessel, Butterworth) Electrical measuring instruments − oscilloscope − spectrum analyzer − eye diagram − eye opening − BER calculator Electrical signal sources − data generator (PRBS sequence) − Dirac delta pulse − sinus generator
Optical components − photodetector − coherent photodetector − delay line − phase shifter − polarization delay − polarization rotator − polarizer − wave plate − bandpass filter Optical measuring instruments − spectrum analyzer − polarization analyzer − power meter Optical sources − CW monochromatic − Gaussian pulse − hyperbolic secant pulse − Dirac delta pulse Optical amplifiers − EDFA power limiter − EDFA with ASE power amplifier
Optical modulators − linear − Mach-Zehnder dual-electrode − Mach-Zehnder single-electrode − phase modulator Optical fibers − linear (w/o the Kerr effect) − non-linear SSLEM − non-linear with 2-pol. modes System transmitters − DPSK − QPSK System receivers − DPSK − QPSK − PM-QPSK
2.1 40 Gbit/s IM-DD Transmission Illustrates the effect of chromatic dispersion and Kerr nonlinearity. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
SSSconfig(40,1280,8,0); global MLA MFR MNB MNT MDT MBR; Pin_mW=50.0; x=SSSeSourceData(1); x=SSSeLPF(x,2*MBR,4,0); X=SSSoSourceLambda(2*Pin_mW,0); X=SSSoModMZ(X,x); StepCtrl=list(1e-4, 5); g_Wkm=1.5; X=SSSFiberLEM(X,list(5,0.0,16,0.08), StepCtrl, g_Wkm); x=SSSoDetector(X); x=SSSeLPF(x,0.6*MBR); x1=SSSeEyeDiagram(x); y=SSSeEyeOpening(x); plot2d(x1); xtitle("Eye Diagram","Time [ns]","Amplitude");
(a) (b) Figure 1: a) Program code ;b) Eye diagram. The 40 Gbit/s IM-DD system, Pin = 5 mW, fiber: L =5 km, D = 16 ps/nm/km, γ = 1.5 W-1km-1. Description of the program code: 1 – On the basis of the input parameters: a) the bit rate [Gbit/s], b) the frequency band [GHz], c) the length of the bit sequence [2n], d) the central wavelength [nm], global constants are created, available in all modules: a) MLA – the center wavelength, b) MFR – the vector frequency, c) MNB – the number of input bits, d) MNT – the number of signal samples (length of the vector which are performed simulations), e) MDT– the bitrate, f) MBR – the duration of the simulated sequence. 4 – Generates a pseudorandom bit sequence of a given amplitude. 5 – The low pass filter with a predetermined 3 dB band, order and type (0 – Bessel, 1 – Butterworth). 9 – Functional extension of linear fiber (SSSFiberLinear), taking into account the non-linearity resulting from the Kerr effect. Propagation of electric field in x-axis polarization is modeled by the nonlinear Schrödinger differential equation [1], solved using symmetrized split step Fourier method (SSFM), in which the fiber is divided into short sections, alternately influenced by dispersion and nonlinearity. The length of these sections is adjusted automatically based on the calculation of the local error in each successive step (SSLEM) [2]. A detailed description of this method and general classification of another methods is given in [3],[4]. For simplicity and numerical efficiency in the y-axis linear model is utilised.
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Kerr effect is a source of self-phase modulation (SPM), cross-modulation (XPM), and four wave mixing (FWM). Stimulated Raman and Brillouin scattering are neglected here. 12 – Eye diagram – superimposed signal waveforms, shifted synchronously by one bit. 14 – Plotting the diagram with a given title and description of the axis. 2.2 The 40 GHz QPSK Transmission Illustrates the operation of quadrature phase shift keying (QPSK) transmission. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
SSSconfig(40,640,7); global MBR MDT MNT MNB MFR MLA; [X,bits]=SSSeQPSKcoder(); Pch_dBm=10; X=SSSoEDFAlimiter(X,Pch_dBm); Fiber=list(50,0.2,16,0.08); DCF=list(Fiber(1),0,-Fiber(3),-Fiber(4)); X=SSSFiberLEM(X,Fiber); X=SSSFiberLinear(X,DCF); X= SSSoPolRotator(X,15); X= SSSoPhaseShift(X,20); [xI,xQ]=SSSoDetectorIQ(X); xI=SSSeLPF(xI,0.6*MBR); xQ=SSSeLPF(xQ,0.6*MBR); [EyeOpening,bRe,bIm]=SSSeQPSKdecoder(xI,xQ,bits); plot2d(bRe,bIm,-3,rect=[-1.5,-1.5,1.5,1.5]); xtitle("Eye Diagram","I","Q")
(a) (b) Figure 2: a) Program code ; b) QPSK constellation. The 40 Gbaud QPSK system with DSP back-propagation, Pin = 10 mW, fiber: 50 km, D = 16 ps/nm/km, γ = 1.5 W-1km-1.
Description of the program code: 3 – The encoder generates independent bit sequences in orthogonal I and Q axes, assigns the instantaneous phase of the bits and encodes optical signal in a linear phase modulator. Moreover, the sequence of bits transmitted is saved as the vector bits. 9 – DSP back-propagation, with parameters defined in 7. 12 – Coherent photodetector produces signals proportional to the square of I and Q field components. 15 – Decoder is a multifunction module based on bits vector and output signals from the coherent photodetector. Estimates the error vector magnitude (EVM) for each constellation points on IQ plane. Digital signal processing involves the following steps: − optimization of the sampling time by maximizing the correlation of the original waveform from the transmitter with the received one, − normalization of amplitude, − separation the received bits to constellation points, − estimation of constellation rotation followed by compensation, − translation of all constellation points to the center of the coordinate system, − finally, estimation of the EVM. 2.3 Optimizing the Signal Power in 40 GHz NRZ 10×50 km Transmission Determining the optimal optical power is particularly important issue in flexible optical networks with dynamic optical path allocation of a given bit rate. Here, two dispersion compensation scenarios are shown: (i) pre- and post-compensation (in the ratio 50% + 50%), by digital signal processing (DSP) at the transmitter and the receiver, (ii) in each regenerative section, together with the regeneration of amplitude – a typical application of the DCF fiber and EDFA. Simulations are executed in a loop with 0.05 dB steps of the input power. From Fig. 3 it is clearly seen that the digital compensation gives approx. 2 dB gain over the use of an optical compensation DCF. Several other demo examples has been included in SSS Toolbox, which are listed below: − − − − − − − −
animation of four wave mixing (FWM); animation of two solitons collision; animation of DWDM 3 ×40 Gbit/s transmission, 50 km SSMF + 16 km DSF; DWDM NRZ 5×40 GHz transmission, 5 channels, SSMF+DSF 5 ×100 km; 40 GHz QPSK transmission, 50 km SSMF + DSP compensation; DWDM QPSK 5×40 GHz transmission , 5×50 km; signal power optimization for QPSK 40 GHz 10×50 km transmission with DSP compensation; 40 GHz 50 km PMD-QPSK transmission using fiber model described in [5] with DSP compensation. 3
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Figure 3. Optimization of signal power in 40 GHz NRZ 10×50 km transmission: blue – DSP, green – DCF+EDFA in each section. D = 16 ps/nm/km, γ = 1.5 W-1km-1. 3. CONSLUSIONS The developed simulator has basic functions implemented, and several demo examples has been included to easily explore and better understand program functioning, some of which are shown in Section 2. However, to effectively support research in the field of flexible optical networks, processing speed improvement is necessary, which should be obtain by using graphical processing units (GPUs) with CUDA architecture [6]. The final goal is to design a specialized simulation tool developed in open-source environment that could be used by many users. To obtain this goal the simulator will be placed in near future in special Scilab toolbox repository at https://atoms.scilab.org/. REFERENCES [1] G.P. Agrawal: Nonlinear Fiber Optics, 3rd ed., Academic Press, San Diego, 2001. [2] O.V. Sinkin et al.: Optimization of the split-step Fourier method in modeling optical-fiber communications systems, IEEE/OSA J. Lightw. Technol., vol. 21, no. 1, pp. 61-68, Jan. 2003. [3] M. Jaworski: Methods of step-size distribution optimisation used in S-SSFM simulations of WDM systems, Journal of Telecommunications and Information Technology, no. 1, pp. 44-50, 2009. [4] M. Karasek, S. Aleksić, M. Jaworski, and J. Leibrich: Software tools and methods for modelling physical layer issues, Lecture Notes in Computer Science. Towards Digital Optical Networks, Springer, vol. 5412, pp. 309-330, Berlin 2009. [5] M.E. Marhic, A.A. Rieznik, G. Kalogerakis, C. Braimiotis, H.L. Fragnito, and L.G. Kazovsky: Accurate numerical simulation of short fiber optical parametric amplifiers, Optics Express, vol. 16, no. 6, Mar. 2008. [6] S. Pachnicke, A. Chachaj, M. Helf, and P.M. Krummrich: Fast parallel simulation of fiber optical communication systems accelerated by a graphics processing unit, in Proc. ICTON 2010, Munich, paper Th.B1.5, Jun. 2010.
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