Modeling of WDM transmission system with high-order phase modulation formats

Modeling of WDM Transmission System with High-Order Phase Modulation Formats Daniel Benedikovic, Jan Litvik, Michal Kuba, Milan Dado, and Jozef Dubovan  Abstract—The objective of this paper is focused on numerical modeling of WDM (Wavelength-Division Multiplex) transmission systems that employ new classes of high-order PSK (Phase-Shift Keying) modulation formats. This paper provides investigation of signals propagation with corresponding degradation mechanisms in physical layer, when high-order phase modulation formats are used for their transmission. The impacts of linear and nonlinear effects on modulated signal in multichannel system are studied. For this purpose, it was created numerical model by solving CNLSE (Coupled Nonlinear Schrödinger´s Equations) through SSFM (Split-Step Fourier Method). The fundamental characteristics of optical fibers, employed modulation format and WDM system parameters are significant for our investigation, because they play important role for behavior of modulated signals. Our results are analyzed and interpreted by the way of finding out the suitable and optimal system settings for transmission of phase modulated signals. Keywords—Coupled Nonlinear Schrodinger´s Equations, Digital phase modulation, Split-Step Fourier Method, Wavelength Division Multiplex significant impact on phase characteristics of transmitted signals from channel to channel. By precise investigation, it can be possible to set optimal parameters of fiber and WDM system for signals transmission and achieve good performance of the multichannel systems [1], [3], [9]. The numerical model was created through SSFM, which provides efficient adaptation for phase modulation formats, fiber and system parameters. The results are discussed and analyzed. The aim of paper is oriented to show suitability of using PSK modulation formats, when they are impaired by different degradation mechanisms of transmission channel. II. THEORETICAL AND MATHEMATICAL DESCRIPTION A. High-order phase modulation formats In general, the implementation of high-order modulation format is one of the biggest challenges in the future of optical communication networks. The range of different types of modulation format is wide and we focus on M-PSK formats. Mathematical description of modulating optical signal is given by Gaussian function I. INTRODUCTION M optical systems provide the best solution for future trends of optical networks, where fundamental requirements for high capacity and dynamic operation are fulfilled. For reach this goal, system design and network optimization must be properly investigated. For the investigation in the design phase, the numerical modeling plays the key role in the last few years. Importance of understanding the physical mechanisms through the creation of various models for such systems can bring new ideas, solutions and improvements for practical applications [1]. This paper presents insight into the modeling of WDM system with high-order phase modulation formats. This kind of digital modulation is interesting for the studying from the point of view that linear and nonlinear effects have g t ULTICHANNEL Manuscript received February 21, 2012. This work was supported by the Slovak Research and Development Agency under the project APVT-20022404 (“Technologies for optical signal processing for next generation optical digital networks”), APVV COST-0041-06 (“Towards Digital Optical Networks”) and Slovak Grant Agency VEGA 1/1271/12. D. Benedikovic is Ph.D student at University of Zilina, Faculty of Electrical Engineering, Dept. of Telecommunications and Multimedia (phone: +421 41 513 2267; e-mail: daniel.benedikovic@fel.uniza.sk). J. Litvik is Ph.D student at University of Zilina, FEE, Dept. of Telecommunications and Multimedia (e-mail: jan.litvik@fel.uniza.sk). M. Kuba is research assistant at University of Zilina, FEE, Dept. of Telecommunications and Multimedia (e-mail: michal.kuba@fel.uniza.sk). M. Dado is professor at University of Zilina, FEE, Dept. of Telecommunications and Multimedia (e-mail: milan.dado@fel.uniza.sk). J. Dubovan is research assistant at University of Zilina, FEE, Dept. of Telecommunications and Multimedia (e-mail: jozef.dubovan@fel.uniza.sk). 978-1-4673-1116-8/12/$31.00 ©2012 IEEE § 1  jC t · ¸ A exp ¨  ¨ 2 T ¸ © 0¹ 2m (1) , where A is amplitude of pulse, C is initial frequency chirp, T0 is initial temporal width of pulse and determines the symbol rate given by Rs = 1/T0 and m is pulse shape parameter. M-PSK modulated signal is described by A t m § 2S m  1 · g t exp ¨ j ¸ exp j 2S fct ; M © ¹ m 1, 2,, M , (2) where m = 1, 2, ..., M, and M is number of possible phases of carrier that express the transmitted information [1], [3], [4]. B. Signal propagation in optical fiber For the description of signal propagation in the singlemode optical fiber we used slowly varying envelope approximation (SVEA) Am(z,t) instead of optical field Em(z,t). Generally, propagation of optical signal is well-described by nonlinear Fig. 1. Constellation diagrams for M-PSK modulation. 325 TSP 2012 Schrödinger equation, which includes all relevant degradation mechanisms in the optical fiber. For the WDM transmission system, where several signals propagate simultaneously, each optical channel is characterized by its own NLSE and all equations are coupled through nonlinear effects, so we obtain set of NLSE called CNLSE. In this paper is considered the scalar approach (we omitted polarization effects) and then the set of CNLSE can be written as [1], [2]: wA wA m, n D · m, n   A  §¨ E E ¸ 1, ref ¹ wt 2 m, n © 1, n wz 2 w A w3 A j m, n 1 m, n  E  E 2 2, n wt 2 6 3, n wt 3 1  E v 1 , E 2 g 3 O 3 2S c 2  O2 D, 2S c O S  2D . 2S n 2 , A O eff m § · ¨ ¸ 2 2¸ N ¨ 2 ¦ A jJ A A . m, n ¨ m, n m, i ¸ i 1 ¨ ¸ ¨ ¸ izn © ¹ A z, Z m, n 0, Z exp H , A m, n §D · ·Z  j E Z2  j E Z3 ¸. H z ¨ lin  §¨ E  E ¸ ¨ 2 © 1, n 1, ref ¹ 2 2, n 6 3, n ¸ © ¹ ª § ·º « ¨ ¸» 2 2 N « ¨ ¸» 2 ¦ A A 0, t exp « jzJ ¨ A . m, n m, n m, i ¸» « ¨ i 1 ¸» « ¨ ¸» i zn ¹¼ ¬ © A z, t m, n (4) (10) Crucial issue for SSFM is determination of step-size h. This parameter is determined by maximal allowed nonlinear phase shift and can be computed as follows [1], [2]: ) h nl , max J A 1, max  (5)  . (11) (0, t )      LA ˆ m ,1 ˆ LA m ,1 ˆ NA m ,1 III. NUMERICAL MODEL OF WDM SYSTEM  A. General description of numerical model The numerical model of WDM system is based on SSFM. For each WDM channel we separated the linear and nonlinear part of CNLSE Lˆ  Nˆ A . m, n (9) Nonlinear effects have solution given by where n2 is nonlinear refractive index and Aeff is effective area of fiber core [2]. wA m, n wz (8) Linear effects have solution given by When optical power becomes key parameter, then response of optical fiber has nonlinear nature. This nonlinear response leads to the changes in the refractive index n, which becomes power dependent and then nonlinear effects come to play the significant role on signal propagation. On the right hand side of eq. (3) are terms describing nonlinear impairments as Self- and Cross-phase modulation (SPM & XPM). These effects are the most important, when signals are modulated by PSK modulation formats, because they have direct influence on the signal phase. Nonlinear coefficient of an optical fiber  is given by J (7) The solutions of each part for corresponding channel of WDM system are found in spectral and time domain, respectively. (3) where on the left hand side of eq. (3) are terms responsible for linear effects as attenuation, first-, second- and third-order dispersion, respectively. These terms are related to the group velocity vg, dispersion coefficient D and dispersion slope S as dE dZ D Nonlinear part is given by ˆ NA m, n § · ¨ ¸ 2 2 N ¨ ¸ jJ A A 2 A ,  ¦ m, n ¨ m, n m, i ¸ i 1 ¨ ¸ ¨ ¸ izn © ¹ E wA · m, n  A  §¨ E E ¸ m n n ref , 1, 1, 2 © ¹ wt w2 A w3 A j m, n 1 m, n .  E  E 2 2, n wt 2 6 3, n wt 3 ˆ LA m, n   LA ˆ m ,2 ˆ LA m ,2 ˆ NA m ,2  (6)   LA ˆ m,n ˆ LA m, n ˆ NA m, n Linear part is described Fig. 2. SSFM for WDM system. 326 TABLE I LINEAR PROPERTIES OF OPTICAL FIBERS AT O0 Fiber type -1 -1 Dch [ps.nm .km ] -1  [dB.km ] SSMF DSF 16.67 0 NZ-DSF 4.03 0.2 0.35 0.275 Fig. 5. Simulation of SSMF length effect. IV. RESULTS AND DISCUSSION Fig. 3. Chromatic dispersion characteristics.  Fig. 4. Spectral domain of WDM system. B. Setup of numerical model It was created numerical model of WDM system and investigation was realized in the C - optical band (1530-1565 nm) for different types of optical fibers, namely SSMF (Standard single-mode fiber, G.652), NZ-DSF (Non-zero dispersion-shifted fiber, G.655) and DSF (Dispersion-shifted fiber, G.653) with corresponding linear properties at 0, which are shown in Table I and dispersion characteristics are shown in fig. 3. The numerical model computes other values of linear properties for each channel for given number of channels Mch [5], [6] – [8]. The reference channel of WDM system is located at 0 = 1550 nm and other channels are symmetrically located around 0 with corresponding properties for given equidistant channel spacing according to the ITU-T standardization on f = 100 GHz. For investigation are considered the same input power in each channel and constant symbol rate Rs. The total bit rate Rb for each channel is given by Rb = Rs log2(M). In the numerical modeling we changed first of all the length of optical fiber for the specified type of optical fiber with corresponding properties and various number of WDM channels. The results are labeled as dependence of fiber length or number of channels on BER (Bit Error Rate). A. Effect of fiber length One of the key parameters of the fiber optic systems is the length of optical fiber. When transmitted optical pulses are modulated by M-PSK modulation format, the length of fiber plays important role. After modulation, each symbol obtains new initial properties and its transmission through the system has specific nature and different behavior in transmission. Our aim was to find out optimal lengths of different optical fibers to ensure the best transmission through the WDM system, where the transmitted symbols are influenced by all relevant degradation mechanisms (dispersion and nonlinear effects of SPM & XPM). These channel impairments are significant, because they have direct impact on the phase and envelope of transmitted symbols. The simulation parameters for three kinds of optical fibers were set up as follows: input power for each channel Pin = 1 mW, bit rate Rb = 100 Gbit/s, value of channel spacing f = 100 GHz, reference wavelength 0 = 1550 nm, number of WDM channels Mch = 3, Signal-to-Noise Ratio SNR = 27 dB. At first, the length L was changed from 20 km to 90 km. Simulation results for SSMF fiber are shown in fig. 5. It can be clearly seen that the most suitable fiber lengths are integer multiples of 30 km. So, we can say that for transmission of high-order phase modulation formats, the most optimal fiber lengths are 30 km, 60 km and 90 km without using any amplifier. At these lengths of fiber, the influence of dispersion and nonlinear effects was very well balanced and transmitted symbols with high-order phase modulation formats have the best results. The phase changes caused by dispersion are compensated by the phase changes through XPM and SPM. For 16-PSK the results was the worst, but we can still observe this fiber length effect. In this case, the phase sensitivity on channel impairment is higher compared to the case of 2-PSK, 4-PSK and 8-PSK. From the simulations for DSF fiber, which are shown in fig. 6, it is obvious that the DSF fiber has the most suitable properties from the view of the fiber length for employing the high-order phase modulation formats. The impact of dispersion and nonlinear effects on the phase of transmitted symbols was the smallest. The phase changes caused by dispersion mechanisms can be omitted for small value of fiber lengths. On the other hand, has to be said that the next influence of dispersion in each channel (with increasing fiber length) can have positive impact for the compensation effect of phase changes, which are caused by nonlinear effects 327 Fig. 8. Simulation of system capacity (with DSF). Fig. 6. Simulation of DSF length effect. Fig. 9. Simulation of system capacity (with SSMF). Fig. 7. Simulation of NZ-DSF length effect. during the transmission. The reason for this advantageous effect is that the nonlinear effects have significant influence on transmitted symbols only at the length corresponding with the effective fiber length, what lead to the result that the transmission with the high-order modulation format is very well. The results for NZ-DSF fiber was the worst and this type of fiber is not very suitable for transmission of high-order phase modulation formats. From fig. 7 is obvious that the phase changes caused by all degradation mechanisms are the worst and interaction between dispersion and nonlinearities has specific behavior. The useful combination of linear and nonlinear impairments it is difficult to achieve, because the lower value of dispersion does not have strong enough impact on phase changes caused by nonlinear effects. The solution for improving the phase is to use lower values of input power for this type of fiber. So, we can say that using of SSMF and DSF is recommended for transmission of high-order phase modulation formats in WDM systems from the point of view of impact linear and nonlinear effects. B. Capacity of transmission system After the simulations of fiber length effect, we focused our investigation for testing the capacity of given transmission system. From the previous results, we found out that exist optimal fiber lengths, where the channel impairments are nearly balanced. We chose one of the optimal fiber lengths for transmission system, which corresponds with the optimal length in today´s communication networks without the necessity of amplification or regeneration of transmitted signals. From this point of view, the most suitable length is L = 60 km. For purpose of simulations, we tested again three kinds of optical fiber and changed the number of WDM transmission channels from Mch = 2 to Mch = 10 for all types of high-order modulation format. Fig. 10. Simulation of system capacity (with NZ-DSF). For this purpose the simulation parameters were set up as follows: Pin = 1 mW, bit rate Rb = 100 Gbit/s, value of channel spacing f = 100 GHz, reference wavelength 0 = 1550 nm, fiber length L = 60 km, Signal-to-Noise Ratio SNR = 27 dB. The simulation results obtained for DSF fiber, fig. 8, shows very good behavior of transmitted symbols. The zero value of dispersion in wide range of WDM channels provide good way for implementation M-PSK modulation formats. For higher number of channels, the BER increases, what is caused by dominant influence of XPM. The nonlinear coupling between co-propagating optical signals is one of the main problems in WDM systems. This type of fiber do not have ability for optimal compensation of nonlinear effects, so the only option is to use low input powers, what would lead to the using of optical amplifiers. The results for SSMF fiber, fig. 9, shows good balanced effects between linear and nonlinear effects. From the point of view of BER, the achieved results for DSF and SSMF fiber are the best for transmission of phase modulated signals. The simulations made for NZ-DSF fiber (fig. 10) again shows that this fiber is not good for using in systems, which employ high-order modulation formats. In general, with higher number of optical channels, the BER estimation has increasing nature. As we mentioned before, the number of WDM channels is crucial parameter of such systems, because the coupling increases between channels through the nonlinear effect of XPM, which is complemented by SPM in each channel. These effects have 328 detrimental impact on phase states of transmitted signals with high-order modulation. The change of phase state of transmitted signal in the first channel automatically leads to the changes of phase states in other channels. On the other hand, has to be mentioned that the nonlinear effects have significant influence on signal propagation only at effective length, which is smaller than real length of the fiber, so then their impact can be eliminated by precise choice of dispersion properties of optical fiber and suitable location of reference channel, then the phase changes are compensated and modulated signals are transmitted with higher value of BER. V. CONCLUSION In this paper was investigated the behavior of signal transmission with high-order phase modulation formats in multichannel systems. For simulation, we changed the types of optical fiber and fundamental system parameters like fiber length and number of WDM channels. For investigation, we created numerical model for signals transmission in WDM system through the solving CLNSE. The design of our numerical model and simulation parameters was chosen for achieving the most real situation in practical communication systems. This paper brings new insight into the optical pulse propagation with phase modulation formats. The results showed that implementation or practical using of high-order phase modulation formats could not be the main problem from the point of view of today´s used types of optical fiber. Each kind of optical fiber, which was used for investigation, has advantageous and disadvantageous properties. The linear degradation caused by dispersion is the most important, because they have ability to compensate the influence of nonlinear effects, which highly depend on value of input power. From this point of view, the higher values of dispersion allow using the higher input power in each channels or increasing the number of channels with lower input power, when we used high-order phase modulation formats. Has to be mentioned that operation regime of WDM systems can obtain good results only in cases, when the value of dispersion in each channel have positive sign. Simulations showed that phase changes can be balanced, when the parameter of transmission system will have good settings. For future improvement of investigation of new modulation formats, it will be necessary to deal with different detection schemes and equalization of received optical signal, but practical realization from the point of signal propagation with high-order modulation formats will not be a crucial issue. 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