An improved channel estimation method for a WDM transmission system derived from the CO-OFDM with PDM 64-QAM

In this study, firstly we presented a wavelength division multiplexed (WDM) transmission system derived from the coherent optical orthogonal frequency division multiplexing (CO-OFDM) with polarization division multiplexing (PDM) and 64 order quadrature amplitude modulation (QAM). We then proposed an improved channel estimation method based on discrete Fourier transform for the system to further improve the performance of the WDM transmission system. Under the experimental conditions employed, the principle and the spectral efficiency of the system, including a proposed algorithm to improve its performance (e.g. the robustness of the transmission impairments of the system) were studied. The simulations results demonstrated that our method improved the system efficient significantly. The system signal at 24 Tb/s can achieve a spectral efficiency of 12.5 bit/s/Hz up to a distance of 2000 km.     

Coherent optical OFDM scheme with inter-carrier interference self-cancellation and common phase error compensation

Schemes integrating inter-carrier interference （ICI） self-cancellation and common phase error （CPE） com- pensation for coherent optical orthogonal frequency division multiplexing （CO-OFDM） systems are investi- gated. The purpose of our research is to counteract the impacts of laser phase noise and fiber nonlinearity. We propose two ICI self-cancellation-based CO-OFDM schemes, and adopt a pilot-aided decision feedback （DFB） loop for CPE compensation. The proposed schemes are compared with conventional CO-OFDM schemes at the same spectral efficiency. Simulations show that our schemes can not only enhance laser linewidth tolerance of the CO-OFDM system, but also present strong robustness against fiber nonlinearity.     

Study on the efficiency of Eb/No algorithm for BER estimation over 112-Gb/s PDM CO-OFDM system with QPSK mapping

We research an efficient BER estimation method for 112-Gb/s polarization division multiplexing coherent optical OFDM (PDM CO-OFDM) with QPSK mapping over 800 km SSMF based on Eb/No algorithm in this paper. We first lay out the related formulas’ derivation to set up the theoretical basis for the feasibility of Eb/No algorithm and then we implement a series of simulations to illustrate the relationship of BER (and Q factor) versus OSNR, launch power of transmitter, chromatic dispersion and nonlinearity in optical fiber link via both Eb/No algorithm and Monte Carlo algorithm. The simulations demonstrate that BER estimated by Eb/No algorithm can achieve a precision up to 10⁻¹⁶ just with 10⁵ bits while Monte Carlo algorithm needs at least 10¹⁸ bits to get the same level. Therefore, Eb/No allows a quick and reliable method for BER estimation instead of the time consuming Monte Carlo method, which can be used to support simulations with various conditions.     

An improved least square channel estimation algorithm for coherent optical OFDM system

This paper presents an improved processing added to conventional least square (LS) channel estimation to modify its performance for coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. By testing selected limitation factors of the existing algorithms, the influence of our improved algorithm to the performance of CO-OFDM system were studied and compared with other published algorithms. The simulation results of the study demonstrated that the proposed approaches achieved better channel estimation performance and are considered as a more appropriate alternative for CO-OFDM system with the tradeoff between complexity and performance.     

基于小波变换的长距离光正交频分复用系统中四波混频引起的相位噪声分析

四波混频（FWM）效应是相干光正交频分复用（CO-OFDM）系统中最主要的非线性作用。分析基于小波变换的相干光正交频分（WT-OOFDM）系统原理,研究小波变换对FWM效应和光放大器自发辐射（ASE）引起的相位噪声的改善效果。数值结果表明,在采用常规G. 652光纤,100 Gbit/s的WT-OOFDM传输1500 km时,非线性相位噪声降低20%,总相位噪声降低15%。     

Novel iteration-free blind phase noise estimation for coherent optical OFDM

We propose a novel iteration-free blind phase noise estimation scheme for coherent optical orthogonal frequency division multiplexing （CO-OFDM） systems. In the new algorithm, the cost function is selected as the similar expression with real and imaginary parts as that in the modified constant modulus algorithm, and the new cost function is derived under some assumptions, where it is infinitely approximated by the sine and cosine functions. By means of the analytical formula of the cost function, the initial coarse common phase error can be obtained with only some samples, where the algorithm avoids computational complexity of conventional blind phase noise compensation scheme. In CO-OFDM systems with high-order modulation format （32 quadrature amplitude modulation） and narrow linewidth lasers, it is proved by the simulation results that the nhase noise can be effectively compensated with the proposed blind estimation method.     

Polarization mode dispersion compensation in a novel dual polarization differential quadrature phase shift keying system

A novel dual polarization differential quadrature phase shift keying (DP-DQPSK) system is proposed, whose receiver is the same as the single polarization DQPSK system, while it does not need polarization de-multiplexing like the conventional polarization division multiplexing QPSK (PDM-QPSK). Polarization mode dispersion (PMD) is mainly considered and PMD compensation for the DP-DQPSK system is studied. As the feedback signal for PMD compensation, the degree of polarization of the signals is discussed in detail. The results show that PMD tolerance can be improved by 89 ps within 1 dB optical signal noise ratio penalty after PMD compensation for the DP-DQPSK system.     

Pilot-based cross-phase modulation compensation for coherent optical orthogonal frequency division multiplexing long-haul optical communications systems

A pilot-based nonlinearity compensator (PB-NLC) is shown in this Letter to be an effective method for compensating cross-phase modulation (XPM) in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. An unmodulated pilot tone is transmitted at the center of each OFDM channel to detect phase errors caused by the Kerr effect, which converts intensity fluctuations from all channels to phase errors. The pilots are then used to cancel the XPM phase errors for each OFDM channel at the receiver after each channel's self-phase modulation (SPM) has been compensated, using its intensity waveform to determine its SPM. Numerical simulations of a 58 Gb/s single polarization 2375 km system with inline dispersion compensation show that the signal quality, Q, at the optimal launch power is increased by 2.4 dB if SPM compensation is used before the PB-NLC. This contrasts with only a 0.9 dB improvement if the PB-NLC is used without an SPM compensator for the same link. This shows the PB-NLC can effectively mitigate XPM but not SPM.     

A novel timing synchronization for CO-OFDM systems using chirp signals

A fast and efficient timing offset correction is an essential function in the coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. The timing synchronization schemes for OFDM systems in wireless communications can be used for CO-OFDM systems. However, the performance of these schemes is reduced due to the chromatic dispersion. To fulfill the requirement of the CO-OFDM systems, a novel symbol timing synchronization scheme based on chirp signals has been proposed. The simulation results show that the proposed method is robust in CO-OFDM systems which is suffering from noise.     

Blind frequency offset estimation based on cyclic prefix and virtual subcarriers in CO-OFDM system

A new blind frequency offset estimation method based on cyclic prefix and virtual subcarriers in coherent optical orthogonal frequency division multiplexing （CO-OFDM） system is presented. It is able to estimate the fractional part and integral part of frequency offset at the same time. Its estimation range is about [-3.5 GHz, 3.5 GHz]. The influence of the integral frequency offset is comprehensively analyzed in COOFDM system. Its performances in the additive white Gaussian noise （AWGN） channel and the dispersive channel are investigated, respectively. Simulation results indicate that even in the dispersive channel, when the optical signal-to-noise ratio （OSNR） is low, it can still work very well.     

Electronic compensator for 100-Gb/s PDM-CO-OFDM long-haul transmission systems

We study an electronic compensator (EC) as a receiver for a 100-Gb/s polarization division multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) system without optical dispersion compensation.EC,including electrical dispersion compensation (EDC),least squares channel estimation and compensation (LSCEC),and phase compensation (PC),is used to compensate for chromatic dispersion (CD),phase noise,polarization mode dispersion (PMD),and channel impairments,respectively.Simulations show that EC is highly effective in compensating for those impairments and that the performance is close to the theoretical limitation of optical signal-to-noise rate (OSNR),CD,and PMD.Its robustness against those transmission impairments and fiber nonlinearity are also systematically studied.     

Electrical nonlinearity pre-compensation for CO-OFDM system

An electrical nonlinearity pre-compensation (ENPC) combined nonlinearity with chromatic dispersion method is introduced for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system. Comparing with existed only nonlinearity pre-compensation (NL Pre-comp) method, ENPC method is not only suitable for low-dispersion fiber system, but also effective for high dispersion fiber transmission system without optical dispersion compensation. For 40 Gbit/s 20 × 80 km standard single mode fiber (SSMF) system, ENPC method can improve the nonlinear threshold (NLT) (for Q > 10 dB) about 2.7, 1.2, and 1.0 dB, and the maximum Q factor about 1.2, 0.4, and 0.3 dB for 2, 8, and 16 ps/nm/km fiber systems, respectively. The method allow the CO-OFDM system can avoid using optical dispersion compensation even for high dispersion fiber system with higher input power, and the 2-step ENPC solution does not increase more computation complexity compared with NL pre-comp method.     

Fiber nonlinearity mitigation by PAPR reduction in coherent optical OFDM systems via biased clipping OFDM

A new method incorporating biased clipping orthogonal frequency division multiplexing (OFDM) is presented, which mitigates fiber nonlinear effects in a long-haul coherent optical OFDM (CO-OFDM) system. Under the scheme of the method, the wanted signal carried by odd subcarriers is orthogonal to clipping noise and a Mach-Zehnder modulator (MZM) performs the optimal OFDM signal up-converter from the radio frequency (RF) domain to the optical domain. Analysis and simulation results show that fiber nonlinear effects can be effectively mitigated by reducing the peak-to-average power ratio (PAPR) in biased clipping CO-OFDM system. The nonlinearity threshold (NLT) is improved by 5 dB with a reach of 240 km. With a fiber length up to 800 km, system Q value is improved by approximately 2.3, 1.2, and 0.6 dB at a chromatic dispersion of 6, 12, and 16 ps/(nm·km), respectively. Additionally, system Q reaches the maximum when direct currect (DC) bias is equal to the mean value of the OFDM waveform.     

A novel adaptive synchronization algorithm for intermediate frequency architecture CO-OFDM system

An adaptive algorithm of fine synchronization for intermediate frequency architecture coherent optical orthogonal frequency division multiplexing (CO-OFDM) transmission system is proposed. The whole synchronization procedure is separated into two steps. In the first step, we use an auto-correlation-style algorithm to achieve the coarse symbol synchronization. In the second step, the proposed algorithm is used to achieve the adaptive fine synchronization. The merit of the proposed algorithm is that it can realize fine synchronization under different environments without adjusting the detect-threshold of timing metric in a dynamically reconfiguration network. And also the algorithm can implement in field-programmable gate array (FPGA) or other digital signal processing (DSP) chips easily. In this paper, the CO-OFDM model is analyzed in theory firstly. Secondly, an analysis on the performance of coarse synchronization algorithm used in this paper is made. Finally, the proposed fine synchronization algorithm is introduced in detail. The simulation experiment result demonstrates that the proposed algorithm achieves fine synchronization under different signal noise ratio (SNR) conditions after 6 fiber-spans transmission.     

偏分复用系统中偏振模色散补偿与偏分解复用一体化方案

本文建立了偏分复用系统中偏振模色散与信号偏振态变化引起信道串扰的数学模型, 分析了偏振模色散对偏分复用信道射频功率的影响, 并提出了适用于偏分复用系统的光域偏振模色散补偿与偏分解复用同时进行的方案: 用信道的射频功率作为反馈控制信号, 监测链路中偏振模色散和偏振态变化引起的信道串扰的大小, 用改进的粒子群优化算法对偏振控制器进行自适应控制, 同时完成偏振模色散补偿与偏分解复用. 在112 Gb/s偏分复用-差分正交相移键控(PDM-DQPSK)传输系统中仿真验证了该方案的有效性. 结果表明该方案可以使112 Gb/s-PDM-DQPSK传输系统完成自适应偏分解复用的同时, 在1 dB的光信噪比代价下, 使系统对偏振模色散的容忍度提高20 ps. 关键词： 偏分复用系统 信道串扰 偏振模色散 偏分解复用     

一种基于星座恢复的相干光OFDM系统非线性抑制方法

鉴于相干光正交频分复用系统（CO-OFDM）易受非线性效应影响,严重制约系统传输性能, 提出一种基于星座恢复的降低系统峰均值功率比（PAPR）的方法。对系统模型及作用机理进行分析,仿真结果显示,以10 Gbit/s的速率通过单模光纤传输720 km,基于星座恢复的CO-OFDM系统Q值较无非线性抑制的CO-OFDM系统有3 dB提高;另外,系统最佳限幅比例系数受色度色散影响,随着色散因子的增大,星座恢复效果也逐渐减弱,在传输240 km条件下,色散因子为12 ps/nmkm较6 ps/nmkm,限幅比例系数从0.9降低至0.8。     

40 Gbit/s 相干偏振复用QPSK传输中基于Manakov方程的非线性补偿

 在40 Gbit/s相干偏振复用正交相移键控（QPSK）传输系统中,为了补偿由于光纤中非线性效应引起的传输信号损伤,采用了基于Manakov方程的反向传播非线性补偿算法.传统的基于标量非线性薛定谔方程（NLSE）的反向传播算法忽略了偏振模色散（PMD）的作用,因此在偏振复用系统中不能补偿由于PMD引起的信号损伤|而基于Manakov方程的数字信号处理方法能够对PMD与克尔非线性效应的耦合作用进行补偿.从仿真与实验两个方面对此方法在40 Gbit/s相干偏振复用QPSK传输系统中的补偿效果进行了验证.结果均表明,与NLSE相比,基于Manakov方程的反向传播算法在400 km长距离QPSK传输中显示出更好的性能.在光信噪比（OSNR）为18 dB时,基于Manakov方程的反向传播算法得到的Q值与NLSE相比提高约3dB.     

Compensation of dynamic phase distortions in the phase conjugation system based on the film of azocontaining liquid-crystalline polymer

The compensation dynamics of phase distortions in optical phase conjugation (OPC) using the film of azocontaining liquid-crystalline polymer was experimentally investigated. The quality of compensation of distortions of the wave front was determined, and the effect of experimental conditions on the OPC dynamics was studied. The coefficient of reflection in OPC reached 35% for a total incident light intensity of ～17 mW/cm² at a wavelength of 532 nm. The response time of the OPC system was ～1 s at a polymer temperature of 69°C. The high-quality compensation of the wave front distortions of the laser radiation was obtained. The residual error of compensation decreased by a factor of ～100 during the transient OPC process. It is demonstrated that the spatially modulated light beam can be retrieved during repeated passages through a phase plate with strong small-scale aberrations.     

偏分复用系统信道串扰的理论模型及消除方案

建立了偏分复用(PDM)系统中信道串扰的数学模型,并提出了消除该串扰的方案,即用解复用端一路光信号的射频(RF)功率作为反馈信号以监测光信号在链路中偏振态的变化和在接收端的串扰情况,用粒子群优化(PSO)算法作为逻辑控制单元的算法,控制偏振控制器以消除信道间的串扰。数值仿真了RF功率与信道串扰大小之间的关系,并在2×50Gb/s偏分复用-差分正交移相键控(PDM-DQPSK)传输系统平台上仿真验证了消除串扰方案的效果。结果表明该方案能够大幅降低系统误码率,改善系统性能。     

Effects of pulse chirp on supercontinuum produced in dispersion decreasing fibre

The supercontinuum (SC) source plays a key role in wavelength division multiplexing over the optical time division multiplexing (WDM/OTDM) transmission system. The SC produced in dispersion decreasing fibre (DDF) is wider and flatter than that produced in dispersion shifted fibre (DSF). In this paper, a SC producing process in DDF is numerically simulated, the effects of pump pulse chirp on the SC width and flatness are initially studied and the corresponding theoretical explanations are given. Particularly, we have analysed and compared the evolutions of the SC along DDF pumped by different chirp pulses. Several valuable conclusions are obtained.