The Affection of Fiber Nonlinearity in Coherent Optical Communication System

013 8th International Conference on Communications and Networking in China (CHINACOM) The Affection of Fiber Nonlinearity in Coherent Optical Communication System Invited Paper Yaojun Qiao*, Yanfei Xu, Zhe Wang, Wenhui Qian, Hongzhan Liu and Yuefeng Ji State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), Beijing, 100876, P. R. China * Corresponding author: qiao@bupt.edu.cn Abstract In this paper, we firstly analyzed the Gordon and Mollenauer (G-M) effect in dual polarization quaternary phase shift keying (DP-QPSK) system, whose simulation results indicate that the G-M is the main impairment which should be given a careful consideration. Secondly, a self-correlation technique was used to extract the cross phase modulation (XPM)-induced phase noise and XPM-induced polarization scattering for analyzing the characteristics of XPM in coherent optical orthogonal frequency division multiplexing (CO-OFDM) wavelength division multiplexed (WDM) transmission systems. The phase noise is verified as the dominant distortion in DP-OFDM systems while the XPM-induced polarization crosstalk is proved to be the decisive distortion in DP-QPSK coherent experiment. Thirdly, we discovered that the statistical characterization of the nonlinear noise in densely spaced 16QAM OFDM system deviate from Gauss distribution in the absence of amplified spontaneous emission (ASE) noise that cannot be regarded as the same in QPSK system. Keywords- Fiber Nonlinearity; G-M effect; XPM;FWM; CO-OFDM I. INTRODCUTION Constrained by the limitation of transmission bandwidth, the continuing growth of network traffic ignite a strong motivation to employ high spectral efficient (SE) transmission systems which aims at reducing the cost per bit as well as up-scaling the total transmission capacity. The coherent detection systems marked a rapid progress during the last few years. While polarization-division-multiplexed quadrature phase shift keying (PDM QPSK) has shown good transmission performance with its high spectral efficiency[1] higher level modulation formats such as PDM quadrature amplitude-modulation with 16 symbols (PDM 16QAM) has been attracting great interests too [], as well as some other higher cardinality formats. As the principle and compensation of amplified spontaneous emission (ASE) noise has been well understood, the nonlinear interference may become the final obstacle to the development of the long-haul broadband optical transmission [3]. In the last few years, various compensation algorithms aiming at solving fiber nonlinearity are proposed, e.g., digital back propagation [4] which is traditional but very complex. Fiber nonlinearity compensation implemented by periodic dispersion maps [5] which is proposed in 009. An optimized optical phase conjugation (OPC) configuration is proposed for nonlinear cancellation [6-9] and the BLAST algorithm [10] which was proposed as the effective method for improving fiber nonlinearity tolerance. In this paper, we would like to give a detailed research description about the fiber nonlinearity from single carrier to multi-carrier. The Gordon and Mollenauer (G-M) effect, which was firstly proposed in 1990 [8] is researched systematically in 11Gbit/s DP-QPSK system. Through comprehensive simulation, G-M is verified as the main impairment which should be given a careful consideration and then we use a self-correlation technique to extract the cross phase modulation (XPM)-induced phase noise and XPM-induced polarization scattering for analyzing the characteristics of XPM in coherent optical orthogonal frequency division multiplexing (CO-OFDM) wavelength division multiplexed (WDM) transmission systems. Through the analysis, we found that XPM is strongly dependent on system parameters such as fiber local dispersion, WDM channel spacing and dispersion map. Additionally, the phase noise is verified as the dominant distortion in DP-OFDM systems while the XPM-induced 765 978-1-4799-1406-7 013 IEEE

polarization crosstalk is proved to be the decisive distortion in DP-QPSK coherent experiment. As to the densely spaced 16QAM OFDM system, we found that the statistical characterization of the nonlinear noise deviate the additive Gaussian noise which has been verified as the additive Gaussian noise in QPSK system. This paper is organized as follows: in section II, we introduce the G-M effect on the 11Gbit/s coherent DP-QPSK system and one can conclude that different residual dispersions of the same magnitude no matter they are under-compensated or over-compensated can derogate the overall system performance to the similar degree. All in all, the G-M effect cannot be ignored. In Section III, we would like to analyze the XPM in WDM PDM CO-OFDM system, and make a comparison with QPSK system. Section IV we give the latest research which shows that the statistic of fiber nonlinearity in 16QAM cannot be seen as the additional Gaussian noise as in the QPSK system. In Section V, we summarize our conclusion. The effect of nonlinear phase noise is segregated through our elaborately designed method employing two separate OSNR setting modules: by changing the transmitted OSNR while maintaining a constant overall system OSNR value through manipulating the value of the OSNR module at the receiver side accordingly at the same time, thus we can draw a conclusion that the deterioration of the system performance result merely from the effect of G-M effect [14, 15]. In order to clearly assess the effectiveness of the ASE noise to the G-M effect, we try to manipulate the two OSNR modules by adding all the white Gaussian noise (WGN) into one module at a time and spare none to the other. Fig. (a) shows that with inline dispersion compensation, the Q factor decreases as a function of input power. II. G-M EFFECT IN DP-QPSK SYSTEM Kerr effect as a kind of deterministic nonlinear effect is the main source of impairment in very high-bit-rate transmission systems [11]. In addition to deterministic nonlinearities, phase modulated systems also suffer from the nonlinear phase noise, called G-M noise, caused by the nonlinear interplay between the signal and the ASE emitted by the inline amplifiers [1]. For the phase-modulated systems, the nonlinear phase noise can become another restrictive factor to damage the phase signal extremely [13]. In this letter, we systematically analyze the effect of G-M phase noise on the 11Gbit/s coherent DP-QPSK system through comprehensive simulation and in depth theoretical study under various system settings. Fig. 1 shows the simulation system setup. (a) (b) Fig.. Q factor VS. input power(a)with inline dispersion compensation Fig. 1 Setup of the G-M Simulation System (b)without inline dispersion compensation(the received OSNR is 14dB) From Fig. (a), the upper red line represents when the WGN is completely loaded through the OSNR module at the receiver side while the black line, on the contrary, shows when the overall WGN is loaded within the OSNR module at the transmitter side. Since the overall system OSNR is fixed at 766

14dB, the difference between the two curves is entirely caused by the G-M effect. With the increase of the input power, the gap between the two lines is increasing as with the G-M effect. We can draw a similar conclusion from Fig. (b) which represents the simulation results under links without inline dispersion compensation. III. XPM INDUCED PHASE NOISE AND POLARIZATION SCATTERING XPM in optical transmission system is rather complex. Not only does it induce nonlinear phase noise, But also it causes nonlinear polarization scattering [16, 17]. Most of the previous investigations handled nonlinear phase noise and polarization scattering separately [18], but [19] describes a whole analytical model including both the two kinds of distortions based on the volterra analysis in Jones space. That proposed model is applied to the 11Gbit/s DP-QPSK dense wavelength-division-multiplexed (DWDM) system, and serves as a guideline on how to mitigate the XPM impact through transmission system design and coherent receiver digital signal processing (DSP). In order to analyze the XPM impacts, the self-correlation computational method is applied to extract the characteristics of XPM-induced phase noise and XPM-induced polarization scattering [0]. A 7-channel, 50GHz spacing WDM transmission system was simulated in VPItransmissionMaker 7.6, which was used with the combination of MATLAB. The channel number is limited to 7 for the reason of nonlinear simulation speed. Fig.3 shows the block diagram of seven-channel 11Gbit/s DP-OFDM WDM transmission system. From Fig. 3, there are seven channels at the transmitter whereas the center channel is the continuous-wave (CW) probe signal, and the pump channels are 11Gbit/s DP CO-OFDM modulated. The number of carrier of one OFDM symbol is set to 18. The ratio of zero padding is 1/4, from which the ratio of zero padding on either side of one OFDM symbol is 1/8, which are used to protect the OFDM symbol from the influence of filter. Ratio of cyclic prefix is set to 1/16, which is long enough to combat the ISI influence. In order to focus on the XPM impact, the fiber launch power of the CW probe channel was -3dBm whereas that of each interfering channel was varying from -3dBm/channel to 3dBm/channel. The polarization of each channel was aligned by polarization controllers before they are transmitted. The 1500 km fiber link is consisted of 5spans. We employ two kinds of fiber during the simulation, one is the SSMF with a local chromatic dispersion (CD) coefficient of 16ps/nm/km, and the other is non-zero dispersion shifted fiber (NZDSF) with a local CD coefficient of 4ps/nm/km. For simplicity, ASE noise was ignored in simulation. In order to use the scalar nonlinear Schrodinger equation, the PMD of fiber link was assumed to be zero. Meanwhile, both of these two kinds of fiber were modeled with a nonlinearity coefficient of -0.6 10 m / w, with an effective area of 80um and an attenuation of 0. db / km. The dispersion compensation fiber (DCF) has a dispersion coefficient of 30 ps/ nm/ km without loss, nonlinearity and polarization mode dispersion (PMD). EDFAs without noise figure were used to compensate for all span losses. The residual dispersion of the whole transmission link was compensated completely before the receiver by the residual dispersion compensation module (RDCM), which was shown in Fig. 3. According to our analysis, we would like to estimate which one is the dominant distortion in OFDM system. The constellation diagrams of X polarization and Y polarization are depicted in Fig. 4. This is depicted when the channel space is 50GHz, and the power of other interfering channels is 3dBm. Fig. 3 The block diagram of seven-channel 11Gbit/s DP-OFDM WDM transmission system RDCM: residual dispersion compensation module PBS: polarization beam splitter 767

from other channels is much higher than single carrier system. IV. FWM THEORY IN DENSELY SPACED OFDM SYSTEM (a) (b) (c) Fig. 4 Constellation diagrams of X polarization and Y polarization (a) The original signal without going through fiber transmission (b) After going through 1500km SSMF with DC ratio equals 0 (c) After going through 1500km SSMF with DC ratio equals 0.8 Just as Fig. 4 shows, Fig. 4 (a) shows the constellation diagrams of the original signal, which didn t go through fiber transmission. The upper one is for X polarization and the nether one is for Y polarization. Fig. 4 (b) and Fig. 4 (c) is the constellation diagrams for both polarizations when dispersion compensation (DC) ratio equals 0 and 0.8, respectively. Apparently, we feel that the phase noise is much stronger than polarization scattering. Firstly, we extract the noises of the two polarizations from the original signal, after calculating the noise power of the two polarizations, we get that the phase noise power in X polarization is 5 4.79 10 w power in Y polarization is while the polarization scattering 6 8.66 10 w when DC ratio is zero. When DC ratio is 0.8, phase noise power and the polarization scattering power are 5.67 10 w 4 1.33 10 w and respectively. So in coherent optical OFDM system, phase noise was the dominant distortion compared with cross talk noise while the cross talk noise was proved to be the decisive distortion in DP-QPSK coherent system [1]. This is because, in our system, the six pump channels are OFDM signals while they are QPSK signals when compared with [19]. OFDM signals are the stacks of many single carrier signals; its density is much higher than the single carrier system. Thus, the phase noise caused by the signal density Closed-form expression for nonlinearity in Dense Spaced-OFDM (DS-OFDM) systems with QPSK modulation format has been proposed based on the assumption that all the nonlinear effects such as XPM, FWM and SPM can be considered as FWM between all the subcarriers within a big single band []. They claimed that the approximated FWM can be modeled as an additive Gaussian noise and that the theory suits for all modulation formats by merely presenting the simulation results in the case of QPSK. Recent research shows that it may be not that intuitive to extend such property directly to 16QAM systems [3]. In 16QAM systems deviation from Gauss distribution for the nonlinear interference in the absence of ASE noise has been observed. The parameters for the analyzed dual-polarization transmission systems are as follows illustrated by Fig. 5: 11 wavelength channels, each covering 3-GHz bandwidth, and no frequency guard band between wavelength channels giving total bandwidth B of 35 GHz; OFDM subcarrier number of 4096 for the whole bandwidth; 16QAM modulation for each subcarrier. Fig. 5 OFDM Signal Structure As you can see from Fig. 5, given no guard band in between, the spectrum structure on the left is completely identical to that on the right only that they are viewed from different aspects. Fig. 6 shows the averaged variance of the Nonlinear Interference (NLI) at the X polarization after a propagation of 100 km as a function of launch power. The transmission is conducted in the absence of ASE noise thus enable us to focus merely on the nonlinearity induced noise within the system. As we can seen in Fig. 6, the slopes of the three red lines are all very close to (circle: 1.9, triangle:.05, diamond:.08 768

respectively), which indicate that 1-dB increase in launch power will introduce about -db increase in the average variance. Thus we can conclude that under all cases, the variance of NLI noise will increase proportionally to the square of the launch power. As shown in Fig. 7, G ( ) Theo. n and G ( ) Simu. n represent the number of the theoretical and simulation Gaussian distribution values located at the n th hist bin respectively. We use 1000 bins for about 90000 samples during the simulation under the case of SMF 0% with the launch power of 1dBm and the histogram shows obvious deviation from the red Gaussian fitting line. Fig.6 Averaged NLI distribution variance as the function of Launch Power. The group of blue lines within Fig. 6 shows the Gauss Fitting Error of the NLI calculated by Eq. (1) as a function of the launch power under the same system configuration. From the trend of these blue lines, the Gauss Fitting Error increases along with the increase of the launch power which indicates a trend of deviating from the gauss distribution especially for the SMF 0% case. GaussFittingError = N / N / G ( n) G ( n) Theo. Simu. N / N / G Simu. ( n) (1) V. CONCLUSTION As the fiber nonlinearity is the last obstacle in coherent optical fiber transmission system. We analyzed the fiber nonlinearity from single carrier to multi-carrier in detail. Firstly we analyzed the G-M effect in 11Gbit/s PDM-QPSK system and one can conclude that different residual dispersions of the same magnitude no matter they are under-compensated or over-compensated can derogate the overall system performance to the similar degree. Secondly we use a self-correlation technique to extract the XPM-induced phase noise and XPM-induced polarization scattering for analyzing the characteristics of XPM in 11Gbit/s dual polarization (DP) CO-OFDM WDM system and made a comparison with QPSK system. Simulation results show that the phase noise is verified as the dominant distortion in DP-OFDM systems while the XPM-induced polarization crosstalk is proved to be the decisive distortion in DP-QPSK coherent experiment which should be closely considered. As to the high modulation 16QAM, we found that we cannot consider the statistical characterization of fiber nonlinearity as addition Gaussian noise as the same in QPSK modulation format in densely spaced coherent optical OFDM system. ACKNOWLEDGMENT This work was supported in part by the National Natural Science Foundation of China (617119, 6093004), National 863 Program of China (013AA013401), P. R. China. REFERENCES [1] Carena, A., et al. "Modeling of the impact of nonlinear propagation Fig. 7 Calculation illustration of Gaussian Fitting Error (SMF 0% at 1dBm). effects in uncompensated optical coherent transmission links." Journal of Lightwave Technology 30.10 (01): 154-1539. [] Zhao, J., and H. Shams. "Fast dispersion estimation in coherent optical 769

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