Matlab Simulink 光通信仿真实例

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MATLAB SIMULINK SIMULATION PLATFORM FOR PHOTONIC TRANSMISSION SYSTEMS Thus, it is the principal incentive for the development ments only. In practice each laser source would be of a simulation package based on matlab Simulink modulated by an cxtcrnal modulation sub-system the latform To the best of my knowledge, this is the first MZIM can bee a single or dual drive type. The schematic Matlab c Simulink -platform photonic transmission test of the modulator is shown in Figure 2(a) and the Simu- bed for modeling advanced high capacity and long-haul link model is in Figure 2(a) for generation of photonic digital optical fiber transmission systems. The simulator signals by multi-level amplitude and phase shift ke eying is used mainly for investigation of performance of ad modulation formats vanced modulation formats, especially the amplitu In 1980s and 1990s. direct modulation of semicon and/or phase shift keying modulation with or without the ductor lasers was the choice for low capacity coherent continuity at the phase transition. Here, a single channel optical systems over short transmission distance. How optical system is of main interest for implementation of ever, direct modulation induces chirping which results in the modeling in this paper severe dispersion penalties. In addition, lascr phasc noise Several noticeable advantages of the developed Mat- and induced from non-zero laser linewidth also limit the lab simulink e modeling platform are listed as follows advance of direct modulation to higher capacity and The simulator provides toolboxes and blocksets ade nigher bit rate transmission quately for setting up any complicated system con- Overcoming the mentioned issues, external modula igurations under test. The initialization process at tion techniques have been the preferred option for digital the start of any simulation for all parameters of sys- photonic systems for over the last decade. External tem components can be automatically conducted. The modulation can be implemented using either elec- initialization file is written in a separate Matlab file tro-absorption modulator or electro-optic modulators so that the simulation parameter can be modified cas- (EOM). The EOM whose operation is based on the prin il ciples of electro-optic effect (i.e. change of refractive Signal monitoring is especially easy to be carried out. index in solid state or poly meric or semiconductor mate Signals can be easily monitored at any point along rial is proportional to the applied clectric ficld) has been the propagation path in a simulation with simple the preferred choice of technology due to better per- plug-and-see monitoring scopes provided by Simu formance in terms of chirp, extinction ratio and modula- link(R tion speed. Over the years, the waveguides of the electro Numerical data including any simulation parameters optic modulators are mainly integrated on the material and the numerical results can be easily stored for platform of lithium niobate(Linbo3)which has been the later processing using Matlab toolboxes. This offers a choice due to their prominent properties of low lo complete package from generating the numerical data of fabrication and high efficiency [4] to processing these data for the achievement of final LiNbO3 modulators have been developed in the results early 1980s, but not popular until the advent of the er A novel modified fiber propagation algorithm has bium-doped optical fiber amplifier (EDFA) in the late been developed and optimized to minimize the simu- 1980s. Prior to the current employment of LiNbO3 modulators for advanced modulation formats, they were lation processing time and enhance its accuracy. employed in coherent optical communications to miti The transmission pcrformance of the optical trans gate the cffccts of broad linewidth duc to direct modula mission systems can be automatically and accurately tion of the laser source. These knowledges have recently evaluated with various evaluation methods These been applied to the in-coherent advanced modulation methods, especially proposal of novel statistical formats for optically amplified transmission systems evaluation techniques are to be presented in Section 6 EOMs are utilized for modulation of either the phase everal Matlab Simulink( modeling frameworks are or the intensity of the lightwave carrier. The later type is demonstrated in the Appendix of this paper. A Simulink a combination of two clcctro-optic phase modulators model of a photonic transmission system can be shown (EOPMs )forming an interferometric configuration In l igure 1(b) 2.l. Optical Phase Modulat 2. Optical transmitters Electro-optic phase modulator employs a single electrod The transmitters would consist of a narrow linewidth as shown in Figure 3. When a rf driving voltage is ap laser source to generate lightwaves of wavelength con lied onto the electrode. the refractive index changes formed to the itu grid. These lightwaves are combined accordingly inducing variation amount of delays of the and then modulated. This form is for laboratory experi- propagating lightwave. Since the delays correspond to the phase changes, EOPM is used to carry out the phase http:/,accessdateAugust22,2008 modulation of the optical carrier Copyright C 2009 SciRes 1 .. Communications, Network and System Sciences, 2009, 2, 91-168 100 L.N.BⅠNH Optical Modulator Laser source Modulated (Phase/Intensity) ighty Electrical precoder PRBS Data and Pulse Shaping Filter →V1 Outputv 1 0 To Workspace Dc bias pi Const omplex Phase CD2 V1/vpi 1550 DFB1 Product 1 Complex ANe Notate 20G User Data and Driver V 1 Ccmplex phase D1 Cod D2 V2'Vpi 0 MZIM Dual drivc Notate Driver v2 D1Coded pi consta utolutV 2 Gain PhPhase Shift Complex Phaso t 1 Complex In8 Gain 2 PhPhase Shift Complex Phase Shift 2 Constant 2 K Gain 3 Figure 2 Structure of external modulation for generation of advanced modulation format lightwave signals. (a) Schematic (b) Simulink model of pre-coder and modulation.(c) Details of MZIM. Copyright C 2009 SciRes 1 .. Communications, Network and System Sciences, 2009, 2, 91-168 MATLAB SIMULINK SIMULATION PLATFORM FOR PHOTONIC TRANSMISSION SYSTEMS 101 The induced phase variation is governed by the fol- shown in Figure 4 and is most popularly well-known as lowing equation the Mach-Zehnder interferometer(MZIM). The opera tional principles are briefly explained in the following P, (1) paragraph. For the rest of the chapters in this paper unless specifically indicated, the term of optical mom where Vn is the rF driving voltage required to create a T lator is referred to the external LiNbO3 MZIM modu phase shift of the lightwave carrier and typically has a lator value within a range of 3V to 6V. The optical field at the The lightwave s split into two arms when entering the output of an EOPM is generated given in following equa- modulator. The power slitter is normally a 3-dB type i.e tion equally splitting the power of the optical signals. Each E。=E j (2) arm of the liNbo3 modulator employs an electro-optic pl hase modulator in order to manipulate the phase of the where Fo is the transmitted optical field at the output the optical carrier if required. At the output of the MZIM MZIM and noted in the low pass equivalent representa- the lightwaves of the two arm phase modulators are cou tion ic the carrier is removed from the expression; v(t) oled and interfered with each other the transfer curve of is the time-varying signal voltage, Vbias is the dc bias an ZIM is shown in Figure 4(c). A LiNbO3 MZIM voltage applied to the phase modulator. modulator can be a single or dual drive type Recently, EOPMs operating at high frequency usin In the case of single-drive mzim, there is only a sin resonant-type electrodes have been studied and proposed gle rf voltage driving one arm of the MZiM. For in in [2, 3. Together with the advent of high-speed elec tronics which has evolved with the ASIC technology stance, there is no rF driving voltage on arm 1, hence V,(0-1 and the rF voltage V2(0 applied on arm 2 is using 0. lum GaAs P-IIEMT or InP IIEMTs [4, the noted as r(t). The transmitted optical field e(t)at the out contemporary EOPMs can now exceed 40Gb/s operating put a single-drive MZIm as a function of the driving volt rate without much difficulty Such phase modulation can be implemented in mat- age v()and a bias dc voltages Vbias can be written as LAB Simulink as shown in Figure 2(b)using a phase E (rio)vbias) shift block of the Common Blockset. The phase bias is in 1+e one phase shift block and then the signal modulation or time dependent is fed into another phase shift block. The (3) (r(t)+vbas signals of the two parallel phase shift/modulation blocks VIt)+r E: cos are then combined to represent the interferometric con struction and destruction, thus an intensity modulation can be achieved as described in the next sub-section where Vu is the required driving voltage to obtain a T phase shift in the lightwave carrier 2.2. Optical Intensity Modulator It can be seen that the phase term in Equation(1)im plies the cxistence of the modulation of the optical car- rier phase and commonly known as the chirping effect Optical intensity modulation is operating based on the hus, by using a single-drive maim, generated optical principle of interference of the optical field of the two signals is not chirp-free. Furthermore, it is reported that lightwave components. A LINbO3 optical intensity a z-cut LiNbo3 MZiM can provide a modest amount of modulator thus employs the interferometric structure as chirping duc to its asymmetrical structure of the electr cal field distributions whereas its counterpart x-cut LiNbO MZIM lectrodes Input optical field VI(L) Output optical field F:/2 Input oplical field Output optical field E E waveguid Va(t) waveguide electrodes Figure 4. Optical intensity modulator based on Mach- Figure 3. Electro-optic optical phase modulator Zehnder interferometric structure Copyright C 2009 SciRes 1 .. Communications, Network and System Sciences, 2009, 2, 91-168 L.N. BINH MZiM is a chirp-free modulator thanks to the symmetri 20 +17 ps/km. nm cal or push-pull configuration of the electrical fields 15 Furthermore, also having a push-pull arrangement, com Nonvzero-dispersion plete elimination of chirping effect in modulation of the Dispersion-shifted lightwave can be implemented with use of a dual-drive 6/km. nm MZIM. The transmitted optical field e(t) at the output a ③/0 ps/km.nm MZIM as a function of the driving and bias voltages can 1.11.2x31.4 1.61.7 be written as Wavelength(um) ((o)+sias -(V()+ba) 10 E +e ((t)+ coS Figure 5. Typical values of dispersion factor for different types of fibe In a dual-drive MZIM, the re driving voltage vi(t) and V2(0 are inverse with each other i. e v2(v-v,(o And 3)B2 is the derivative of group velocity with re Equation(4)indicates that there is no longer phase spect to frequency. Hence, it clearly shows th modulation component, hence the chirping cffcct is to- quency-dependence of the group velocity. This means tally eliminated that different frequency components of an optical pulse travel at different velocities, hence leading to the 3. Fiber transmission dynamics spreading of the pulse or known as the dispersion P2 therefore is known as the famous group velocity disper sion (GVD). The fiber is said to exhibit normal disper 3.1. Chromatic Dispersion(CD) sion for B2>0 or anomalous dispersion if B2<0 a pulse having the spectral width of A@ is broad This section briefly presents the key theoretical concepts ened by△=B2LΔo. In practice, a more commonly describing the properties of chromatic dispersion in a single-mode fiber, Another aim of this section is to in used factor to represent the chromatic dispersion of a troduce the key parameters which will be commonly single mode optical fiber is known as d(ps/nm. km). The mentioned in the rest of the paper dispersion factor is closely related to the GVD B2 and The initial point when mentioning to the chromatic given by: D=_2m B, at the operating wavelength x dispersion is the expansion of the mode propagation con- stant or wave number"parameter, B, using the taylor where B3 defined as B dp, contributes to the calcu- m ana β(a Bo+B14a+B24o2+B34o3(5) lations of the dispersion slope, s(a), which is an essen tial dispersion factor for high-Speed DWDM transmis where o is the angular optical frequency, n( o)is the sion. s(n) can be obtained from the higher order de frequency-dependent refractive index of the fiber. The rivatives of the propagation constant as dD( 2Ic 4T. d have different physi- (=( cal meanings as 1)Bo is involved in the phase velocity of a well-known parameter to govern the cffccts of chro- the optical carrier which is defined as p Oo_c matic dispersion imposing on the transmission length of an optical system is known as the dispersion length LD Con- ventionally, the dispersion length LD corresponds to the 2)BIdetermines the group velocity vg which is related to distance after which a pulse has broadened by one bit in the mode propagation constant p of the guided mode by terval. For high capacity long-haul transmission employ- [5,6 ing external modulation, the dispersion limit can be esti mated in the following Equation [8] d (6) DB Copyright C 2009 SciRes 1 .. Communications, Network and System Sciences, 2009, 2, 91-168 MATLAB SIMULINK SIMULATION PLATFORM FOR PHOTONIC TRANSMISSION SYSTEMS 103 where B is the bit rate(Gb/s), D is the dispersion factor differential group delay dgd) between two principle (ps/nm km) and Lp is in km orthogonal states of polarization(PSP) of the propagat Equation(8) provides a reasonable approximation ing optical field even though the accurate computation of this limit that One of the intrinsic causes of Pmd is due to the asym- depends the modulation format, the pulse shaping and metry of the fiber core. The other causes are derived the optical receiver design. It can be seen clearly from(8) from the deformation of the fiber including stress applied that the severity of the effects caused by the fiber chro on the fiber, the aging of the fiber, the variation of tem matic dispersion on externally modulated optical signals perature over time or effects from a vibration source is inversely proportional to the square of the bit rate. These processes are random resulting in the dynamic of Thus, for 10 Gb/s OC-192 optical transmission on a PMD. The imperfection of the core or deformation of the standard single mode fiber(SSMF)medium which has a fiber may be inherent from the manufacturing process or dispersion of about +17 ps/nm km, the dispersion length as a result of mechanical stress on the deployed fiber Lp has a value of approximately 60 km i. e corresponding resulting in a dynamic aspect of PMD to a residual dispersion of about +1000 ps/nm and less The delay between these two PSP is normally negli han 4 km or equivalently to about+60 psinm in the case gibly small in 10Gb/s optical transmission systems of 40Gb/s OC-768 optical systems. These lengths are a However, at high transmission bit rate for long-haul and great deal smaller than the length limited by ASE noise ultra long-haul optical systems, the PMD effect becomes accumulation. The chromatic dispersion therefore, be much more severe and degrades the system performance comes the one of the most critical constraints for the [9-12]. The dGd value varies along the fiber following modern high-capacity and ultra long-haul transmission a stochastic process. It is proven that these dgd values optical systems complies with a Maxwellian distribution as shown in Figure7[10,13,14] 3. 2. Polarization Mode Dispersion(PMD) (△z) Polarization mode dispersion(PmD) represents another 4r)ep/-4 32(△r) z>0 type of the pulse spreading. The PMd is caused by th where At is differential group delay over a segment of Fast axis the optical fiber 8z. The mean DGD value (Ar)is commonly termed as the fiber PMD'and normally Fiber with high PMD given by the fiber manufacturer An estimate of the transmission limit due to pmd ef- fect is given as 0.02 Slow axis △τ △r) (10 where r is the transmission bit rate. Thercforc, (Ar) Figure 6. Demonstration of delay between two polarization states when lightwave propagating optical fiber. ps/km (older fiber vintages ) Bit rate =40 Gbit/s Lmax=12.5 Km: Bit rate=10 Gbit/s: Lmax=200 Km; Normalized dgd distribution At)=0.1 ps/km(contemporary fiber for modern optical 0.025 systems ); Bit rate =40 Gbit/s; Lmax=1250 Km; thence for bit rate- 10 Gbit/s: Lmax-20. 000 Km Maxwellian PDF 0.02 Thus PMD is an important impairment of ultra long experiment distance transmission system even at 10 Gbis optical 0.015 transmission. Upgrading to higher bit rate and higher capacity pmd together with cd become the most two 0.01 critical impairments imposing on the limitation of the optical systems 0.005 3.3. Fiber nonlinearity 020406080 100 120 The fiber refractive index is not only dependent of Figure 7. The Maxwellian distribution is governed by the wavelength but also of intensity of the lightwave. This following expression: Equation ( 9). well-known phenomenon which is named as the Kerr Copyright C 2009 SciRes 1 .. Communications, Network and System Sciences, 2009, 2, 91-168 104 L.N. BINH effect is normally referred as the fiber nonlinearity. The ening of the signal spectrum. The spectral broadening Sa power dependence of the refractive index nr is shown in which is well-known as frequency chirping can be ex the following expression plained based on the time dependence of the nonlinear n,=n, +n, (P/Ar) (11) phase shift and given by the expression oP P is the average optical intensity inside the = (13) aT is the nonlinear-index coefficient and Aetf is the effective area of the fiber From(13), the amount of Sw is proportional to the There are several non-linearity phenomena induced time derivative of the signal power P. Correspondingly, from the Kerr effects including intra-channel self-phasc the generation of new spectral components may mainly modulation(SPM), cross phase modulation between in- occur the rising and falling edges of the optical pulse ter-channels (XPM). four wave mixing (FWM), stimu shapes, i.e. the amount of generated chirp is larger for an lated Raman scattering (SRS)and stimulated Brillouin increased steepness of the pulse edges scattering(SBS). SRS and sbs are not main degrading factors compared to the others. FWM effect degrades 4. Modeling of Fiber Propagation performance of an optical system severely if the local phase of the propagating channels are matched with the 4.1. Non-linear Schrodinger Equation(NLSE) introduction of the ghost pulse. However, with high local dispersion parameter such as in SSMF or even in Nz- Evolution of the slow varying complex envelope A(z, t)of DSF, cffect of the FWM becomes negligible. XPM is the optical pulses along a single mode optical fib strongly dependent on the channel spacing between the governed by the well-known nonlinear Schroedinger channels and also on local dispersion factor of the optical equation NLSE) fiber [refs]. [ref] also report about the negligible effects of XPM on the optical signal compared the SPm effect Q4,)+a北(:)+B024:4 Furthermore, XPM can be considered to be negligible in (14) a DWDM system in the following scenarios: 1)highly 10A(z, 4 locally dispersive system e.g SSMF and dCf deployed 1(2)2(z:) systems;2)large channel spacing and 3)high spectral efficiency [15-19]. However, the XPM should be taken where z is the spatial longitudinal coordinate, a accounts in to account for the systems deploying Non-zero disper for fiber attenuation, B, indicates the differential group sion shifted fiber(NZ-DSF)where the local dispersion delay ( dGD), B, and B, represent 2 and 3 order factor is low. The values of the Nz-dsf dispersion fac- factors of the group velocity dispersion(GVD)and y is tors can be obtained from Figure 5. Among nonlinearity impairments, SPM is considered to be the major short the nonlinear coefficient. Equation(14)involves the fol falls in the system lowing effects in a single-channel transmission fiber: 1) In this paper, only the SPM non-linearity is generally the attenuation, 2) chromatic dispersion, 3 )3 order dis considcrcd. This is the main degradation factor for high persion factor 1.e the dispersion slope, and 4) self phase bit rate transmission system where the signal spectrum is modulation nonlinearity. Other critical degradation fa broadened. The effect of SPM is normally coupled with tors such as the non-linear phase noise due to the fluctua- the nonlinear phase shift which is defined as tion of the optical intensity caused by Ase noise via Gordon-Mollenauer effect 20 is mutually included in ox=」yP(=LmP the equation y=an,/(Afrc) (12) 4.2. Symmetrical Split Step Fourier Method In this Paper, solutions of the nLSe and hence the model of pulse propagation in a single mode optical fiber is where @c is the lightwave carrier, Leff is the eftective numerically solved by using the popular approach of the transmission length and a is the attenuation factor of a split step fourier method(SSFM)[5] in which the fiber SSMF which normally has a value of 0. 17-0. 2 dB/km for length is divided into a large number of segments of the currently operating wavelengths within the 1550nm small step size 5z window. The temporal variation of the non-linear phase In practice, dispersion and nonlinearity are mutually ONL while the optical pulses propagating along the fiber interactive while the optical pulses propagate through the results in the generation of new spectral components far fiber. However, the SSFM assumes that over a small apart from the lightwave carrier implying the broad- length ]z, the effects of dispersion and the nonlinearity Copyright C 2009 SciRes 1 .. Communications, Network and System Sciences, 2009, 2, 91-168 MATLAB SIMULINK SIMULATION PLATFORM FOR PHOTONIC TRANSMISSION SYSTEMS 105 on the propagating optical field are independent. Thus, in (16) SSFM, the linear operator representing the effects of as(D+MA fiber dispersion and attenuation and the nonlinearity op erator taking into account fiber nonlinearities are defined and the complex amplitudes of optical pulses propagat- separately as ing from z to z+ Sz is calculated using the approxima tion as given 2 OT 15 (=+h,T)=(hD exphN a(z,) N=计y4 Equation (14)is accurate to second order in the step size Sz. The accuracy of SSFM can be improved b where A replace s A(z, 1) for simpler notation and including the effect of the nonlinearity in the middle of T-t-a/vg is the reference time frame moving at the group the segment rather than at the segment boundary as illus velocity. The nlse Equation(14)can be rewritten as trated in Equation(17) can now modified as onlinear operator Linear operator C Terminator 4 Check average input signal po Probe if too high -- pop up ERi T dt baud number of fFt TIme Step Real-Imag to Step Size(km) MATLAB alpha Complex 2 MATLAB Fcn alpha in dB /km Propagation Constants beta bela 1 bela 2 bela 3.] ear cott to Gamla(krmr.1. W-1)Complex 5 max number of Real-Imag to iteration for convergence nonlinearthreshod of Split Step methoc Tolerance number of FFt 1 def ault 1e-5) Real-Imag to Real-Imag to Figure &(a) Schematic illustration of the split-step Fourier method.(h )MATLAB Simulink model Copyright C 2009 SciRes 1 .. Communications, Network and System Sciences, 2009, 2, 91-168 106 L.N. BINH A(z+Oz, T 4. 4. Fiber Propagation in Linear Domain 2+2 ≈exP\、2 bexp∫M(2)dxp°4(z,r) Here, the low pass cquivalent frequency response of the optical fiber, noted as H(f) has a parabolic phase profile and can be modeled by the following equation, [22] (18) (20) This method is accurate to third order in the step size &z. The optical pulse is propagated down segment where, ap=I B,L,B, represents the Group Velocity from segment in two stages at each step. First, the optical Distortion (GVD) parameter of the fiber and l is the pulse propagates through the first linear operator(step of length of the fiber. The parabolic phase profile is the 5z/2)with dispersion effects taken into account only result of the chromatic dispersion of the optical fiber [23] The nonlinearity is calculated in the middle of the seg ment. It is noted that the nonlincarity cffects is consid The 3 order dispersion factor B, is not considered in this ered as over the whole segment. Then at z+ dz/2, the transfer function of the fiber due to negligible effects on pulse propagates through the remaining 5z/2 distance of 40Gb/s transmission systems. Ilowever, if the transmis the linear operator. The process continues repetitively in sion bit rate is higher than 40Gb/s, the B3 should be taken executive segments Sz until the end of the fiber. This method requires the careful selection of step sizes Sz In the model of the optical fiber, it is assumed that to reserve the required accuracy the signal is propagating in the linear domain, i. e. the The Simulink model of the lightwave signals propaga fiber nonlinearities are not included in the model tion through optical fiber is shown in Figure 8(b). all These nonlinear effects are investigated numerically. It parameters required for the propagation model are fed as is also assumed that the optical carrier has a line spec- the inputs into the block. The propagation algorithm trum. This is a valid assumption considering the state split-steps and FfT are written in. m files in order to of-the-art laser sources nowadays with very narrow simplify the model. This demonstrates the effectiveness linewidth and the use of external modulators in signal of the linkage between MATLAB and Simulink. A Mat- transmission lab program is used for modeling of the propagation of A pure sinusoidal signal of frequency f, propagating the guided lightwave signals over very long distance is through the optical fib delay of 27DB2/ given in the appendix The standard fibers used in optical communications have a negative B, and thus, in low pass equivalent repre 43. Modeling of Polarization Mode Dispersion sentation, sinusoids with positive frequencies (i.e. fre (PMD) quencies higher than the carrier) have negative delays, i.e arrive early compared to the carrier and the ones with The first order PMd effect can be implemented by split negative frequcncics (i.c. frequencies lower than the car ting the optical field into two distinct paths representing rier)have positive delays and arrive delayed. The disper two states of polarizations with different propagating sion compensating fibers have positive B, and so have delays At, then implementing SSFM over the segment reverse effects. The low pass equivalent channel impulse d before superimposing the outputs of these two paths response of the optical fiber, hc(t) has also followed a for the output optical field parabolic phase profile and is given as The transfer function for first-order PMd is given by 21] h() 2l) H,()=H1()+H1( (19) ()=cap|n2|-4 5. Optical Amplifier an 5.1. ASE Noise of Optical Amplifier H()=vex|/2 T The following formulation accounts for all noise terms that can be treated as gaussian noise with y is the splitting ratio. The usual assumption is r=1/2. Finite impulse response filter blocks of the digi- mn.hvG-1)B tal signal processing blocksets of Simulink can be ap- G=amplifier gain; nsp= spontaneous emission factor; m plied here without much difficulty to represent the PMd -number of polarization modes(1 or 2): PN=mean noise ffects with appropriate delay difference in bandwidth; OSNR at the output of edFa Copyright C 2009 SciRes 1 .. Communications, Network and System Sciences, 2009, 2, 91-168

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