Efficiency of nonlinear compensation for wdm-pon based ofdm using optical back propagation

Nội dung text: Efficiency of nonlinear compensation for wdm-pon based ofdm using optical back propagation

1. Ngo Thi Thu Trang, Tran Thuy Binh, Bui Trung Hieu, Nguyen Duc Nhan EFFICIENCY OF NONLINEAR COMPENSATION FOR WDM-PON BASED OFDM USING OPTICAL BACK PROPAGATION Ngo Thi Thu Trang , Tran Thuy Binh, Bui Trung Hieu, Nguyen Duc Nhan Posts and Telecommunications Institute of Technology *Abstract: The Kerr nonlinearity is the main obstacle or higher transmitting power is required to extend the that limits the performance of the orthogonal frequency range of LR-PONs. Therefore, the nonlinear Kerr effects division multiplexing wavelength division multiplexing become a critical concern in these networks, especially in (OFDM-WDM) system. Moreover, the nonlinear WDM LR-PONs. compensation method that is feasible and adds no more There are many solutions in the digital domain which complexity to the receiver is very necessary for the long- have been proposed to compensate the nonlinearity of the range passive optical network (LR-PON) applications. In systems [4-8]. Almost these techniques provide a good this paper, we investigate the nonlinear and dispersion PAPR reduction to eliminate the nonlinearity in all parts compensation efficiency in OFDM-WDM system using of the system, the transmitter, fiber channel and the an advanced optical back propagation (OBP) approach receiver. However, each nonlinear compensator can only based on split-step Fourier method. In the OBP, the real applied to each channel so that they make the complexity optical devices such as the high-nonlinear fiber (HNLF), and cost of the OFDM-WDM system increase fiber Bragg grating (FBG) and nonlinear waveguide are exponentially. used as a nonlinear operator, a dispersive operator and Nonlinearity in the fiber, especially the Kerr effect, phase conjugated media, respectively. The advanced can be mitigated by mid-span spectrum inversion (MSSI) OBP is located in the transmitter site that is very suitable method in the optical domain [9]. The MSSI using optical for LR-PON applications. The compensation efficiency phase conjugation (OPC) module can reduce significantly of the OBP in OFDM-WDM systems is evaluated by an not only Kerr nonlinearities but also group velocity analytical model and then Monte-Carlo simulations. The dispersion in WDM systems [10], [11]. However, this obtained results from both analytical evaluation and method requires the OPC module placed in the middle of simulation show that the OBP can improve remarkably transmission link to ensure the power symmetry that is not the system performance when the parameters of OBP feasible in LR-PON. The optical back propagation (OBP) such as dispersion and pump power are properly selected. solution using dispersion compensation fibers (DCFs) and high nonlinear fibers (HNLFs), proposed by Kumar et al Keywords: Orthogonal Frequency Division [12], is placed in the receiver site of the optical systems. Multiplexing (OFDM), Wavelength Division The OBP addresses the main drawback about strict location requirement of MSSI. Moreover, this solution has Multiplexing (WDM), Nonlinear compensation, Optical been proposed in the single channel OFDM based LR- Back Propagation (OBP), Long-range Passive Optical PON that demonstrated its nonlinearity compensation Network (LR-PON). efficiency [13]. I. INTRODUCTION In this paper, we investigate the efficiency of optical The orthogonal frequency division multiplexing back propagation technique in nonlinearity compensation (OFDM) has become the promising solution for the for OFDM-WDM system. The OBP module is located at WDM-based long-range passive optical networks (WDM the transmitter site that is similar to that proposed in [13]. LR-PONs) [1], [2]. The OFDM WDM LR-PON can be This OBP consists of HNLFs, fiber Bragg gratings extended both the capacity and the range thanks to the (FBGs) and an OPC. The HNLF is the nonlinear operator advantages such as highly spectral efficiency, highly to compensate the nonlinearity. The FBG is the linear chromatic dispersion tolerance. Moreover, the systems operator to compensate the dispersion. The signal after can get the simple design and cost efficiency when the HLNFs and FBGs is conjugated by the OPC to transmit intensity modulation and direct-detection (IM-DD) via the standard single mode fiber to the receiver. A method is employed [3]. However, a larger power budget theoretical analysis model is also used to evaluate the efficiency of nonlinearity compensation in this study. Correspondence: Ngo Thi Thu Trang Both analytical evaluation and simulation results show Email: trangntt1@ptit.edu.vn that our proposed OBP technique can improve remarkably Manuscript communication: received: 10/05/2020, revised: the performance of the OFDM WDM system when the 11/25/2020, accepted: 11/30/2020. parameters of OBP module are properly selected. These
2. EFFICIENCY OF NONLINEAR COMPENSATION FOR WDM-PON BASED OFDM USING OPTICAL BACK PROPAGATION achieved results also show that the advanced OBP is very Nonlinear Kerr effects in the fiber including self-phase suitable to deploy in OFDM WDM LR-PON. modulation (SPM), cross phase modulation (XPM), and four-wave mixing (FWM) are the dominant obstacle to The rest of this paper is organized as follows. Section extend the capacity and transmission distance of the 2 gives analytical descriptions of nonlinear wave mixing multichannel optical communication systems [14]. In such efficiencies of OFDM WDM systems that influence to the systems, all the nonlinear effects such as XPM, SPM are nonlinearity compensation efficiency of OBP technique. considered as FWM between all subcarriers. Thus, the Simulations are discussed in section 3. Finally, section 4 evolution of the FWM field (spectrally located at 휔 ) concludes this paper. 퐹 resulting from the nonlinear wave mixing between three II. THEORETICAL EVALUATION other optical waves (k, l, m such that 휔퐹 = 휔 + 휔푙 − 휔 ) can be expressed as [15] (−훼+푖∆훽)퐿 훾 ∗ 푖훽퐿 푒 −1 Optical OFDM Transmitter #N (퐿) = 푖 (0) (0) (0)푒 (1) 퐹 3 푙 −훼+푖∆훽 Optical OFDM Transmitter #2 where 푠( ) is the optical field spectrally located at 휔푠 x i f e OBP measured at distance z, and L is the transmission fiber r M g P D n i c T C length. γ, α and β are nonlinear, attenuation coefficients S P Data input i p W l F / / A p c F S P I D a y and propagation factor of a fiber, respectively. D is the C M d degeneracy factor of FWM. SPM is considered that three d EDFA A waves of FWM are coincided, 휔 = 휔푙 = 휔 , and = LD MZM 1. While XPM is considered as degenerate FWM effect, Optical OFDM Transmitter #1 in which two of mixing components have the same F frequency, 휔 = 휔푙 ≠ 휔 , and = 3 . The remaining M S case that three mixing components are totally different, 휔 ≠ 휔푙 ≠ 휔 , is called non-degenerate FWM x i f e or simply FWM, and = 6. ∆훽 = 훽 + 훽푙 − 훽 − 훽퐹 is r n P g o n c i the phase mismatch coefficient of the fiber, relates to the i i t l p a c C S T Data output P p z y / / i F D dispersion coefficient as follows [15] a l C P S F A a m e u e v q PD 2 D o LPF OBF 2 휆 OFDM E 2 m ∆훽 = ∆ ( − )(푙 − ) (2) e Receiver R where ∆ is channel spacing. It can be obviously seen Figure 1. Block diagram of IM-DD OFDM WDM system from Eq. 1 that the amplitude of FWM field depends using OBP as pre-compensation. much on channel spacing. To evaluate how the OBP could Fig. 1 shows the schematic of IM-DD optical OFDM compensate the nonlinearity of the OFDM WDM LR- WDM system where the OBP module is located at the PON, the powers of FWM field in two cases a link with transmitter site. The OBP module consists of steps of OBP and a link without OBP are compared. Thus, Eq. 1 HLNF and FBG, an OPC module and an Erbium Doped describes the FWM field in case of the OFDM WDM LR- Fiber Amplifier (EDFA) as described in details in [13]. PON link without OBP. The total power of nonlinear | |2 With the advantages of system design and cost efficiency, product 퐹(퐿) with assumption that the signal powers the IM-DD OFDM WDM is the good solution for LR- in all channels are equal can be written as [16] PON applications. For the sake of simplicity, we assume 2 2 훼2퐿2 −훼퐿 2 훾 3 푒 4푒 푠푖푛 (∆훽퐿/2) that insertion loss of all components of the LR-PON is 푃퐹(퐿) = 푃 [ 2 2] [1 + −훼퐿 2 ] ignored. Here, our OBP plays a role as pre-compensation 9 훼 + ∆훽 (1 − 푒 ) in optical domain of the LR-PON. The OFDM transmitted (3) signals are multiplexed in wavelength domain before they where P is the power of each mixing component −αL propagates via the OBP section, and then it is phase launched into the fiber and Leff = (1 − e )/α is the conjugated before propagating in the transmission fiber effective length. link. The nonlinear and dispersion distortions of the OBP section are based on the split-step Fourier method in the We next consider the nonlinear Kerr power in OBP- optical domain [14]. The FBG is used as dispersive step assisted OFDM WDM LR-PON link. The link can be because of its pros such as negligible nonlinearity and divided into two segments, OBP segment and SMF insertion loss, very compact size, and dispersive segment. The OFDM signal first is sent through the OBP tunability. The HNLF is used as nonlinear step due to its segment, phase conjugated at OPC and then transmitted very low dispersion distortion and negligible loss. The via the SMF segment. The nonlinearity arisen in the OBP segment will be compensated in the SMF segment. Given OPC using the nonlinear waveguide produces the that after two segments all dispersion effect are conjugated signal by four-wave mixing (FWM) process to compensated, so the total FWM field in this case will be transmit along the single mode fiber (SMF) to the receiver site. The EDFA is used to control the signal input power ∗ 푖훽퐿 퐹(퐿) = 퐹(푆 퐹) + [ 퐹( 푃)] 푒 (4) of the SMF link. By using real photonic device, our OBP overcomes the cons of digital back propagation (DBP) Applying the Eq. 1 for the OBP segment, the nonlinear method including the computational complexity and less- field can be obtain as flexible configuration [8].
3. Ngo Thi Thu Trang, Tran Thuy Binh, Bui Trung Hieu, Nguyen Duc Nhan 퐹( 푃) = Figure 2 demonstrates the dependent of nonlinear Kerr 훾 푒(−훼+푖∆훽 푃)퐿 푃−1 power in the OBP-assisted OFDM WDM LR-PON link 푃 ∗ 푖훽 푃퐿 푃 푖 (0) 푙(0) (0)푒 3 −훼+푖∆훽 푃 on the factor K with the channel spacing of 12.5 GHz and (5) the fiber link length of 80 km. As can be seen from the In the OBP segment, both the loss of HLNFs and figure, when K is small, the phase mismatch of the OBP is FBGs is negligible so that the attenuation coefficient of small that makes the nonlinear effect arisen by OBP OBP can be omitted. To ensure that the dispersion arisen become too strong. At the value of K is smaller than 5, the in the OBP segment is fully compensated in the SMF nonlinear power in the link with OBP evenly exceeds that segment, 훽 퐿 = 훽퐿 or 훽 퐿 = 훽퐿 . For more in the link with our OBP. When K increases, the nonlinear 푃 푃 퐹 푃 Kerr power of the OBP reduces remarkably. However, convenient in calculation, we define 퐾 = 훽퐹 /훽. Hence, the nonlinear field from the OBP segment can be reduced under the asymmetry power condition, the OBP cannot as compensate perfectly the nonlinearity of the SMF. That’s why the residual nonlinear FWM power in the case of 훾 푒푖훽퐿−1 ( 푃) = 푖 퐿 퐹 (0) (0) ∗ (0)푒푖훽퐿 (6) using OBP become saturation when K is very large 퐹 3 푙 푖퐾∆훽 although this value is always smaller than the FWM power in the case of not using OBP. Consequently, there By the end of the OBP segment, the mixing fields (k, l is an optimum value of K where the nonlinear Kerr power and m) are phase shifted due to the accumulation of in the link with OBP is minimum. dispersion along the OBP segment 푒푖(∆훽 푃+훽 푃)퐿 푃 = 푒푖(∆훽+훽)퐿. Then they are conjugated to propagation via the 10 w/o OBP SMF segment that results the following nonlinear field 0 w OBP 훾 푒(−훼+푖∆훽)퐿−1 ∗ ∗ −푖∆훽퐿 ) -10 퐹(푆 퐹) = 푖 (0) 푙 (0) (0)푒 m 3 −훼+푖∆훽 B d ( -20 (7) r e w o p -30 Substituting Eq. (6) and Eq. (7) into Eq. (4), we can M W obtain the total nonlinear field generated by the OBP- F -40 assisted OFDM WDM LR-PON link as follow -50 푒(−훼+푖∆훽)퐿−1 ∗ ∗ −푖∆훽퐿 -60 퐹(퐿) = 푖 (0) 푙 (0) (0) [훾푒 − 0 5 10 15 20 25 30 35 40 45 50 3 −훼+푖∆훽 Factor K −푖훽퐿 푒 −1 Figure 2. FWM power as a function of factor K with the 훾 퐿퐹 ] (8) −푖퐾∆훽 channel spacing of 12.5 GHz and the SMF fiber length of 80km. Deploying lossless for the SMF segment (훼 = 0), the signal power symmetry for the link with OBP can be 0 satisfied. In this case, Eq. (8) shows that the fully w/o OBP nonlinear compensation will be attained in the OBP- -20 w OBP assisted OFDM WDM LR-PON link with fully dispersion ) m -40 B management. Unfortunately, the attenuation coefficient of d ( r the SMF fiber cannot be omitted that breaks the power e -60 w o symmetric condition. This reduces the efficiency of the p OBP in nonlinear compensation in comparison with MSSI M -80 W technique. Thence, the total FWM power of the OBP- F assisted OFDM WDM LR-PON link is given as -100 2 2 2 2 −훼퐿 2 훾 훼 퐿푒 4푒 푠푖푛 (∆훽퐿/2) -120 3 0 5 10 15 20 25 30 35 40 45 50 푃퐹(퐿) = 푃 [ 2 2 (1 + −훼퐿 2 ) + 9 훼 +∆훽 (1−푒 ) Channel spacing (GHz) 2 훾 퐿 퐹 2 ∆훽퐿 4 훾훾 퐿 퐹 ∆훽퐿 Figure 3. FWM power as a function of channel 2 2 4푠푖푛 ( ) − 2 2 sin ( ) [훼(1 − 퐾 ∆훽 2 퐾∆훽 (훼 +∆훽 ) 2 spacing with the factor K of 12 and the SMF fiber ∆훽퐿 ∆훽퐿 푒−훼퐿) 표푠 ( ) + ∆훽(1 + 푒−훼퐿)sin ( )]] (9) length of 80km. 2 2 Figure 3 shows that not only the FWM power depends The first term of Eq. 9 describes the nonlinear FWM on the channel spacing but also the compensation power arisen in the SMF segment, which only depends on efficiency of the OBP does. The increase in channel the SMF coefficients. The second term in Eq. 9 is the spacing causes the increase in the phase mismatch that added nonlinear FWM power because of the presence of makes the average FWM power decrease. However, in the OBP, which only depends on the OBP coefficients. case of the OBP-assisted OFDM WDM LR-PON link, the The third one is the mixing nonlinear power that power of the FWM varies with the channel spacing as an compensates for nonlinearities of the both SFM and OBP oscillation but it is always smaller than or equal to the segments. Therefore, the compensation efficiency of the Kerr nonlinear power in case of not using OBP. OBP will increase when the third term is larger than the Dependence of the mixing power on the dispersion at second term. And this depends much on the factor K and different channel spacing is shown in Figure 4. The the coefficients of both segments. dispersion dependence of the mixing power has a similar tendency to the channel spacing dependence. The
4. EFFICIENCY OF NONLINEAR COMPENSATION FOR WDM-PON BASED OFDM USING OPTICAL BACK PROPAGATION oscillation of the mixing power dependent on dispersion cannot be negligible. It can be seen that from Fig. 3, if can be observed and shows a reduction of the mixing channel spacing is smaller than 5GHz, the Kerr nonlinear power in the OBP-assisted OFDM WDM LR-PON link power in the case of using OBP is always 10 dB smaller compared to that in the OFDM WDM LR-PON link than that in the case of not using OBP. Fortunately, without OBP. channel spacing of an OFDM signal is much smaller than 5 GHz. For example, if the OFDM signal in the OFDM In the OFDM WDM system, the Kerr nonlinear noise WDM LR-PON at the very high bitrate of 100 Gb/s using imposed on each subscriber of OFDM signals results from 64QAM and DCO-OFDM scheme has 190 data two main sources: subcarriers and 66 zero-padded subcarriers, the channel (i) FWM effect between subcarriers of each spacing is about 0.18 GHz. Thus, the OBP can OFDM channel. The Kerr nonlinear powers in compensate the Kerr nonlinearity caused by OFDM the link with and without OBP caused by subcarriers in the OFDM WDM LR-PON. When channel OFDM OFDM subcarriers, PF (L), are derived from spacing is larger than 5 GHz, which is the range of the Eq. 3 and Eq. 9, respectively in which P is the channel spacing of WDM systems, the Kerr nonlinear power of each OFDM subcarrier and ∆β is power in case of using OBP fluctuates with large dependent on channel spacing between OFDM amplitude. By choosing suitable value of K and channel subcarriers, and spacing, the OBP can compensate significantly the Kerr nonlinearity caused by optical channels in the OFDM (ii) FWM effect between optical channels of WDM WDM LR-PON. The performance improvement of the system. The Kerr nonlinear powers in the link OFDM WDM LR-PON thanks to OBP will be clarified with and without OBP caused by WDM optical by Monte- Carlo simulation in the next section. WDM carriers, PF (L), are also derived from Eq. 3 and Eq. 9, respectively in which P is the power III. SIMULATIONS AND RESULTS of each optical channel and ∆β is dependent on A MATLAB based simulation model of IM-DD OBP the channel spacing of WDM system. assisted OFDM WDM LR-PON is developed to investigate the nonlinear compensation efficiency of -10 proposed OBP method. The simulation setup of the -20 w/o OBP system is similar to the block diagram described in Figure ) w OBP m -30 1 that includes three main components: optical transmitter, B d transmission link and optical receiver. The DCO-OFDM ( r -40 e signal is generated from the OFDM modulator in digital w o -50 domain that consists of 190 data subcarriers and 66 zero- p padded subcarriers. The MZM is used to optically M -60 W modulate the OFDM signal before launching into the F -70 OBP. After pre-compensating at the OBP, the signal is sent to the receiver via the transmission link of 80 km -80 0 5 Dispersion10 (ps/nm.km)15 20 25 30 standard single mode fiber (SSMF). Here, the data is a) recovered with the reverse process of the transmitter. The important system parameters and constants used in our -10 simulation are shown in Table 1. -20 w/o OBP Table 1. Simulation parameters ) -30 w OBP m B -40 Name Symbol Value d ( r -50 e SMF parameters w o -60 p -70 Attenuation coefficient SMF 0.2 dB/km M W -80 F Dispersion coefficient DSMF 17 ps/nm.km -90 -1 -1 Nonlinear coefficient SMF 1.4 W .km -100 0 5 10 15 20 Dispersion (ps/nm.km) Fiber length LSMF 80 km b) Figur 4. FWM power as a function of dispersion at HNLF parameters different channel spacing: (a) 12.5 GHz, (b) 25 GHz. Attenuation coefficient HNLF 0.5 dB/km Therefore, the total FWM power on each subcarrier in Dispersion coefficient DHNLF 1.7 ps/nm.km case of using or not using OBP has the following form: -1 -1 Nonlinear coefficient HNLF 6.9 W .km 푡표푡 푙 푊 퐹 푃퐹 (퐿) = 푃퐹 (퐿) + 푃퐹 (퐿) (10) Fiber length LHNLF 150 m Let’s consider the FWM effect caused by subcarriers NW parameters of an OFDM signal. Because the number of subcarriers of an OFDM is quite large, the power of each subcarrier is Attenuation coefficient NW 50 dB/m small but the channel spacing is very small too. Thus, the Dispersion coefficient DNW 28 ps/nm.km FWM power caused by subcarriers of an OFDM signal
5. Ngo Thi Thu Trang, Tran Thuy Binh, Bui Trung Hieu, Nguyen Duc Nhan 4 -1 -1 channel spacing. At the optimum power range of SMF in Nonlinear coefficient NW 10 W .km each optical WDM channel from -6 dBm to -2 dBm, the Waveguide length LNW 7 cm OBP can improve the BER performance of the OFDM WDM LR-PON up to 4 orders of magnitude at channel System parameters spacing of 50 GHz. Optical signal frequency fs 193.1 THz PD responsivity R 0.6 A/W Dark current Id 0.2 nA -23 1/2 Thermal noise PSD ST 2x10 A/(Hz) M-ary M 64 Data rate Rb 100 Gbit/s Pump power Pp 450 mW Optical pump frequency fp 193.3 THz In the OBP, the OFDM signal after nonlinear and dispersion pre-compensating is phase conjugated by an OPC before transmitting via SSMF to the receiver. Thus, the quality of the conjugated signal through FWM process in the OPC plays an important role in the performance of the OBP. In our simulation, the pump power and the input power of the OPC are chosen carefully to ensure that the conjugated signal does not add any more impairment to the performance of the system [13]. The parameters of the OFDM modulator need to be fixed to keep the data bitrate of each optical channel of 100 Gbps. Hence, the channel spacing between OFDM subcarriers is constant in all simulations, only the channel spacing between optical WDM channels is varied to examine the system’s performance. Figure 6. BER vs dispersion of SMF in each optical WDM channel: a) with different channel spacing, b) Figure 5. BER vs optical launched power of SMF in with and without OBP at channel spacing of 25GHz, c) each optical WDM channel with different channel with and without OBP at channel spacing of 50GHz. spacing. The BER performance in each optical WDM channel Figure 5 demonstrates that the OBP can improve of OFDM WDM LR-PON versus dispersion of the SMF significantly the performance of the OFDM WDM LR is plotted in Fig. 6 in three cases: a) using OBP with PON. By adjusting the EDFA gain properly, the optical different channel spacing, b) with and without OBP at power at the input of the SMF is always varied in the channel spacing of 25 GHz, and c) with and without OBP range from -14 dBm to 2 dBm. At the given power of the at channel spacing of 50 GHz. In these simulations, the OBP, the best efficiency of the OBP is obtained at the power of OBP and the power of the SMF are kept power range of the SMF that reaches to the system’s unchanged at the value of 3.7 mW. It can be seen from the power symmetry at any channel spacing. When the power Fig. 6a that the BER varies with the dispersion coefficient of the SMF is too small or too high, the residual FWM of the SMF as an oscillation. This oscillation is attributed power after two segments of the link is large that degrades by the dependence of the FWM efficiency on the phase the efficiency of the OBP. In the case of the channel mismatch as indicated in the analytical evaluation. spacing of 50 GHz, the BER is always lower about one Because the Kerr nonlinearity occurs strongly at the small order of magnitude than that in the case of 25 GHz value of dispersion so that the BER curve fluctuates with because nonlinear Kerr power is inversely proportional to large magnitude. When the dispersion increases, the
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Al-Khateeb et. al, “Analysis of the nonlinear Kerr OFDM WDM system by choosing suitable parameters. effects in optical transmission systems that deploy optical The simulation model of the OBP-assisted OFDM WDM phase conjugation,” Optics Express, vol. 26, no. 3, (2018), LR-PON at 100 Gbps is setup to validate the efficiency pp. 3145-3160. of the proposed compensation method in real conditions. The obtained results show that the BER performance of GIẢI PHÁP BÙ PHI TUYẾN DỰA TRÊN KĨ the system can be improved many orders of magnitude THUẬT TRUYỀN NGƯỢC TRONG MIỀN QUANG compared with that of the system without OBP. ỨNG DỤNG CHO HỆ THỐNG OFDM-WDM Consequently, the implementation of the OBP-assisted OFDM WDM LR-PON with very high bitrate of 100 Abstract: Hiệu ứng phi tuyến Kerr là một trong các Gbps is feasible in real conditions. yếu tố chính giới hạn hiệu năng của hệ thống OFDM- WDM. Hơn nữa, có một giải pháp bù phi tuyến khả thi mà không làm tăng thêm độ phức tạp cho phía thu là rất REFERENCES cần thiết cho các ứng dụng của mạng quang thụ động [1] A. Emsia, M. Malekizandi, Q. T. Le, I. B. Djordjevic, F. Kueppers, “1 Tb/s WDM-OFDM-PON power budget khoảng cách dài (LR-PON). Trong bài báo này, chúng tôi extension techniques,” Photonics Conf. (IPC), (2013). đề xuất một mô hình bộ truyền ngược trong miền quang [2] H. He, J. Li, M. Bi, W. Hu, “20-Gbps low cost WDM- (OBP) cải tiến, dựa trên phương pháp Fourier tách bước, OFDM-PON downstream transmission with tunable filter để bù lại ảnh hưởng phi tuyến và tán sắc trong hệ thống and linear APD module,” Chinese Optics Leters, (2014). OFDM-WDM. Bộ OBP đề xuất gồm các phần tử quang [3] Trang. T. T. Ngo, Thu. A. Pham, Nhan. D. Nguyen, Ngoc. có sẵn trong thực tế, trong đó sợi quang phi tuyến lớn T Dang, “Hybrid OFDM RoF-Based WDM-PON/MMW Backhaul Architechture for Heterogeneous Wireless (HNLF) đóng vai trò toán tử phi tuyến, cách tử Bragg sợi Networks,” REV J. Elect. and Comm., vol.7, no. 3-4, (FBG) đóng vài trò toán tử tuyến tính và ống dẫn sóng (2017), pp. 57-64. phi tuyến đóng vai trò phần tử liên hợp pha và được đặt [4] F. Offiong, S. Sinanovic, W. Popoola, “On PAPR tại phía phát nên rất phù hợp cho các ứng dụng LR-PON. reduction in pilot-assisted optical OFDM communication systems,” IEEE Access, vol. 5, (2017), pp. 8916-8929. Hiệu quả của bộ OBP đề xuất trong hệ thống OFDM- [5] Y. Xiao, M. Chen, F. Li, J. Tang, Y. Liu, L. Chen, “PAPR WDM được đánh giá dựa trên các tính toán lý thuyết và reduction based on chaos combined with SLM technique in kiểm chứng dựa trên mô phỏng Monte-Carlo. Các kết quả thu được từ phân tích đánh giá và mô phỏng đều cho thấy
7. Ngo Thi Thu Trang, Tran Thuy Binh, Bui Trung Hieu, Nguyen Duc Nhan bộ OBP đề xuất cải thiện đáng kể hiệu năng của hệ thống khi mà các tham số như hệ số tán sắc và công suất bơm được lựa chọn thích hợp. Keywords: Ghép kênh phân chia theo tần số trực giao (OFDM), Ghép kênh phân chia theo bước sóng (WDM), Các giải pháp bù phi tuyến, Truyền ngược trong miền quang (OBP), Mạng quang thụ động khoảng cách dài (LR-PON). Ngo Thi Thu Trang, M.E degree of Computer and Communication Engineering from Chungbuk National University, Korea in 2005. Now, she is a lecturer in Telecommunications Faculty 1 of Posts and Telecommunications Institute of Technology (PTIT). Her research interests include optical communications, digital signal processing, broadband networks. Email: trangntt1@ptit.edu.vn Tran Thi Thuy Binh, M.E degree of Telecommunications from PTIT in 2003. At present, she is a lecturer in PTIT, Telecommunicatons Faculty 1. Her professional fields involve nonlinearities in optical communications, optical broadband access networks. Email: tran.binh95@gmail.com Bui Trung Hieu received the PhD degree in Czech and Slovakia in 1992. He is currently an Associate Professor of PTIT. His research interests include optical communication systems, optical transport network, photonic devices. Email: hieubt@ptit.edu.vn Nguyen Duc Nhan, PhD degree of Electrical Engineering and Computer Systems from Monash University, Australia in 2011. Now, he is a lecturer in PTIT, Telecommunications Faculty 1. His research interests are numerical modeling and analysis, signal processing and its applications in optical communications and nonlinear fiber optics applications. Email: nhannd@ptit.edu.vn