数字相干PM-QPSK光传输系统中的非线性损伤与系统的性能估计
|
摘要
近年来,随着高速数字信号处理技术(digital signal processing,DSP)和模数转换技术的进步,加上相关光通信器件如光学混频器的发展,相干光传输技术重新成为光通信领域的研究热点。相干检测与DSP技术相结合,使得在电域进行可编程处理的载波相位恢复及(信号和本振光的)偏振态匹配成为可能,这样就清除了传统相干光通信系统的两大主要技术障碍。基于DSP技术的相干接收机结构简单,具有硬件透明性；可在电域补偿线性或非线性传输损伤,简化传输链路,降低传输成本；支持多进制调制格式和偏振态复用,易实现高频谱效率的光纤传输。众多优势使得基于DSP技术的相干光传输系统成为下一代光通信系统的重要选择,有关其传输特性和接收算法的研究迅速展开。基于DSP技术的相干检测技术与诸如正交相移键控(quadrature phase shift keying, QPSK)、正交幅度调制(quadrature amplitude modulation, QAM)等高级调制格式相结合,可以大大提升系统的传输容量,简化系统复杂度；如果再结合偏振复用技术(polarization-multiplexed, PM),则可以成倍的提升系统的谱效率
偏振复用正交相移键控(PM-QPSK)调制格式结合相干检测技术已成为实现40/100G光网络的首选方案。采用这种方案,光信号在传输过程中引入的线性损伤,诸如群速度色散(group velocity dispersion,GVD)和偏振模色散(polarization mode dispersion, PMD)都可以在接收机处补偿。因此,限制这一方案通信性能的主要问题来自于光信号在传输过程中受到的非线性损伤,包括自相位调制(self-phase modulation, SPM)、交叉相位调制(cross-phase modulation, XPM)、四波混频(four-wave mixing, FWM)以及非线性相位噪声(nonlinear phase noise, NLPN)等等。对于常见的多信道的波分复用(wavelength division multiplexing, WDM)系统,信道间的XPM效应对于偏振复用系统的影响尤其严重。它不但使得信号的相位受到扰动,而且还会引起另一种严重的非线性损伤,称之为信道间交叉偏振调制(cross-polarization modulation, XPolM)。已经有实验以及仿真研究表明,对于40G的色散管理PM-QPSK波分复用系统来说,XPolM已成为限制系统性能的主要损伤源。对于100G的系统,XPolM会造成和其他非线性损伤同样量级的传输代价。本论文针对100G (40G)PM-QPSK数字相干传输系统中的非线性损伤及系统的性能估计进行了较深入的研究,取得了一定的创新性研究成果。本文的主要创新点和研究工作包括：
(1)首次研究了单信道色散管理PM-QPSK系统中,SPM效应引起的偏振态散射的现象。研究表明,由于SPM效应对双偏振信号的X和Y偏振态上的脉冲的相位的不同扰动,因此信号在光纤的传输过程中,任意脉冲对的X和Y偏振分量间的相位差不再保持恒定,而会发生一定程度的抖动。结果会导致它们的合偏振态发生显著的偏振态散射。研究结果进一步表明,SPM导致的偏振散射的程度和PM-QPSK信号的脉冲对两正交偏振分量之间的相位差的抖动程度成线性正相关。相位差的抖动越厉害(方差越大),偏振散射就越严重。除此之外,我们发现合适的色散图谱(即预色散补偿量和每跨段的残留色散量)能够明显地抑制这类偏振散射。上述结论对非归零码(non-return-to-zero, NRZ)和归零码(return-to-zero, RZ)脉冲均成立。
(2)论文针对色散管理PM-QPSK系统中的非线性信号-噪声相互作用(nonlinear signal-noise interactions, NSNI)进行了较深入的研究。我们发现,对于符号同步格式(symbol-aligned format)的相干PM-QPSK系统,NSNI对系统的影响很小；而对于符号交错(symbol-interleaved format)格式,NSNI对PM-QPSK传输系统的影响比较严重。这一现象在低速率(比如42.8-Gbit/s)、采用RZ脉冲的PM-QPSK传输系统中尤其明显。数值研究结果表明,对于19个信道、速率为42.8-Gbit/s的RZ-PM-QPSK系统,当信号在标准单模光纤上传输1000公里后,由于NSNI的影响,符号交错RZ-PM-QPSK系统的非线性限(nonlinear threshold, NLT)将会从5.8dBm下降为0.6dBm。而对于符号同步格式的RZ-PM-QPSK系统,由于NSNI的影响,其NLT仅由-0.6dBm下降至-1.5dBm。进一步研究发现,造成上述区别的原因在于信道间交叉偏振调制(XPoIM)。XPolM效应对NSNI并不敏感。在速率42.8-Gbit/s、采用全光色散补偿的PM-QPSK传输系统中,XPolM损伤的大小主导了系统的性能。而XPolM效应又对NSNI不敏感,所以这样的系统对NSNI效应也不敏感。而对于使用符号交错格式的PM-QPSK传输系统来说,链路中的XPolM损伤已得到极大地压缩,其他对NSNI有贡献的非线性效应占主导地位。此时的系统对NSNI高度敏感。这部分的研究成果发表在Optics Express期刊上,并得到了较好的评价。
(3)论文分析了PM-QPSK系统中,偏振模色散(PMD)对NSNI效应导致的传输代价的影响。结果表明,对于单信道传输系统,PMD效应引起的差分群时延(differentail group delay, DGD)能够使得双偏振信号的X和Y偏振分量之间发生“走离”效应,继而降低了它们的合光场的峰值功率,从而减弱了非线性效应。而非线性损伤的大小与NSNI损伤的大小成正相关的关系。因此,PMD效应有助于降低单信道PM-QPSK系统中NSNI引起的传输代价。对于多信道的PM-QPSK传输系统,同样由于PMD效应引起的X和Y偏振分量之间的“走离”效应,它减少了参与XPolM效应的偏振态的数目,继而大大减弱了XPolM损伤。另一方面,与符号交错格式类似,对XPolM效应的抑制意味着系统开始对NSNI效应变得敏感。因此,PMD效应恶化了PM-QPSK系统中NSNI引起的传输代价。对于给定的传输链路,光纤的PMD系数越大,上述恶化效果越明显。这部分的研究成果发表在Optics Express期刊上,并得到了较好的评价。
(4)研究了基于PM-QPSK调制格式的密集波分复用系统中,光复用器的滤波函数形状及带宽对系统通信性能的影响。我们以1至4阶超高斯光滤波器来代表光复用器的滤波效果。研究发现,虽然高阶的滤波器在合适的滤波带宽处,光纤传输系统能获得相对于使用低阶滤波器更好的通信性能,但是它对滤波器的带宽及中心波长的抖动非常敏感。低阶滤波器虽然获得次之的性能,但是滤波器的带宽抖动对系统的影响不像高阶滤波器那么严重。信道间隔越窄,上述现象越明显。在背靠背的情形下,研究发现对于波特率为Rs,信道间隔为50GHz的PM-QPSK系统来说,如果滤波器的带宽超过1.1Rs,那么各阶滤波器的性能几乎一致。在带宽低于1.1R。的区域,信道内符号间干扰(intra-channel symbol interference, ISI)主导了系统的性能。在这个区域,高阶滤波器更容易激发起严重的ISI损伤,从而获得次于低阶滤波器的性能。对信道间隔等于波特率Rs的Nyquist-WDM系统的研究表明,滤波器的带宽存在一个最优值。滤波带宽过低会引起严重的ISI损伤,带宽过大又会引起严重的信道间线性串扰(inter-channel coherent crosstalk, ICC)。研究结果表明,对于10个信道,每信道速率为111-Gbit/s (波特率Rs=27.75GBaud)并采用NRZ-PM-QPSK调制的Nyquist-WDM系统来说,4阶超高斯滤波器在最优带宽值在0.95Rs=26.4GHz处,系统能获得最好的性能。此外我们还发现,滤波器的阶数越高,它对光信号在传输过程中受到的信道间的非线性损伤的抑制能力越强。这部分的研究成果发表在Optical Engineering期刊上,并得到了较好的评价。
(5)论文提出了一种评估数字相干PM-QPSK传输系统误码性能的方法。该方法引入了平均偏振度(degree of polarization, DOP)的概念,平均偏振度DOP (DOPmean)由信号经相干接收机解调后的信号星座图得到。通过对112-Gbit/s RZ-PM-QPSK传输系统的模拟,我们发现系统在长途传输结束后的Q因子与平均偏振度DOP的大小成确定的线性关系。越小的DOPmean意味着越差的误码性能。我们还发现,Q因子与DOPmean之间的确定的线性关系(即系统Q因子与DOPmean之间的比例常数)和系统的其他参数无关。比如,系统是单信道还是多信道、传输链路是全光色散补偿或全电色散补偿、系统有无经过长途非线性传输等因素无关。我们只需在背靠背的情形下得到Q-DOPmean的关系曲线,那么在其他的任意场景,从信号的星座图计算得到的DOPmean的大小可直接得到系统的Q因子。
Over the past few years, with the improvement of high-speed digital signal processing (DSP) and analog-to-digital conversion, coherent optical transmission has become a research hotspot again. The combination of coherent detection and DSP technique make it possible to perform linear impairments electrically, such as chromatic dispersion and polarization mode dispersion in electrical domain. Also this combination enables carrier phase recovery and polarization tracking digitally, which have been recognized as major obstacles for the conventional coherent optical transmission. Coherent receiver based on DSP technique has the simple configuration, with the significant hardware-transparent. Due to its ability to perform linear/nonlinear transmission impairment compensation in the electrical domain, the coherently-detected receiver makes it possible to streamline the transmission links and reduce costs. Also, multi-level modulation formats are supported by the digital coherent receiver, on which the high spectral efficiency (SE) can be achieved easily. Due to these advantages, the coherently-detected fiber-optics systems are considered to be the very promising candidate for the next generation optical network. The fiber-optics transmission capacity can be improved significantly with the combination of coherent receiver and quadrature phase shift keying (QPSK)/quadrature amplitude modulation (QAM). If the polarization-multiplexing (PM) technique is used, the capacity is doubled.
The combination of polarization-multiplexing quadrature phase shift keying(PM-QPSK) and the digitally coherently-detected has been consided to be the most promising candidate for the implementation of40/100optical networks. Any linear impairment, such as roup velocity dispersion (GVD) and polarization mode dispersion (PMD), can be compensated by this transmission system in electrical domain. As a result, nonlinear transmission impairments expericenced by signals durng transmission has become a major concern for coherently-detected PM-QPSK modulated signals. These nonlinear transmission distortions include self-phase modulation(SPM)、cross phase modulation(XPM)、 four-wave-mixing(FWM), nonlinear phase noise(NLPN) and so on. For wavelength-division-multiplexing transmission, inter-channel XPM is the major nonlinearity, especially for PM signals. XPM results in not only the phase disturbance experienced by optical signal, but the other severe nonlinear impairments-the so called inter channel cross polarization modulation (XPolM). Some previous experimental and analytical foundings indicate that the XPolM-induced distortions have become the major limiting factor for40G WDM PM-QPSK signals. For100G WDM signals, XPolM leads to the same level of nonlinear penalty as the other fiber nonlinearities. We have investigated the nonlinearities in40/100G PM-QPSK transmission systems in this paper. The major studies and contributions of this paper including:
(1) We have studied, for the first time, the SPM-induced polarization scattering for single-channel PM-QPSK over dispersion managed link. We found that due to the different disturbance experienced by the X and Y polarization component of arbitrary pulse pair, the phase difference of them is no longer constant but randomized around the ideal value. This random process leads to polarization scattering for arbitrary pulse pair. Moreover, we found that appropriate pre-compensation is helpfui to reduce the SPM-induced polarization scattering. These results hold true for both non return-to-zero (NRZ) and return-to-zero (RZ) pulse format.
(2) Using numerical simulations, the impact of nonlinear signal-noise interactions (NSNI) between the amplified spontaneous emission noise (ASE) and the information signal on polarization-multiplexed quadrature phase-shift keying (PM-QPSK) systems at42.8(112)-Gbit/s is investigated over dispersion-managed (DM) link. Both symbol-aligned and symbol-interleaved formats are considered and compared. We find that for symbol-aligned PM-QPSK systems, the impact of NSNI on system performance seems rather weak due to the strong inter-channel cross-polarization modulation (XPolM). However, when the symbol-interleaved format is used, in which the XPolM is suppressed significantly, the system performance is seriously degraded by NSNI, especially at low bit-rate. Results of1000-km transmission employing standard single-mode fiber (SSMF) over DM link show that for42.8-Gbit/s coherent PM-QPSK systems, the nonlinear threshold (NLT) will decrease from5.8dBm to0.6dBm due to the nonlinear signal-noise interactions when symbol-interleaved RZ format is used.
(3) Considering the polarization mode dispersion(PMD), the transmission penalty induced by nonlinear signal-noise interactions (NSNI) between the amplified spontaneous emission noise (ASE) and the information signal is investigated numerically for40(100)G dispersion-managed PM-QPSK systems. We show that for single-channel PM-QPSK systems, PMD is helpful to reduce the NSNI-induced penalty because differentail group delay (DGD), introduced by PMD, walk off the X and Y component of PM signals. The walking off of the X and Y component means lower spike power and thus smaller nonlinearities. For multi-channel PM-QPSK system, however, the NSNI-induced nonlinear penalty is significantly enhanced by PMD, especially at low bit-rate. The walking off between X and Y component, caused by DGD, reduce the polarizations that make contribution to XPolM and thus the XPolM-induced impairment is reduced. On the other hand, just as it for symbol-interleaved format, the suppression of XPolM means that the systems are sensitive to NSNI. Our results show that due to the NSNI, the reduction of allowed input power that gives1-dB Q penalty after1600-km nonlinear transmission will increase from1dB without PMD to3.7dB with PMD for42.8-Gbit/s coherent return-to-zero (RZ)-PM-QPSK systems.
(4) The impact of filter shape and filter bandwidth on closed-spaced PM-QPSK systems is investigated. The optical multiplexer is modeled by super-Gaussian (SG) filter with1to4order. We found that, although a higher-order filter generally leads to better system performance at the optimal filter bandwidth, this benefit comes at the cost of reduced tolerance to variation in filter bandwidth and center-frequency shifts. The closer channel spacing, the more pronounced these findings. It is found that all filters exhibit the same performance if they have more than1.1Rs bandwidth for WDM PM-QPSK systems with Rs symbol-rate and50GHz spacing in b2b operation. The intra-channel symbol interference (ISI) is the major distortion if the filter's bandwidth is less than1.1RS. Compared with lower-order filter, in this narrow bandwidth domain, a higher-order filter generally leads to more severe ISI impairment.
(5) A method estimating the system performance of digital coherent PM-QPSK systems was presented in this paper. The quality parameter, mean degree of polarization (DOP) of PM-QPSK signals, obtained through the complex signal constellation after coherent receiver, was introduced to assess system performance. With the help of the simulative results of112-Gbit/s PM-QPSK transmission systems, we found that the mean DOP is proportional to the Q-factor of the systems. Moreover, it is shown that the linear relation between the mean DOP and Q-factor is uncorrelated with the other system parameters such as the channel number, the dispersion map and so on.
偏振复用正交相移键控(PM-QPSK)调制格式结合相干检测技术已成为实现40/100G光网络的首选方案。采用这种方案,光信号在传输过程中引入的线性损伤,诸如群速度色散(group velocity dispersion,GVD)和偏振模色散(polarization mode dispersion, PMD)都可以在接收机处补偿。因此,限制这一方案通信性能的主要问题来自于光信号在传输过程中受到的非线性损伤,包括自相位调制(self-phase modulation, SPM)、交叉相位调制(cross-phase modulation, XPM)、四波混频(four-wave mixing, FWM)以及非线性相位噪声(nonlinear phase noise, NLPN)等等。对于常见的多信道的波分复用(wavelength division multiplexing, WDM)系统,信道间的XPM效应对于偏振复用系统的影响尤其严重。它不但使得信号的相位受到扰动,而且还会引起另一种严重的非线性损伤,称之为信道间交叉偏振调制(cross-polarization modulation, XPolM)。已经有实验以及仿真研究表明,对于40G的色散管理PM-QPSK波分复用系统来说,XPolM已成为限制系统性能的主要损伤源。对于100G的系统,XPolM会造成和其他非线性损伤同样量级的传输代价。本论文针对100G (40G)PM-QPSK数字相干传输系统中的非线性损伤及系统的性能估计进行了较深入的研究,取得了一定的创新性研究成果。本文的主要创新点和研究工作包括：
(1)首次研究了单信道色散管理PM-QPSK系统中,SPM效应引起的偏振态散射的现象。研究表明,由于SPM效应对双偏振信号的X和Y偏振态上的脉冲的相位的不同扰动,因此信号在光纤的传输过程中,任意脉冲对的X和Y偏振分量间的相位差不再保持恒定,而会发生一定程度的抖动。结果会导致它们的合偏振态发生显著的偏振态散射。研究结果进一步表明,SPM导致的偏振散射的程度和PM-QPSK信号的脉冲对两正交偏振分量之间的相位差的抖动程度成线性正相关。相位差的抖动越厉害(方差越大),偏振散射就越严重。除此之外,我们发现合适的色散图谱(即预色散补偿量和每跨段的残留色散量)能够明显地抑制这类偏振散射。上述结论对非归零码(non-return-to-zero, NRZ)和归零码(return-to-zero, RZ)脉冲均成立。
(2)论文针对色散管理PM-QPSK系统中的非线性信号-噪声相互作用(nonlinear signal-noise interactions, NSNI)进行了较深入的研究。我们发现,对于符号同步格式(symbol-aligned format)的相干PM-QPSK系统,NSNI对系统的影响很小；而对于符号交错(symbol-interleaved format)格式,NSNI对PM-QPSK传输系统的影响比较严重。这一现象在低速率(比如42.8-Gbit/s)、采用RZ脉冲的PM-QPSK传输系统中尤其明显。数值研究结果表明,对于19个信道、速率为42.8-Gbit/s的RZ-PM-QPSK系统,当信号在标准单模光纤上传输1000公里后,由于NSNI的影响,符号交错RZ-PM-QPSK系统的非线性限(nonlinear threshold, NLT)将会从5.8dBm下降为0.6dBm。而对于符号同步格式的RZ-PM-QPSK系统,由于NSNI的影响,其NLT仅由-0.6dBm下降至-1.5dBm。进一步研究发现,造成上述区别的原因在于信道间交叉偏振调制(XPoIM)。XPolM效应对NSNI并不敏感。在速率42.8-Gbit/s、采用全光色散补偿的PM-QPSK传输系统中,XPolM损伤的大小主导了系统的性能。而XPolM效应又对NSNI不敏感,所以这样的系统对NSNI效应也不敏感。而对于使用符号交错格式的PM-QPSK传输系统来说,链路中的XPolM损伤已得到极大地压缩,其他对NSNI有贡献的非线性效应占主导地位。此时的系统对NSNI高度敏感。这部分的研究成果发表在Optics Express期刊上,并得到了较好的评价。
(3)论文分析了PM-QPSK系统中,偏振模色散(PMD)对NSNI效应导致的传输代价的影响。结果表明,对于单信道传输系统,PMD效应引起的差分群时延(differentail group delay, DGD)能够使得双偏振信号的X和Y偏振分量之间发生“走离”效应,继而降低了它们的合光场的峰值功率,从而减弱了非线性效应。而非线性损伤的大小与NSNI损伤的大小成正相关的关系。因此,PMD效应有助于降低单信道PM-QPSK系统中NSNI引起的传输代价。对于多信道的PM-QPSK传输系统,同样由于PMD效应引起的X和Y偏振分量之间的“走离”效应,它减少了参与XPolM效应的偏振态的数目,继而大大减弱了XPolM损伤。另一方面,与符号交错格式类似,对XPolM效应的抑制意味着系统开始对NSNI效应变得敏感。因此,PMD效应恶化了PM-QPSK系统中NSNI引起的传输代价。对于给定的传输链路,光纤的PMD系数越大,上述恶化效果越明显。这部分的研究成果发表在Optics Express期刊上,并得到了较好的评价。
(4)研究了基于PM-QPSK调制格式的密集波分复用系统中,光复用器的滤波函数形状及带宽对系统通信性能的影响。我们以1至4阶超高斯光滤波器来代表光复用器的滤波效果。研究发现,虽然高阶的滤波器在合适的滤波带宽处,光纤传输系统能获得相对于使用低阶滤波器更好的通信性能,但是它对滤波器的带宽及中心波长的抖动非常敏感。低阶滤波器虽然获得次之的性能,但是滤波器的带宽抖动对系统的影响不像高阶滤波器那么严重。信道间隔越窄,上述现象越明显。在背靠背的情形下,研究发现对于波特率为Rs,信道间隔为50GHz的PM-QPSK系统来说,如果滤波器的带宽超过1.1Rs,那么各阶滤波器的性能几乎一致。在带宽低于1.1R。的区域,信道内符号间干扰(intra-channel symbol interference, ISI)主导了系统的性能。在这个区域,高阶滤波器更容易激发起严重的ISI损伤,从而获得次于低阶滤波器的性能。对信道间隔等于波特率Rs的Nyquist-WDM系统的研究表明,滤波器的带宽存在一个最优值。滤波带宽过低会引起严重的ISI损伤,带宽过大又会引起严重的信道间线性串扰(inter-channel coherent crosstalk, ICC)。研究结果表明,对于10个信道,每信道速率为111-Gbit/s (波特率Rs=27.75GBaud)并采用NRZ-PM-QPSK调制的Nyquist-WDM系统来说,4阶超高斯滤波器在最优带宽值在0.95Rs=26.4GHz处,系统能获得最好的性能。此外我们还发现,滤波器的阶数越高,它对光信号在传输过程中受到的信道间的非线性损伤的抑制能力越强。这部分的研究成果发表在Optical Engineering期刊上,并得到了较好的评价。
(5)论文提出了一种评估数字相干PM-QPSK传输系统误码性能的方法。该方法引入了平均偏振度(degree of polarization, DOP)的概念,平均偏振度DOP (DOPmean)由信号经相干接收机解调后的信号星座图得到。通过对112-Gbit/s RZ-PM-QPSK传输系统的模拟,我们发现系统在长途传输结束后的Q因子与平均偏振度DOP的大小成确定的线性关系。越小的DOPmean意味着越差的误码性能。我们还发现,Q因子与DOPmean之间的确定的线性关系(即系统Q因子与DOPmean之间的比例常数)和系统的其他参数无关。比如,系统是单信道还是多信道、传输链路是全光色散补偿或全电色散补偿、系统有无经过长途非线性传输等因素无关。我们只需在背靠背的情形下得到Q-DOPmean的关系曲线,那么在其他的任意场景,从信号的星座图计算得到的DOPmean的大小可直接得到系统的Q因子。
Over the past few years, with the improvement of high-speed digital signal processing (DSP) and analog-to-digital conversion, coherent optical transmission has become a research hotspot again. The combination of coherent detection and DSP technique make it possible to perform linear impairments electrically, such as chromatic dispersion and polarization mode dispersion in electrical domain. Also this combination enables carrier phase recovery and polarization tracking digitally, which have been recognized as major obstacles for the conventional coherent optical transmission. Coherent receiver based on DSP technique has the simple configuration, with the significant hardware-transparent. Due to its ability to perform linear/nonlinear transmission impairment compensation in the electrical domain, the coherently-detected receiver makes it possible to streamline the transmission links and reduce costs. Also, multi-level modulation formats are supported by the digital coherent receiver, on which the high spectral efficiency (SE) can be achieved easily. Due to these advantages, the coherently-detected fiber-optics systems are considered to be the very promising candidate for the next generation optical network. The fiber-optics transmission capacity can be improved significantly with the combination of coherent receiver and quadrature phase shift keying (QPSK)/quadrature amplitude modulation (QAM). If the polarization-multiplexing (PM) technique is used, the capacity is doubled.
The combination of polarization-multiplexing quadrature phase shift keying(PM-QPSK) and the digitally coherently-detected has been consided to be the most promising candidate for the implementation of40/100optical networks. Any linear impairment, such as roup velocity dispersion (GVD) and polarization mode dispersion (PMD), can be compensated by this transmission system in electrical domain. As a result, nonlinear transmission impairments expericenced by signals durng transmission has become a major concern for coherently-detected PM-QPSK modulated signals. These nonlinear transmission distortions include self-phase modulation(SPM)、cross phase modulation(XPM)、 four-wave-mixing(FWM), nonlinear phase noise(NLPN) and so on. For wavelength-division-multiplexing transmission, inter-channel XPM is the major nonlinearity, especially for PM signals. XPM results in not only the phase disturbance experienced by optical signal, but the other severe nonlinear impairments-the so called inter channel cross polarization modulation (XPolM). Some previous experimental and analytical foundings indicate that the XPolM-induced distortions have become the major limiting factor for40G WDM PM-QPSK signals. For100G WDM signals, XPolM leads to the same level of nonlinear penalty as the other fiber nonlinearities. We have investigated the nonlinearities in40/100G PM-QPSK transmission systems in this paper. The major studies and contributions of this paper including:
(1) We have studied, for the first time, the SPM-induced polarization scattering for single-channel PM-QPSK over dispersion managed link. We found that due to the different disturbance experienced by the X and Y polarization component of arbitrary pulse pair, the phase difference of them is no longer constant but randomized around the ideal value. This random process leads to polarization scattering for arbitrary pulse pair. Moreover, we found that appropriate pre-compensation is helpfui to reduce the SPM-induced polarization scattering. These results hold true for both non return-to-zero (NRZ) and return-to-zero (RZ) pulse format.
(2) Using numerical simulations, the impact of nonlinear signal-noise interactions (NSNI) between the amplified spontaneous emission noise (ASE) and the information signal on polarization-multiplexed quadrature phase-shift keying (PM-QPSK) systems at42.8(112)-Gbit/s is investigated over dispersion-managed (DM) link. Both symbol-aligned and symbol-interleaved formats are considered and compared. We find that for symbol-aligned PM-QPSK systems, the impact of NSNI on system performance seems rather weak due to the strong inter-channel cross-polarization modulation (XPolM). However, when the symbol-interleaved format is used, in which the XPolM is suppressed significantly, the system performance is seriously degraded by NSNI, especially at low bit-rate. Results of1000-km transmission employing standard single-mode fiber (SSMF) over DM link show that for42.8-Gbit/s coherent PM-QPSK systems, the nonlinear threshold (NLT) will decrease from5.8dBm to0.6dBm due to the nonlinear signal-noise interactions when symbol-interleaved RZ format is used.
(3) Considering the polarization mode dispersion(PMD), the transmission penalty induced by nonlinear signal-noise interactions (NSNI) between the amplified spontaneous emission noise (ASE) and the information signal is investigated numerically for40(100)G dispersion-managed PM-QPSK systems. We show that for single-channel PM-QPSK systems, PMD is helpful to reduce the NSNI-induced penalty because differentail group delay (DGD), introduced by PMD, walk off the X and Y component of PM signals. The walking off of the X and Y component means lower spike power and thus smaller nonlinearities. For multi-channel PM-QPSK system, however, the NSNI-induced nonlinear penalty is significantly enhanced by PMD, especially at low bit-rate. The walking off between X and Y component, caused by DGD, reduce the polarizations that make contribution to XPolM and thus the XPolM-induced impairment is reduced. On the other hand, just as it for symbol-interleaved format, the suppression of XPolM means that the systems are sensitive to NSNI. Our results show that due to the NSNI, the reduction of allowed input power that gives1-dB Q penalty after1600-km nonlinear transmission will increase from1dB without PMD to3.7dB with PMD for42.8-Gbit/s coherent return-to-zero (RZ)-PM-QPSK systems.
(4) The impact of filter shape and filter bandwidth on closed-spaced PM-QPSK systems is investigated. The optical multiplexer is modeled by super-Gaussian (SG) filter with1to4order. We found that, although a higher-order filter generally leads to better system performance at the optimal filter bandwidth, this benefit comes at the cost of reduced tolerance to variation in filter bandwidth and center-frequency shifts. The closer channel spacing, the more pronounced these findings. It is found that all filters exhibit the same performance if they have more than1.1Rs bandwidth for WDM PM-QPSK systems with Rs symbol-rate and50GHz spacing in b2b operation. The intra-channel symbol interference (ISI) is the major distortion if the filter's bandwidth is less than1.1RS. Compared with lower-order filter, in this narrow bandwidth domain, a higher-order filter generally leads to more severe ISI impairment.
(5) A method estimating the system performance of digital coherent PM-QPSK systems was presented in this paper. The quality parameter, mean degree of polarization (DOP) of PM-QPSK signals, obtained through the complex signal constellation after coherent receiver, was introduced to assess system performance. With the help of the simulative results of112-Gbit/s PM-QPSK transmission systems, we found that the mean DOP is proportional to the Q-factor of the systems. Moreover, it is shown that the linear relation between the mean DOP and Q-factor is uncorrelated with the other system parameters such as the channel number, the dispersion map and so on.
引文
[1]S. Sjodin, et al, "Comparison of 128-SP-QAM with PM-16QAM", Opt. Express, vol.20, Issue.8, pp.8356-8366 (2012).
[2]J. D. Downie, et al, "Ultra-long-haul 112Gb/s PM-QPSK transmission systems using longer spans and Raman amlification", Opt. Express, vol.20, Issue.9, pp.10353-10358(2012).
[3]D. Chang, et al, "Real-time processed 34×120Gb/s transmission over 432.8km unrepeatered link with legacy fiber and span loss of 74.4dB", ECOC2011, paper.P4.02.
[4]Q. Yang et al, "Experimental demonstration and numerical simulation of 107Gb/s high spectral efficiency cohernt optical OFDM", J. Lightwave Technol. vol.27, Issue.3, pp.168-176 (2009).
[5]V. A. J. M. Sleiffer, et al, "A comparison berween SSMF and large-Aeff Pure-silica core fiber for ultra long-haul 100G transmission", Opt. Express.vol.19, Issue.26, pp.B710-B715(2011).
[6]X. Zhou, et al, "High spectral efficiency 400Gb/s transmission using PDM time-domain hybrid 32-64 QAM and traning-assisted carrier recovery", J. Lightwave Technol. vol.31, Issue.7, pp.999-1005(2013).
[7]Fong, et al, "Linewidth-insentive coherent AM optical links:design, performance, and potential applications", J. Lightwave Technol. vol.12, Issue.3, pp.526-534(1994).
[8]Sabido, et al, "Experimental linewidth-insentive coherent analog optical link", J. Lightwave Technol. vol.12, Issue.11, pp.1976-1985(1994).
[9]Roudas, et al, "Accurate model of the semiconductor laser nonuniform FM response for the study of coherent optical systems", IEEE Photon. Technol. Lett, vol.6, Issue.ll pp.1389-1391(1994).
[10]Roudas, et al, "Recursive simulation models of the semiconductor laser modulation characteristics for accurate performance evaluation of coherent optical CPFSK systems", J. Lightwave Technol. vol.13, Issue.11, pp.2258-2269(1995).
[11]Linke, et al, "High-capacity coherent lightwave systems", J. Lightwave Technol. vol.6, Issue.11, pp.1750-1769(1988).
[12]Norimatsu, et al."The influence of cross-phase modulation on optical FDM PSK homodyne transmission systems", J. Lightwave Technol. vol.11, Issue.5, pp.795-804(1993).
[13]Kazovsky, et al, "ASK multiport optical homodyne receivers", J. Lightwave Technol. vol.5, Issue.6,pp.770-791(1987).
[14]Kazovsky, et al, "Decision-driven phase-locked loop for optical homodyne receivers: performance analysis and laser linewidth requirements ", J. Lightwave Technol. vol.3, Issue.6, pp.1238-1247(1985).
[15]Kikuchi, "Proposal and performance analysis of novel optical homodyne receiver having an optical preamplifier for achieving the receiver sensitivity beyond shot-noise limit", IEEE Photon. Technol. Lett, vol.4, Issue.2 pp.195-197(1992).
[16]Krom, et al, "Impact of laser phase noise on the performance of a{3×3} phase and polarization diversity optical homodyne DPSK receiver", J. Lightwave Technol. vol.8, Issue.11, pp.1709-1715(1990).
[17]Okoshi, "Polarization-state control schemes for heterodyne or homodyne optical fiber communications", J. Lightwave Technol. vol.3, Issue.6, pp.1232-1237(1985).
[18]Cheng, et al, "Performance analysis and experiment of a homodyne receiver insensitive to both polarization and phase fluctuations", J. Lightwave Technol. vol.7, Issue.2, pp.368-374(1989).
[19]Hodgkinson, "Receiver analysis for synchronous coherent optical fiber transmission systems", J. Lightwave Technol. vol.5, Issue.4, pp.573-586(1987).
[20]Carena, et al, "Maximum reach versus transmission capacity for terabit superchannels based on 27.75-GBaud PM-QPSK, PM-8QAM, or PM-16QAM", IEEE Photon. Technol. Lett. vol.22, Issue.11, pp.829-831(2010).
[21]Charlet, et al, "Transmission of 16.4-bit/s capacity over 2550kn using PDM QPSK modulation format and coherent receiver", J. Lightwave Technol. vol.27, Issue.3, pp.153-157(2009).
[22]Lavery, et al, "Digital coherent receivers for long-reach optical access networks", J. Lightwave Technol. vol.31, Issue.4, pp.609-620(2013).
[23]Y. T. and W. Shieh, "Coherent optical OFDM transmission up to 1Tb/s per channel", J. Lightwave Technol. vol.27, Issue.16, pp.3511-3517(2009).
[24]J. Yu and X. Zhou, "Ultra-high-capacity DWDM transmission systems for 100G and beyond", IEEE Communications Magazine, vol.48, Issue.3, pp.556-564(2010).
[25]Akihide, et al, "No-guard-interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission", J. Lightwave Technol. vol.27, Issue.16, pp.3705-3713(2009).
[26]Akihide, et al, "Ultra-high capacity WDM transmission using spectrally-efficient PDM 16-QAM modulation and C-and extended L-band wideband optical amplification", J. Lightwave Technol. vol.29, Issue.4, pp.578-586(2011).
[27]Fatadin, et al, "Blind equalization and Ccarrier phase recovery in a 16-QAM optical coherent system", J. Lightwave Technol. vol.27, Issue.15, pp.3042-3049(2009).
[28]Yamanaka, et al, "11×171Gb/s PDM 16-QAM transmission over 1440km with a spectral efficiency of 6.4b/s/Hz using high-speed DAC", ECOC2011, paper.
[29]Koizumi, et al, "1024 QAM (60Gbit/s) single-carrier coherent optical transmission over 150km", Opt. Express, vol.20, Issue.11, pp.12508-12514(2012).
[30]Chandrasekhar, et al, "Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of SSMF", ECOC2009, paper.PD2.6.
[31]Charlet, et al,"Transmission of 81 channels at 40Gbit/s over a transpacific-distance erbium-only link, using PDM-BPSK modulation, coherent detection, and a new large effective area fiber", ECOC2008, paper.Th.3.E.3.
[32]Bosco, et al, "On the performance of Nyquist-WDM terabit superchannels based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM subcarriers", J. Lightwave Technol. vol.29, Issue.1, pp.53-61(2011).
[33]Wu K.-T., et al, "Comparison of high order modulation formats for 40Gb/s and 100Gb/s", IEEE/LEOS2009, paper.MC4.1.
[34]Bertolini, et al, "Monte Carlo estimation of PDM-QPSK/OOK and DQPSK/OOK hybrid systems tolerance against nonlinear effects", IEEE Photon. Technol. Lett. vol.21, Issue.1 pp.15-17(2009).
[35]D. V D. Borne, et al, "Polmux-QPSK modulation and coherent detection:the challenge of long-haul 100G transmission", ECOC2009, paper.3.4.1.
[36]S. J. Savory, "Digital coherent optical receivers:algorithms and subsystems", IEEE J. sel. Top. Quan. Electr, vol.16, Issue.5, pp.1164-1179(2010).
[37]Gavioli, et al, "Ultra-norrow-spacing 10-channel 1.12Tb/s D-WDM long-haul transmission over uncompensated SMF and NZDSF", IEEE Photon. Technol. Lett, vol.22, Issue.19, pp.1419-1421(2010).
[38]S. J. Savory, "Digital filters for coherent optical receivers", Opt. Express, vol.16, Issue.2, pp.804-817(2008).
[39]Ribeiro, et al, "Enhanced digital polarization demultiplexation via CMA step size adaptation for PM-QPSK coherent receivers", OFC2012, technical digest.
[40]Kikuchi, "Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers", Opt. Express, vol.19, Issue.10, pp.9868-9880(2011).
[41]Ezra, et al, "Coherent detection in optical fiber systems", Opt. Express, vol.16, Issue.2, pp.753-791(2008).
[42]S. J. Savory, "Digital coherent receivers for uncompensated 42.8Gbit/s transmission over high PMD fibre", ECOC2007
[43]Roudas, et al, "Optimal polarization demultiplexing for coherent optical communications systems", J. Lightwave Technol. vol.28, Issue.7, pp.1121-1134(2010).
[44]Mantzoukis, et al, "Performance comparison of electronic PMD equalizers for coherent PDM QPSK systems",J. Lightwave Technol. vol.29, Issue.11, pp.1721-1728(2011).
[45]Ezra. Ip, et al, "Compensation of dispersion and nonlinear impairments using digital backpropagation", J. Lightwave Technol. vol.26, Issue.20, pp.3416-3425(2008).
[46]J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. vol.15, Issue 23, pp.1351-1353 (1990).
[47]C. Xie, et.al, "Effect of cross-phase-modulation-induced polarization scattering on optical polarization mode dispersion compensation in wavelength-division-multiplexed systems", Opt. Lett, vol.28, Issue.23, pp.2303-2305(2003).
[48]M. Winter, et al,"Cross-polarization modulation in polarization-division multiplex transmission", IEEE Photon. Technol. Lett. vol.22, Issue.8, pp.742-744 (2010).
[49]C. Xie, "Interchannel nonlinearities in coherent polarization-division-multiplexed quafrature-phase-shift-keying systems", IEEE Photon. Technol. Lett. vol.21, Issue.5, pp.274-276 (2009).
[50]A. Bononi, P. Serena and N. Rossi,"Modeling of signal-noise inreactions in nonlinear fiber transmission with different modulation formats", ECOC2009, paper 10.4.6.
[51]A. Bononi, P.Serena, and N.Rossi,"Nonlinear sinal-noise interactions in dispersion-managed links with various modulation formats", Opt.Fiber Technol, vol.16, Issue.2, pp.73-85(2010).
[52]A. Bononi, P.Serena, N.Rossi, and D.Sperti,"Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?", ECOC2010,paper Th.10.E.1.
[53]X. Yi, Y. Li, J. Wu, K. Xu, and J. Lin, "Impact of nonlinear signal-noise interactions on symbol-aligned and -interleaved formats in dispersion managed coherent PM-QPSK systems," Opt. Express vol.20, Issue 15, pp.17183-17191 (2012).
[54]Sangin, "Optimal choice of compensation PMD vector in feedforward-type second-order PMD compensation", J. Lightwave Technol. vol.22, Issue.8, pp.1872-1876(2004).
[55]W. Shieh, "On the second-order approximation PMD", IEEE Photon. Technol. Lett. vol.12, Issue.3, pp.290-292 (2000).
[56]J. H. Lee, et al, "Statistical PMD emulator using variable DGD elements", IEEE Photon. Technol. Lett, vol.15, Issue.1, pp.54-56 (2003).
[57]P. Serena and A. Bononi, "Nonlinear phase noise mitigation by polarization mode dispersion in dispersion managed coherent PDM-QPSK systems", ECOC2009, paperP4.12.
[58]C. Xia, et al., "PMD-induced nonlinear penalty reduction in coherent polarization-multiplexed QPSK transmission", ECOC2010, paper.Th.10.E.5.
[59]X. Yi, J. Wu, Y. Li, W. Li, X. Hong, Y. Zuo, and J. Lin, "Nonlinear signal-noise interactions in dispersion managed coherent PM-QPSK systems in the presence of PMD", Opt. Express, vol.20, Issue.25, pp.27596-27602(2012).
[60]G. Bosco, et al, "Investigation on the robustness of a Nyquist-WDM terabit superchannel to transmitter and receiver non-idealities", ECOC2010, paperTu.3.A.4.
[61]G. Bosco et.al, "Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems", IEEE Photon. Technol. Lett. vol.22, Issue.15,pp.1129-1131 (2010).
[62]L. Zong, J. Veselka, H. Sardesai, and M. Frankel, "Influence of filter shape and bandwidth on 44Gb/s DQPSK systems", OFC2009, paper JWA17.
[63]X. Yi, Yan Li, Jian Wu, Wei Li, Xiaobin Hong, Yong Zuo, and Jintong Lin, "Impact of filter shape and bandwidth on terabit polarization-multiplexed quadrature phase-shift keying transmission with baud-rate spacing" Opt. Engineering,51(10),105505(2012).
[64]G. P. Agrawal, Nononlinear Fiber Optics,3rd ed, New York:Academic,2001
[65]I.-B. Djordjevic, et al, "PMD compensation in multilevel coded-transmission schemes with coherent detection using BLAST algorithm and iterative polarization cancellation", Opt. Express, vol.16, Issue.19, pp.14845-14852(2008).
[66]P. Frascella, et al, "PMD tolerance of 288 Gbit/s coherent WDM and transmission over unrepeatered 124km of field-installed single mode optical fiber", Opt. Express, vol.18, Issue. 13,13908-13914(2010).
[67]J. Renaudier,m et al, "Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK bhy digital precessing in a coherent receiver", J. Lightwave Technol. vol.26, Issue.1, pp.36-42(2008).
[68]K. Nosu, "Advanced cohernt lightwave technonlogies", IEEE Communications Magazine, vol.26, Issue.2, pp.15-21(1988).
[69]R. A. Linke and A. H. Gnauck, "High-capacity coherent lightwave systems", J. Lightwave Technol. vol.6, Issue.11, pp.1750-1769(1988).
[70]S. Ryu, et al, "Polarization diversity techniques for the use of coherent optical fiber submarine cable systems", J. Lightwave Technol. vol.9, Issue.5, pp.675-682(1991).
[71]A. J. Viterbi and A. M. Viterbi, "Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission", IEEE Transactions on Information Theory, vol. IT-29, Issue.4, pp.543-551(1983).
[72]K.Kikuchi, "Coherent optical communication systems" Chapter 3 in Optical fiber Telecommunications V A (edited by I. P. Kaminow, T. Li and A. E. Willner, Academic Press, (2008).
[73]T. Pfau, et al, "First real-time data recovery for synchronous QPSK transmission with standard DFB lsers", IEEE Photon. Technol. Lett. vol.18, pp.1907-1909(2006).
[74]A. Leven, et al, "Coherernt receiver for practical optical communiction systems", OFC2007, paper.OthK4.
[75]S. J. Svory, et al,"Transmission of 42.8Gbit/s polariztion multiplexed NRZ-QPSK over 6400km of standard fiber with no optical dispersion compensation", OFC2007, paper. OTuA1.
[76]K. Sekine, et al, "40Gbit/s,16-ary (4bit/symbol) optical modulation/demodulation scheme", Electron. Lett, vol.41, pp.430-432(2005).
[77]J. Hongo, et al, "1-Gsymbol/s 64-QAM cohernt optical transmission over 150km", IEEE Photon. Technol. Lett. vol.19, pp.638-640(2007).
[78]T. Omiya, et al, "400Gbit/s 256QAM-OFDM transmission over 720km with a 14bit/s/Hz spectral efficiency by using high-resolution FDE", Opt. Express, vol.21, Issue.3, pp.2632-2641(2013).
[79]O. Bertran-Pardo, et al, "Nonlinearity limitations when mixing 40-Gb/s coherent PDM-QPSK channels with preexisting 10-Gb/s NRZ channels", IEEE Photon. Technol. Lett. vol.20, Issue.15, pp.1314-1316(2008).
[80]C. Xie, "Inter-channel nonlinearities in hybrid OOK and coherent PDM-QPSK transmission systems with dispersion management", IEEE Photonics Society Summer Topical Meeting Series, paper.TuA3.2 (2010).
[81]J. Renaudier, et al, "Investigation on WDM nonlinear impairments arising from the insertion of 100-Gb/s coherent PDM-QPSK over legacy optical networks", IEEE Photon. Technol. Lett. vol.21, Issue.24, pp.1816-1818(2009).
[82]M. Bertolini, et al, "On the XPM-induced distortion in DQPSK-OOK and coherent QPSK-OOK hybrid systems", OFC2009, paper.OTuD4.
[83]C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation", Opt. Express, vol.17, Issue.6, pp.4815-4823(2009).
[84]P. Poggiolini, et al, "Performance dependence on channel baud-rate of PM-QPSK systems over uncompensated links", IEEE Photon. Technol. Lett. vol.23, Issue.1, pp.15-17(2011).
[85]P. Serena, N. Rossi, O. B. Pardo, J. Renaudier, A. Vannucci, and A. Bononi, "Intra- versus inter-channel PMD in linearly compensated coherent PDM-PSK nonlinear transmission," J. Lightwave Technol. vol.29, Issue.11, pp.1691-1700 (2011).
[1]S. Vorbeck and M. Schneiders, "Cumulative nonlinear phase shift as engineering rule for performance estimation in 160-Gb/s transmission systems", IEEE Photon. Technol. Lett. vol.16, Issue. 11,pp.2571-2573 (2004).
[2]J.-C. Antona, S. Bigo, and J.-P. Faure, "Nonlinear cumulated phase as a criterion to assess performance of terrestrial WDM systems", OFC2002, pp.365-367.
[3]P. Poggiolini, et.al, "Analytical modeling of nonlinear propagation in uncompensated optical transmission links", IEEE Photon. Technol. Lett. vol.23, Issue.11, pp.742-744 (2011).
[4]G. Bosco, et.al, "Performance prediction for WDM PM-QPSK transmission over uncompensated link", OFC2011, paper. OThO7.
[5]E. Grellier and A. Bononi, "Quality parameter for coherent transmission with Gaussian-distributed nonlinear noise", Opt. Express, vol.19, Issue.13, pp.12781-12788(2011).
[6]Z. Avi, etal, "Vector analysis of simulated Brillouin scattering amplification in standard single-mode fibers", Opt. Express, vol.16, Issue.26, pp.21692-21707(2008).
[7]K. Shiraki, et.al, "SBS threshold of a fiber with a Brillouin frequency shift distribution", J. Lightwave Technol. vol.17, Issue.1, pp.50-57 (1996).
[8]P. Ebrahimi, et.al, "Effect of SBS and Rayleigh scattering in densedly-spaced bidirectional transmission using Raman amplification", CLEO2002 vol.1 pp.465-467.
[9]C. Xie, et.al, "Effect of cross-phase-modulation-induced polarization scattering on optical polarization mode dispersion compensation in wavelength-division-multiplexed systems", Opt. Lett, vol.28, Issue.23, pp.2303-2305(2003).
[10]M. Winter, et.al, "Cross-polarization modulation in polarization-division multiplex transmission", IEEE Photon. Technol. Lett.vol.22, Issue.8, pp.742-744 (2010).
[11]L. F. Mollenauer, J. P. Gordon, and F. Heismann, "Polarization scattering by soliton-soliton collisions", Opt. Lett., vol.20, Issue.20, pp.2060-2062 (1995).
[12]A. Mecozzi and F. Matera, "Polarization scattering by intra-channel collisions", Opt. Express, vol.20, Issue.2, pp.1213-1218(2012).
[13]X. Yi, J. Wu, Yan. Li, Wei, Li, and J. Lin, "SPM-induced nonlinear polarization scattering in single-channel coherent PM-QPSK systems over dispersion managed link", submitted to IEEE Photon. Technol. Lett.
[14]Haiqing Wei, et al, "Intra-channel nonlinearity compensation with scaled translational symmetry", Opt. Express, vol.12, Issue.18, pp.4282-4296(2004).
[15]M. J. Ablowitz and T. Hirooka, "Resonant nonlinear intrachannel interactions in strongly dispersion-mamaged transmission systems", Opt. Lett, vol.25, Issue.24, pp.1750-1752(2000).
[16]A. Mecozzi, et al, "Intra-channel nonlinearity in differentially phase-modulated transmission", Opt. Express, vol.19, Issue.5, pp.3990-3995(2011).
[17]A. Mecozzi and F. Matera, "Polarization scattering by intra-channel collisions," Opt. Express, vol.20, Issue.2, pp.1213-1218 (2012).
[18]P. Johannisson, "Interaction range and generation rate of nonlinear intrachannel signal distortion", JOSA B, vol.24, Issue.4, pp.729-738(2007).
[19]P. V. Mamyshev and N. A. Mamysheva, "Pulse-overlapped dispersion-managed data transmission and intrachannel four-wave mixing", Opt. Lett, vol.24, Issue.21, pp.1454-1456(1999).
[20]Xiaogang Yi, et al, "SPM-induced nonlinear polarization scattering in single-channel coherent PM-QPSK systems over dispersion managed link", submitted to Optics Letters
[21]G. P. Agrawal, Nononlinear Fiber Optics,3rd ed, New York:Academic,2001
[22]L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of pisecond pulse narrowing and solitons in optical fibers", Phys. Rev. Lett. vol.45, Issue.13, pp.1095-1098(1980).
[23]J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. vol.15, Issue 23, pp.1351-1353 (1990).
[24]S. Ryu, "Signal linewidth broadening due to nonlinear Kerr effect in long-haul coherent systems using cascaded optical amplifiers", J. Lightwave Technol. vol.10, Issue.10, pp.1450-1457 (1992).
[25]M. Zitelli, F. Matera, and M. Settembre, "Single-channel transmission in dispersion management links in conditions of very strong broadening:application to 40Gb/s signals on step-index fibers" J. Lightwave Technol. vol.17, Issue.12, pp.2498-2505 (1999).
[26]X. Xiao, S. Gao, Y. Tian, and C. Yang, "Analytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems," J. Lightwave Technol. vol.24, Issue.5, pp.2038-2044(2006).
[27]F. Zhang, et.al, "Optimum dispersion mapping of single-channel 40Gbit/s return-to-zero differential phase-shift keying transmission systems", Opt. Express, vol.14, Issue.15, pp.6613-6618(2006).
[28]M. Karlsson, and H. Sunnerud, "Effect of nonlinearities on PMD-induced system impairments", J. Lightwave Technol. vol.24, Issue.11, pp.4127-4137(2006).
[29]C. Xie, "Suppression of inter-channel nonlinearities in WDM coherent PDM-QPSK systems using periodic-group-delay dispersion compensators", ECOC2009, paper.P4.08.
[30]M.-N. Chughtai, et.al, "Influence of polarization state, baud rate and PMD on nonlinear impairments in WDM systems with mixed PM(D)QPSK and OOK channels", Opt. Express, vol.20, Issue.7, pp.8155-8160(2012).
[31]C. Xia, et.al, "PMD-induced nonlinear pemalty reduction in coherent polarization-multiplexed QPSK transmission", ECOC2010, paper.Th.10.E.5.
[32]C. Xie, "Nonlinear polarization effects and mitigation in polarization-division-multiplexed coherent transmission systems," Chin. Opt. Lett.vol.8, Issue.9, pp.844-851 (2010).
[33]P. Serena, N. Rossi, and A. Bononi, "PDM-iRZ-QPSK vs. PS-QPSK at 100Gbit/s over dispersion-managed links", Opt. Express, vol.20, Issue.7, pp.7895-7900(2012).
[34]C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation", Opt. Express, vol.17, Issue.6, pp.4815-4823(2009).
[1]J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. vol.15, Issue 23, pp.1351-1353 (1990).
[2]X. Li, F. Zhang, Z. Chen, and A. Xu, "Supperssion of XPM and XPM-induced nonlinear phase noise for RZ-DPSK signals in 40Gbit/s WDM transmission systems with optimum dispersion mapping", Opt. Express, vol.15, Issue.26,pp.18247-18285(2007).
[3]O. Vassilieva, et.al., "Symbol rate dependency of XPM-induced phase noise penalty on QPSK-based modulation formats", ECOC2008, paper. We. 1.E.4.
[4]A. G. Green, P. P. Mitra, and L. G. L. Wegener, "Effect of chromatic dispersion on nonlinear phase noise", Opt. Lett, vol.28, pp.2455-2457(2003).
[5]K.-P, Ho, "Error probability of DPSK signals with cross-phase molation induced nonlinear phase noise", IEEE J Sel Top Quant, vol.10, Issue.2, pp.421-427(2004).
[6]K.-P. Ho, "Probability density of nonlinear phase noise," J. Opt. Am. B, vol.20, Issue.9, 1875-1879(2003).
[7]P. Serena, A. Orlandini, and A. Bononi, "Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightwave Technol. vol.24, Issue.5, pp.2026-2037 (2006).
[8]A. P. T. Lau and J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightwave Technol.vol.25, pp.3008-3016 (2007).
[9]H. Kim, "Nonlinear phase noise in phase-coded transmission," OFC2005, paper OThO3.
[10]H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. vol.15, pp.320-322 (2003).
[11]A. Bononi, P. Serena and N. Rossi,"Modeling of signal-noise inreactions in nonlinear fiber transmission with different modulation formats", ECOC2009, paper 10.4.6
[12]A.Bononi, P.Serena, and N.Rossi,"Nonlinear sinal-noise interactions in dispersion-managed links with various modulation formats", Opt.Fiber Technol, vol.16, Issue.2, pp.73-85(2010).
[13]A.Bononi, P.Serena, N.Rossi, and D.Sperti,"Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?", ECOC2010,paper Th.10.E.1.
[14]M. Winter, et.al, "A statistics treatment of cross-phase polarization modulation in DWDM systems", J. Lightwave Technol. vol.27, Issue.17, pp.3739-3751(2009).
[15]Optical Amplifiers User's Manual, Chapter 2 in VPIcomponentMaker8.6.
[16]C. Xie, "Nonlinear polarization effects and mitigation in polarization-division-multiplexed coherent transmission systems," Chin. Opt. Lett.vol.8,Issue.9, pp.844-851 (2010).
[17]X. Xiao, S. Gao, Y. Tian, and C. Yang, "Analytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems," J. Lightwave Technol. vol.24, pp.2038 (2006).
[18]C. Xie, "Dispersion management in WDM coherent PDM-QPSK systems", ECOC2009, paper.9.4.3
[19]X. Li, F. Zhang, Z. Chen, and A. Xu, "Suppression of XPM and XPM-induced nonlinear phase noise for RZ-DPSK in 40Gbit/s WDM transmission systems with optimum dispersion maping", Opt. Express, vol.15, Issue.26, pp.18247-18252(2007).
[20]M. Zitelli, F. Matera, and M. Settembre, "Single-channel transmission in dispersion management links in conditions of very strong broadening:application to 40Gb/s signals on step-index fibers" J. Lightwave Technol. vol.17, Issue.12, pp.2498-2505 (1999).
[21]X. Yi, Y. Li, J. Wu, K. Xu, and J. Lin, "Impact of nonlinear signal-noise interactions on symbol-aligned and -interleaved formats in dispersion managed coherent PM-QPSK systems," Opt. Express vol.20, Issue 15, pp.17183-17191 (2012).
[22]P. Serena and A. Bononi, "Nonlinear phase noise mitigation by polarization mode dispersion in dispersion managed coherent PDM-QPSK systems", ECOC2009, paperP4.12.
[23]G. P. Agrawal, Nononlinear Fiber Optics,3rd ed, New York:Academic,2001.
[1]Biondini. G, W. L. Kath, "Non-Maxwellian DGD distribution of PMD emulators", OFC (2001), paperThA5.
[2]A. Bononi, A. Vannuccifi, "Statistics of the Jones matrix of fibers affected by polarization mode dispersion", Opt. Lett, vol.26, Issue10, pp.675-677(2001).
[3]Adamczyk, et al., "Statistics of PMD-induced power fading for double sideband and single sideband subcarriermultiplexing signals", OFC (2001), paperM05.
[4]A. J. Barlow, J. J. R-H, and D. N. Payne, "Birefringence and polarization mode dispersion in spun single-mode fibers", Appl. Opt. vol.20, pp.2962-2968(1981).
[5]D. Beltrame, et al., "Statistics behavior of the Q-factor in optical transmission systems due to the polarization mode dispersion", ECOC (2000).
[6]M. Rochette, C. Baker, and R. Ahmad, "All-optical polarization-mode dispersion monitor for return-to-zero optical signals at 40Gbit/s and beyond", Opt. Lett. Vol.35, pp.3703-3705(2010).
[7]X. Steve, X. Chen, T. J. Xia, G. Wellbrock, D. Chen. D. Peterson, P. Zhang, A. Belisle, L. Dong, and T. Yu, "In-service light path PMD (polarization mode dispersion) monitoring by PMD compensation", Opt. Express, vol.18, Issue26, pp.27306-27318(2010).
[8]L. Xu, S. X. Wang, H. Miao, and A. M. Weiner, "Polarization mode dispersion spectrum measurement via high-speed wavelength-parallel polarimeter", Appl. Opt. vol.48, pp.4688-4697(2009).
[9]K. H. Han and W. J. Lee, "First-order polarization mode dispersion compensator using two independent feedback signals enabling separation of principal states of polarization and differential group delay controls", Opt. Express, vol.20, Issue4, pp.3541-3549(2012).
[10]Y. Zheng, B.-J. Yang, and X.-G. Zhang, "Three-stage polarization mode dispersion compensator capable of compensating second-order polarization mode dispersion", IEEE Photon. Technol. Lett., vol.14, Issue10, pp.1412-1414(2002).
[11]H. Miao and C. Yang, "Scheme for Feed-Forward Polarization Mode Dispersion Compensation," Appl. Opt. vol.43, pp.1577-1582 (2004).
[12]L. Yan, Yao. X. S, Hauer. M.C, and A. E. Willner, "Practical solutions to polarization-mode-dispersion emulation and compensation", Journal of Lightwave Technology. vol.24, Issue 11,pp.3992-4005(2006).
[13]T. Do, H. Dong, and P. Shum, "Measurement of the complex polarization mode dispersion vector using Jones matrix analysis," Appl. Opt. vol.46, pp.916-921 (2007).
[14]J. Kim, H. Yoon, N. Park, and B. Lee, "Polarization-Mode-Dispersion Compensator Using a Polarization Beam Splitter and Quarter-Wave Plates," Appl. Opt. vol.40, pp.4473-4475 (2001).
[15]S. J. Savory, "Digital filters for coherent optical receivers", Opt. Express, vol.16, Issue2, pp.804-817(2008).
[16]S. J. Savory, "Digital coherent optical receivers:algorithms and subsystems", IEEE J Sel Top Quant, vol.16, Issue.5, pp.1164-1179(2010).
[17]N. Mantzoukis, et al., "Performance comparison of electronics PMD equalizers for coherent PDM QPSK systems", Journal of Lightwave Technology, vol.29, Issue 11(2011).
[18]P. Serena and A. Bononi, "Nonlinear phase noise mitigation by polarization mode dispersion in dispersion managed coherent PDM-QPSK systems", ECOC2009, paperP4.12.
[19]C. Xia, et al., "PMD-induced nonlinear penalty reduction in coherent polarization-multiplexed QPSK transmission", ECOC2010,paper.Th.10.E.5.
[20]X. Yi, J. Wu, Y. Li, W. Li, X. Hong, Y. Zuo, and J. Lin, "Nonlinear signal-noise interactions in dispersion managed coherent PM-QPSK systems in the presence of PMD", Opt. Express, vol.20, Issue.25, pp.27596-27602(2012).
[21]H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. vol.15, pp.320-322 (2003).
[22]A. Bononi, P. Serena, and N. Rossi, "Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats, " Opt. Fiber Technol.vol.16,Issue 2, pp.73-85 (2010).
[23]J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. vol.15, Issue 23, pp.1351-1353 (1990).
[24]X. Yi, Y. Li, J. Wu, K. Xu, and J. Lin, "Impact of nonlinear signal-noise interactions on symbol-aligned and -interleaved formats in dispersion managed coherent PM-QPSK systems," Opt. Express vol.20, Issue 15, pp.17183-17191 (2012).
[25]A. Bononi, P. Serena, N. Rossi, and D. Sperti, "Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?", ECOC2010, paper Th.10.E.1.
[26]A. Mecozzi and F. Matera, "Intrachannel nonlinearity enhancement in polarization multiplexed phase modulated systems with differential detection", Opt. Lett. vol.36, Issue 19,pp.3903-3905(2011).
[27]F. Curti. B. Daino, G. D. Marchis, and F. Matera, "Statistical treatment of the evolution of the principal states of polarization in single-mode fibers," J. Lightwave Technol. vol.8, Issue 8, pp.1162-1165 (1990).
[28]C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation," Opt. Express, vol.17, Issue.6, pp.4815-4823 (2009).
[29]H. Kim, "Nonlinear phase noise in phase-coded transmission," OFC2005, paper OThO3.
[30]P. Serena, N. Rossi, O. B. Pardo, J. Renaudier, A. Vannucci, and A. Bononi, "Intra- versus inter-channel PMD in linearly compensated coherent PDM-PSK nonlinear transmission," J. Lightwave Technol. vol.29, Issue.11, pp.1691-1700 (2011).
[31]C. Xie, "Dispersion management in WDM coherent PDM-QPSK systems", ECOC2009, paper.9.4.3.
[1]A. Hodzic, et.al, "Optimized filtering for 40-Gb/s/ch-based DWDM transmission systems over standard single-mode fiber', IEEE Photon. Technol. Lett. vol.15, Issue7, pp.1002-1004 (2003).
[2]C. J. Anderson and J. A. Lyle,"Technique for evaluation system performance using Q in numerical simulations exhibiting intersymbol interference", Electron. Lett., vol.30, Issue.1, pp.71-72(1994).
[3]G. Bosco, et.al, "On the use of NRZ, RZ, and CSRZ modulation at 40Gb/s with narrow DWDM channel spacing", J. Lightwave Technol. vol.20, Issue.9, pp.1694-1704(2002).
[4]P. J. Winzer and R.-J. Essiambre, "Advanced optical modulation formats", Proceddings of the IEEE, vol.94, Issue.5, pp.952-985(2006).
[5]L. Zong, J. Veselka, H. Sardesai, and M. Frankel, "Influence of filter shape and bandwidth on 44Gb/s DQPSK systems", OFC2009, paper JWA17.
[6]G. Bosco etal, "Investigation on the robustness of a Nyquist-WDM terabit superchannel to transmitter and receiver non-idealities", ECOC2010, paperTu.3.A.4.
[7]G. Bosco et.al, "On the performance of Nyquist-WDM terabit superchannels based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM subcarriers", J. Lightwave Technol. vol.29, Issue.1, pp.53-61(2011).
[8]G. Bosco et.al, "Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems", IEEE Photon. Technol. Lett. vol.22, Issue.15, pp.1129-1131 (2010).
[9]P. Poggiolini et al. "Analytical modeling of nonlinear propagation in uncompensated optical transmission links", IEEE Photon. Technol. Lett. vol.23, Issue.ll, pp.742-744 (2011).
[10]M. Nolle et al,"Transmission of 562Gbit/s DWDM coherent OFDM with a spectral efficiency of 7.2Bit/s/Hz using joint 64-QAM and 16-QAM modulation", OFC2010, paper.OMR4.
[11]O. Gaete, et al,"A digital subcarrier multiplexing technique for increased spectral efficiency in optical systems uding direct detection", OFC2010, paperOThM5.
[12]J.-X. Cai, "100G transmission over transoceanic distance with high spectral efficiency and large capacity", J. Lightwave Technol. vol.30, Issue.24, pp.3845-3856(2012).
[13]P. J. Winzer, "High-spectral-efficiency optical modulation formats", J. Lightwave Technol. vol.30, Issue.24, pp.3824-3835(2012).
[14]H. Takhashi, "Coherent OFDM transmission with high spectral efficiency", ECOC2009, paper.1.3.3.
[15]M. Pfennigbauer and P. J. Winzer, "Choice of MUX/DEMUX filter characteristics for NRZ, RZ, and CSRZ DWDM systems", J. Lightwave Technol. vol.24, Issue.4, pp.1689-1696(2006).
[16]P. Poggiolini, et al, "Performance dependence on channel baud-rate of PM-QPSK systems over uncompensated links", IEEE Photon. Technol. Lett. vol.23, Issue.1, pp.15-17(2011
[17]X. Yi, Yan Li, Jian Wu, Wei Li, Xiaobin Hong, Yong Zuo, and Jintong Lin, "Impact of filter shape and bandwidth on terabit polarization-multiplexed quadrature phase-shift keying transmission with baud-rate spacing" Opt. Engineering,51(10),105505(2012).
[1]G. Goldfard and G. Li, "BER estimation of QPSK ohomodyne detection with carrier phase estimation using digital signal processing", Opt. Express, vol.14, Issue.18, pp.8043-8053(2006).
[2]F. Zhang, et al, "Stochastic BER estimation for coherent QPSK transmission systems with digital carrier phase recovery", Opt. Express, vol.18, Issue.9, pp.9592-9599(2010).
[3]F. Zhang, et al, "Experimental comparison of different BER estimation methods for coherent optical QPSK transmission systems", IEEE Photon. Technol. Lett., vol.23, Issue18, pp.1343-1345(2011).
[4]E. Ciarameiia, et al, "BER estimation for performance monitoring in high-speed digital optical signals", J. Lightwave Technol. vol.30, Issue.13, pp.2117-2124 (2012).
[5]P. Serena, et al, "A stratified sampling Monte Carlo algorithm for efficient BER measurement and its application to DQPSK terrestrial systems", ECOC2008, paper.We.1.E.2
[6]廖延彪《偏振光学》北京：科学出版社2003.
[2]J. D. Downie, et al, "Ultra-long-haul 112Gb/s PM-QPSK transmission systems using longer spans and Raman amlification", Opt. Express, vol.20, Issue.9, pp.10353-10358(2012).
[3]D. Chang, et al, "Real-time processed 34×120Gb/s transmission over 432.8km unrepeatered link with legacy fiber and span loss of 74.4dB", ECOC2011, paper.P4.02.
[4]Q. Yang et al, "Experimental demonstration and numerical simulation of 107Gb/s high spectral efficiency cohernt optical OFDM", J. Lightwave Technol. vol.27, Issue.3, pp.168-176 (2009).
[5]V. A. J. M. Sleiffer, et al, "A comparison berween SSMF and large-Aeff Pure-silica core fiber for ultra long-haul 100G transmission", Opt. Express.vol.19, Issue.26, pp.B710-B715(2011).
[6]X. Zhou, et al, "High spectral efficiency 400Gb/s transmission using PDM time-domain hybrid 32-64 QAM and traning-assisted carrier recovery", J. Lightwave Technol. vol.31, Issue.7, pp.999-1005(2013).
[7]Fong, et al, "Linewidth-insentive coherent AM optical links:design, performance, and potential applications", J. Lightwave Technol. vol.12, Issue.3, pp.526-534(1994).
[8]Sabido, et al, "Experimental linewidth-insentive coherent analog optical link", J. Lightwave Technol. vol.12, Issue.11, pp.1976-1985(1994).
[9]Roudas, et al, "Accurate model of the semiconductor laser nonuniform FM response for the study of coherent optical systems", IEEE Photon. Technol. Lett, vol.6, Issue.ll pp.1389-1391(1994).
[10]Roudas, et al, "Recursive simulation models of the semiconductor laser modulation characteristics for accurate performance evaluation of coherent optical CPFSK systems", J. Lightwave Technol. vol.13, Issue.11, pp.2258-2269(1995).
[11]Linke, et al, "High-capacity coherent lightwave systems", J. Lightwave Technol. vol.6, Issue.11, pp.1750-1769(1988).
[12]Norimatsu, et al."The influence of cross-phase modulation on optical FDM PSK homodyne transmission systems", J. Lightwave Technol. vol.11, Issue.5, pp.795-804(1993).
[13]Kazovsky, et al, "ASK multiport optical homodyne receivers", J. Lightwave Technol. vol.5, Issue.6,pp.770-791(1987).
[14]Kazovsky, et al, "Decision-driven phase-locked loop for optical homodyne receivers: performance analysis and laser linewidth requirements ", J. Lightwave Technol. vol.3, Issue.6, pp.1238-1247(1985).
[15]Kikuchi, "Proposal and performance analysis of novel optical homodyne receiver having an optical preamplifier for achieving the receiver sensitivity beyond shot-noise limit", IEEE Photon. Technol. Lett, vol.4, Issue.2 pp.195-197(1992).
[16]Krom, et al, "Impact of laser phase noise on the performance of a{3×3} phase and polarization diversity optical homodyne DPSK receiver", J. Lightwave Technol. vol.8, Issue.11, pp.1709-1715(1990).
[17]Okoshi, "Polarization-state control schemes for heterodyne or homodyne optical fiber communications", J. Lightwave Technol. vol.3, Issue.6, pp.1232-1237(1985).
[18]Cheng, et al, "Performance analysis and experiment of a homodyne receiver insensitive to both polarization and phase fluctuations", J. Lightwave Technol. vol.7, Issue.2, pp.368-374(1989).
[19]Hodgkinson, "Receiver analysis for synchronous coherent optical fiber transmission systems", J. Lightwave Technol. vol.5, Issue.4, pp.573-586(1987).
[20]Carena, et al, "Maximum reach versus transmission capacity for terabit superchannels based on 27.75-GBaud PM-QPSK, PM-8QAM, or PM-16QAM", IEEE Photon. Technol. Lett. vol.22, Issue.11, pp.829-831(2010).
[21]Charlet, et al, "Transmission of 16.4-bit/s capacity over 2550kn using PDM QPSK modulation format and coherent receiver", J. Lightwave Technol. vol.27, Issue.3, pp.153-157(2009).
[22]Lavery, et al, "Digital coherent receivers for long-reach optical access networks", J. Lightwave Technol. vol.31, Issue.4, pp.609-620(2013).
[23]Y. T. and W. Shieh, "Coherent optical OFDM transmission up to 1Tb/s per channel", J. Lightwave Technol. vol.27, Issue.16, pp.3511-3517(2009).
[24]J. Yu and X. Zhou, "Ultra-high-capacity DWDM transmission systems for 100G and beyond", IEEE Communications Magazine, vol.48, Issue.3, pp.556-564(2010).
[25]Akihide, et al, "No-guard-interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission", J. Lightwave Technol. vol.27, Issue.16, pp.3705-3713(2009).
[26]Akihide, et al, "Ultra-high capacity WDM transmission using spectrally-efficient PDM 16-QAM modulation and C-and extended L-band wideband optical amplification", J. Lightwave Technol. vol.29, Issue.4, pp.578-586(2011).
[27]Fatadin, et al, "Blind equalization and Ccarrier phase recovery in a 16-QAM optical coherent system", J. Lightwave Technol. vol.27, Issue.15, pp.3042-3049(2009).
[28]Yamanaka, et al, "11×171Gb/s PDM 16-QAM transmission over 1440km with a spectral efficiency of 6.4b/s/Hz using high-speed DAC", ECOC2011, paper.
[29]Koizumi, et al, "1024 QAM (60Gbit/s) single-carrier coherent optical transmission over 150km", Opt. Express, vol.20, Issue.11, pp.12508-12514(2012).
[30]Chandrasekhar, et al, "Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of SSMF", ECOC2009, paper.PD2.6.
[31]Charlet, et al,"Transmission of 81 channels at 40Gbit/s over a transpacific-distance erbium-only link, using PDM-BPSK modulation, coherent detection, and a new large effective area fiber", ECOC2008, paper.Th.3.E.3.
[32]Bosco, et al, "On the performance of Nyquist-WDM terabit superchannels based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM subcarriers", J. Lightwave Technol. vol.29, Issue.1, pp.53-61(2011).
[33]Wu K.-T., et al, "Comparison of high order modulation formats for 40Gb/s and 100Gb/s", IEEE/LEOS2009, paper.MC4.1.
[34]Bertolini, et al, "Monte Carlo estimation of PDM-QPSK/OOK and DQPSK/OOK hybrid systems tolerance against nonlinear effects", IEEE Photon. Technol. Lett. vol.21, Issue.1 pp.15-17(2009).
[35]D. V D. Borne, et al, "Polmux-QPSK modulation and coherent detection:the challenge of long-haul 100G transmission", ECOC2009, paper.3.4.1.
[36]S. J. Savory, "Digital coherent optical receivers:algorithms and subsystems", IEEE J. sel. Top. Quan. Electr, vol.16, Issue.5, pp.1164-1179(2010).
[37]Gavioli, et al, "Ultra-norrow-spacing 10-channel 1.12Tb/s D-WDM long-haul transmission over uncompensated SMF and NZDSF", IEEE Photon. Technol. Lett, vol.22, Issue.19, pp.1419-1421(2010).
[38]S. J. Savory, "Digital filters for coherent optical receivers", Opt. Express, vol.16, Issue.2, pp.804-817(2008).
[39]Ribeiro, et al, "Enhanced digital polarization demultiplexation via CMA step size adaptation for PM-QPSK coherent receivers", OFC2012, technical digest.
[40]Kikuchi, "Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers", Opt. Express, vol.19, Issue.10, pp.9868-9880(2011).
[41]Ezra, et al, "Coherent detection in optical fiber systems", Opt. Express, vol.16, Issue.2, pp.753-791(2008).
[42]S. J. Savory, "Digital coherent receivers for uncompensated 42.8Gbit/s transmission over high PMD fibre", ECOC2007
[43]Roudas, et al, "Optimal polarization demultiplexing for coherent optical communications systems", J. Lightwave Technol. vol.28, Issue.7, pp.1121-1134(2010).
[44]Mantzoukis, et al, "Performance comparison of electronic PMD equalizers for coherent PDM QPSK systems",J. Lightwave Technol. vol.29, Issue.11, pp.1721-1728(2011).
[45]Ezra. Ip, et al, "Compensation of dispersion and nonlinear impairments using digital backpropagation", J. Lightwave Technol. vol.26, Issue.20, pp.3416-3425(2008).
[46]J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. vol.15, Issue 23, pp.1351-1353 (1990).
[47]C. Xie, et.al, "Effect of cross-phase-modulation-induced polarization scattering on optical polarization mode dispersion compensation in wavelength-division-multiplexed systems", Opt. Lett, vol.28, Issue.23, pp.2303-2305(2003).
[48]M. Winter, et al,"Cross-polarization modulation in polarization-division multiplex transmission", IEEE Photon. Technol. Lett. vol.22, Issue.8, pp.742-744 (2010).
[49]C. Xie, "Interchannel nonlinearities in coherent polarization-division-multiplexed quafrature-phase-shift-keying systems", IEEE Photon. Technol. Lett. vol.21, Issue.5, pp.274-276 (2009).
[50]A. Bononi, P. Serena and N. Rossi,"Modeling of signal-noise inreactions in nonlinear fiber transmission with different modulation formats", ECOC2009, paper 10.4.6.
[51]A. Bononi, P.Serena, and N.Rossi,"Nonlinear sinal-noise interactions in dispersion-managed links with various modulation formats", Opt.Fiber Technol, vol.16, Issue.2, pp.73-85(2010).
[52]A. Bononi, P.Serena, N.Rossi, and D.Sperti,"Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?", ECOC2010,paper Th.10.E.1.
[53]X. Yi, Y. Li, J. Wu, K. Xu, and J. Lin, "Impact of nonlinear signal-noise interactions on symbol-aligned and -interleaved formats in dispersion managed coherent PM-QPSK systems," Opt. Express vol.20, Issue 15, pp.17183-17191 (2012).
[54]Sangin, "Optimal choice of compensation PMD vector in feedforward-type second-order PMD compensation", J. Lightwave Technol. vol.22, Issue.8, pp.1872-1876(2004).
[55]W. Shieh, "On the second-order approximation PMD", IEEE Photon. Technol. Lett. vol.12, Issue.3, pp.290-292 (2000).
[56]J. H. Lee, et al, "Statistical PMD emulator using variable DGD elements", IEEE Photon. Technol. Lett, vol.15, Issue.1, pp.54-56 (2003).
[57]P. Serena and A. Bononi, "Nonlinear phase noise mitigation by polarization mode dispersion in dispersion managed coherent PDM-QPSK systems", ECOC2009, paperP4.12.
[58]C. Xia, et al., "PMD-induced nonlinear penalty reduction in coherent polarization-multiplexed QPSK transmission", ECOC2010, paper.Th.10.E.5.
[59]X. Yi, J. Wu, Y. Li, W. Li, X. Hong, Y. Zuo, and J. Lin, "Nonlinear signal-noise interactions in dispersion managed coherent PM-QPSK systems in the presence of PMD", Opt. Express, vol.20, Issue.25, pp.27596-27602(2012).
[60]G. Bosco, et al, "Investigation on the robustness of a Nyquist-WDM terabit superchannel to transmitter and receiver non-idealities", ECOC2010, paperTu.3.A.4.
[61]G. Bosco et.al, "Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems", IEEE Photon. Technol. Lett. vol.22, Issue.15,pp.1129-1131 (2010).
[62]L. Zong, J. Veselka, H. Sardesai, and M. Frankel, "Influence of filter shape and bandwidth on 44Gb/s DQPSK systems", OFC2009, paper JWA17.
[63]X. Yi, Yan Li, Jian Wu, Wei Li, Xiaobin Hong, Yong Zuo, and Jintong Lin, "Impact of filter shape and bandwidth on terabit polarization-multiplexed quadrature phase-shift keying transmission with baud-rate spacing" Opt. Engineering,51(10),105505(2012).
[64]G. P. Agrawal, Nononlinear Fiber Optics,3rd ed, New York:Academic,2001
[65]I.-B. Djordjevic, et al, "PMD compensation in multilevel coded-transmission schemes with coherent detection using BLAST algorithm and iterative polarization cancellation", Opt. Express, vol.16, Issue.19, pp.14845-14852(2008).
[66]P. Frascella, et al, "PMD tolerance of 288 Gbit/s coherent WDM and transmission over unrepeatered 124km of field-installed single mode optical fiber", Opt. Express, vol.18, Issue. 13,13908-13914(2010).
[67]J. Renaudier,m et al, "Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK bhy digital precessing in a coherent receiver", J. Lightwave Technol. vol.26, Issue.1, pp.36-42(2008).
[68]K. Nosu, "Advanced cohernt lightwave technonlogies", IEEE Communications Magazine, vol.26, Issue.2, pp.15-21(1988).
[69]R. A. Linke and A. H. Gnauck, "High-capacity coherent lightwave systems", J. Lightwave Technol. vol.6, Issue.11, pp.1750-1769(1988).
[70]S. Ryu, et al, "Polarization diversity techniques for the use of coherent optical fiber submarine cable systems", J. Lightwave Technol. vol.9, Issue.5, pp.675-682(1991).
[71]A. J. Viterbi and A. M. Viterbi, "Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission", IEEE Transactions on Information Theory, vol. IT-29, Issue.4, pp.543-551(1983).
[72]K.Kikuchi, "Coherent optical communication systems" Chapter 3 in Optical fiber Telecommunications V A (edited by I. P. Kaminow, T. Li and A. E. Willner, Academic Press, (2008).
[73]T. Pfau, et al, "First real-time data recovery for synchronous QPSK transmission with standard DFB lsers", IEEE Photon. Technol. Lett. vol.18, pp.1907-1909(2006).
[74]A. Leven, et al, "Coherernt receiver for practical optical communiction systems", OFC2007, paper.OthK4.
[75]S. J. Svory, et al,"Transmission of 42.8Gbit/s polariztion multiplexed NRZ-QPSK over 6400km of standard fiber with no optical dispersion compensation", OFC2007, paper. OTuA1.
[76]K. Sekine, et al, "40Gbit/s,16-ary (4bit/symbol) optical modulation/demodulation scheme", Electron. Lett, vol.41, pp.430-432(2005).
[77]J. Hongo, et al, "1-Gsymbol/s 64-QAM cohernt optical transmission over 150km", IEEE Photon. Technol. Lett. vol.19, pp.638-640(2007).
[78]T. Omiya, et al, "400Gbit/s 256QAM-OFDM transmission over 720km with a 14bit/s/Hz spectral efficiency by using high-resolution FDE", Opt. Express, vol.21, Issue.3, pp.2632-2641(2013).
[79]O. Bertran-Pardo, et al, "Nonlinearity limitations when mixing 40-Gb/s coherent PDM-QPSK channels with preexisting 10-Gb/s NRZ channels", IEEE Photon. Technol. Lett. vol.20, Issue.15, pp.1314-1316(2008).
[80]C. Xie, "Inter-channel nonlinearities in hybrid OOK and coherent PDM-QPSK transmission systems with dispersion management", IEEE Photonics Society Summer Topical Meeting Series, paper.TuA3.2 (2010).
[81]J. Renaudier, et al, "Investigation on WDM nonlinear impairments arising from the insertion of 100-Gb/s coherent PDM-QPSK over legacy optical networks", IEEE Photon. Technol. Lett. vol.21, Issue.24, pp.1816-1818(2009).
[82]M. Bertolini, et al, "On the XPM-induced distortion in DQPSK-OOK and coherent QPSK-OOK hybrid systems", OFC2009, paper.OTuD4.
[83]C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation", Opt. Express, vol.17, Issue.6, pp.4815-4823(2009).
[84]P. Poggiolini, et al, "Performance dependence on channel baud-rate of PM-QPSK systems over uncompensated links", IEEE Photon. Technol. Lett. vol.23, Issue.1, pp.15-17(2011).
[85]P. Serena, N. Rossi, O. B. Pardo, J. Renaudier, A. Vannucci, and A. Bononi, "Intra- versus inter-channel PMD in linearly compensated coherent PDM-PSK nonlinear transmission," J. Lightwave Technol. vol.29, Issue.11, pp.1691-1700 (2011).
[1]S. Vorbeck and M. Schneiders, "Cumulative nonlinear phase shift as engineering rule for performance estimation in 160-Gb/s transmission systems", IEEE Photon. Technol. Lett. vol.16, Issue. 11,pp.2571-2573 (2004).
[2]J.-C. Antona, S. Bigo, and J.-P. Faure, "Nonlinear cumulated phase as a criterion to assess performance of terrestrial WDM systems", OFC2002, pp.365-367.
[3]P. Poggiolini, et.al, "Analytical modeling of nonlinear propagation in uncompensated optical transmission links", IEEE Photon. Technol. Lett. vol.23, Issue.11, pp.742-744 (2011).
[4]G. Bosco, et.al, "Performance prediction for WDM PM-QPSK transmission over uncompensated link", OFC2011, paper. OThO7.
[5]E. Grellier and A. Bononi, "Quality parameter for coherent transmission with Gaussian-distributed nonlinear noise", Opt. Express, vol.19, Issue.13, pp.12781-12788(2011).
[6]Z. Avi, etal, "Vector analysis of simulated Brillouin scattering amplification in standard single-mode fibers", Opt. Express, vol.16, Issue.26, pp.21692-21707(2008).
[7]K. Shiraki, et.al, "SBS threshold of a fiber with a Brillouin frequency shift distribution", J. Lightwave Technol. vol.17, Issue.1, pp.50-57 (1996).
[8]P. Ebrahimi, et.al, "Effect of SBS and Rayleigh scattering in densedly-spaced bidirectional transmission using Raman amplification", CLEO2002 vol.1 pp.465-467.
[9]C. Xie, et.al, "Effect of cross-phase-modulation-induced polarization scattering on optical polarization mode dispersion compensation in wavelength-division-multiplexed systems", Opt. Lett, vol.28, Issue.23, pp.2303-2305(2003).
[10]M. Winter, et.al, "Cross-polarization modulation in polarization-division multiplex transmission", IEEE Photon. Technol. Lett.vol.22, Issue.8, pp.742-744 (2010).
[11]L. F. Mollenauer, J. P. Gordon, and F. Heismann, "Polarization scattering by soliton-soliton collisions", Opt. Lett., vol.20, Issue.20, pp.2060-2062 (1995).
[12]A. Mecozzi and F. Matera, "Polarization scattering by intra-channel collisions", Opt. Express, vol.20, Issue.2, pp.1213-1218(2012).
[13]X. Yi, J. Wu, Yan. Li, Wei, Li, and J. Lin, "SPM-induced nonlinear polarization scattering in single-channel coherent PM-QPSK systems over dispersion managed link", submitted to IEEE Photon. Technol. Lett.
[14]Haiqing Wei, et al, "Intra-channel nonlinearity compensation with scaled translational symmetry", Opt. Express, vol.12, Issue.18, pp.4282-4296(2004).
[15]M. J. Ablowitz and T. Hirooka, "Resonant nonlinear intrachannel interactions in strongly dispersion-mamaged transmission systems", Opt. Lett, vol.25, Issue.24, pp.1750-1752(2000).
[16]A. Mecozzi, et al, "Intra-channel nonlinearity in differentially phase-modulated transmission", Opt. Express, vol.19, Issue.5, pp.3990-3995(2011).
[17]A. Mecozzi and F. Matera, "Polarization scattering by intra-channel collisions," Opt. Express, vol.20, Issue.2, pp.1213-1218 (2012).
[18]P. Johannisson, "Interaction range and generation rate of nonlinear intrachannel signal distortion", JOSA B, vol.24, Issue.4, pp.729-738(2007).
[19]P. V. Mamyshev and N. A. Mamysheva, "Pulse-overlapped dispersion-managed data transmission and intrachannel four-wave mixing", Opt. Lett, vol.24, Issue.21, pp.1454-1456(1999).
[20]Xiaogang Yi, et al, "SPM-induced nonlinear polarization scattering in single-channel coherent PM-QPSK systems over dispersion managed link", submitted to Optics Letters
[21]G. P. Agrawal, Nononlinear Fiber Optics,3rd ed, New York:Academic,2001
[22]L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of pisecond pulse narrowing and solitons in optical fibers", Phys. Rev. Lett. vol.45, Issue.13, pp.1095-1098(1980).
[23]J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. vol.15, Issue 23, pp.1351-1353 (1990).
[24]S. Ryu, "Signal linewidth broadening due to nonlinear Kerr effect in long-haul coherent systems using cascaded optical amplifiers", J. Lightwave Technol. vol.10, Issue.10, pp.1450-1457 (1992).
[25]M. Zitelli, F. Matera, and M. Settembre, "Single-channel transmission in dispersion management links in conditions of very strong broadening:application to 40Gb/s signals on step-index fibers" J. Lightwave Technol. vol.17, Issue.12, pp.2498-2505 (1999).
[26]X. Xiao, S. Gao, Y. Tian, and C. Yang, "Analytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems," J. Lightwave Technol. vol.24, Issue.5, pp.2038-2044(2006).
[27]F. Zhang, et.al, "Optimum dispersion mapping of single-channel 40Gbit/s return-to-zero differential phase-shift keying transmission systems", Opt. Express, vol.14, Issue.15, pp.6613-6618(2006).
[28]M. Karlsson, and H. Sunnerud, "Effect of nonlinearities on PMD-induced system impairments", J. Lightwave Technol. vol.24, Issue.11, pp.4127-4137(2006).
[29]C. Xie, "Suppression of inter-channel nonlinearities in WDM coherent PDM-QPSK systems using periodic-group-delay dispersion compensators", ECOC2009, paper.P4.08.
[30]M.-N. Chughtai, et.al, "Influence of polarization state, baud rate and PMD on nonlinear impairments in WDM systems with mixed PM(D)QPSK and OOK channels", Opt. Express, vol.20, Issue.7, pp.8155-8160(2012).
[31]C. Xia, et.al, "PMD-induced nonlinear pemalty reduction in coherent polarization-multiplexed QPSK transmission", ECOC2010, paper.Th.10.E.5.
[32]C. Xie, "Nonlinear polarization effects and mitigation in polarization-division-multiplexed coherent transmission systems," Chin. Opt. Lett.vol.8, Issue.9, pp.844-851 (2010).
[33]P. Serena, N. Rossi, and A. Bononi, "PDM-iRZ-QPSK vs. PS-QPSK at 100Gbit/s over dispersion-managed links", Opt. Express, vol.20, Issue.7, pp.7895-7900(2012).
[34]C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation", Opt. Express, vol.17, Issue.6, pp.4815-4823(2009).
[1]J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. vol.15, Issue 23, pp.1351-1353 (1990).
[2]X. Li, F. Zhang, Z. Chen, and A. Xu, "Supperssion of XPM and XPM-induced nonlinear phase noise for RZ-DPSK signals in 40Gbit/s WDM transmission systems with optimum dispersion mapping", Opt. Express, vol.15, Issue.26,pp.18247-18285(2007).
[3]O. Vassilieva, et.al., "Symbol rate dependency of XPM-induced phase noise penalty on QPSK-based modulation formats", ECOC2008, paper. We. 1.E.4.
[4]A. G. Green, P. P. Mitra, and L. G. L. Wegener, "Effect of chromatic dispersion on nonlinear phase noise", Opt. Lett, vol.28, pp.2455-2457(2003).
[5]K.-P, Ho, "Error probability of DPSK signals with cross-phase molation induced nonlinear phase noise", IEEE J Sel Top Quant, vol.10, Issue.2, pp.421-427(2004).
[6]K.-P. Ho, "Probability density of nonlinear phase noise," J. Opt. Am. B, vol.20, Issue.9, 1875-1879(2003).
[7]P. Serena, A. Orlandini, and A. Bononi, "Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightwave Technol. vol.24, Issue.5, pp.2026-2037 (2006).
[8]A. P. T. Lau and J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightwave Technol.vol.25, pp.3008-3016 (2007).
[9]H. Kim, "Nonlinear phase noise in phase-coded transmission," OFC2005, paper OThO3.
[10]H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. vol.15, pp.320-322 (2003).
[11]A. Bononi, P. Serena and N. Rossi,"Modeling of signal-noise inreactions in nonlinear fiber transmission with different modulation formats", ECOC2009, paper 10.4.6
[12]A.Bononi, P.Serena, and N.Rossi,"Nonlinear sinal-noise interactions in dispersion-managed links with various modulation formats", Opt.Fiber Technol, vol.16, Issue.2, pp.73-85(2010).
[13]A.Bononi, P.Serena, N.Rossi, and D.Sperti,"Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?", ECOC2010,paper Th.10.E.1.
[14]M. Winter, et.al, "A statistics treatment of cross-phase polarization modulation in DWDM systems", J. Lightwave Technol. vol.27, Issue.17, pp.3739-3751(2009).
[15]Optical Amplifiers User's Manual, Chapter 2 in VPIcomponentMaker8.6.
[16]C. Xie, "Nonlinear polarization effects and mitigation in polarization-division-multiplexed coherent transmission systems," Chin. Opt. Lett.vol.8,Issue.9, pp.844-851 (2010).
[17]X. Xiao, S. Gao, Y. Tian, and C. Yang, "Analytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems," J. Lightwave Technol. vol.24, pp.2038 (2006).
[18]C. Xie, "Dispersion management in WDM coherent PDM-QPSK systems", ECOC2009, paper.9.4.3
[19]X. Li, F. Zhang, Z. Chen, and A. Xu, "Suppression of XPM and XPM-induced nonlinear phase noise for RZ-DPSK in 40Gbit/s WDM transmission systems with optimum dispersion maping", Opt. Express, vol.15, Issue.26, pp.18247-18252(2007).
[20]M. Zitelli, F. Matera, and M. Settembre, "Single-channel transmission in dispersion management links in conditions of very strong broadening:application to 40Gb/s signals on step-index fibers" J. Lightwave Technol. vol.17, Issue.12, pp.2498-2505 (1999).
[21]X. Yi, Y. Li, J. Wu, K. Xu, and J. Lin, "Impact of nonlinear signal-noise interactions on symbol-aligned and -interleaved formats in dispersion managed coherent PM-QPSK systems," Opt. Express vol.20, Issue 15, pp.17183-17191 (2012).
[22]P. Serena and A. Bononi, "Nonlinear phase noise mitigation by polarization mode dispersion in dispersion managed coherent PDM-QPSK systems", ECOC2009, paperP4.12.
[23]G. P. Agrawal, Nononlinear Fiber Optics,3rd ed, New York:Academic,2001.
[1]Biondini. G, W. L. Kath, "Non-Maxwellian DGD distribution of PMD emulators", OFC (2001), paperThA5.
[2]A. Bononi, A. Vannuccifi, "Statistics of the Jones matrix of fibers affected by polarization mode dispersion", Opt. Lett, vol.26, Issue10, pp.675-677(2001).
[3]Adamczyk, et al., "Statistics of PMD-induced power fading for double sideband and single sideband subcarriermultiplexing signals", OFC (2001), paperM05.
[4]A. J. Barlow, J. J. R-H, and D. N. Payne, "Birefringence and polarization mode dispersion in spun single-mode fibers", Appl. Opt. vol.20, pp.2962-2968(1981).
[5]D. Beltrame, et al., "Statistics behavior of the Q-factor in optical transmission systems due to the polarization mode dispersion", ECOC (2000).
[6]M. Rochette, C. Baker, and R. Ahmad, "All-optical polarization-mode dispersion monitor for return-to-zero optical signals at 40Gbit/s and beyond", Opt. Lett. Vol.35, pp.3703-3705(2010).
[7]X. Steve, X. Chen, T. J. Xia, G. Wellbrock, D. Chen. D. Peterson, P. Zhang, A. Belisle, L. Dong, and T. Yu, "In-service light path PMD (polarization mode dispersion) monitoring by PMD compensation", Opt. Express, vol.18, Issue26, pp.27306-27318(2010).
[8]L. Xu, S. X. Wang, H. Miao, and A. M. Weiner, "Polarization mode dispersion spectrum measurement via high-speed wavelength-parallel polarimeter", Appl. Opt. vol.48, pp.4688-4697(2009).
[9]K. H. Han and W. J. Lee, "First-order polarization mode dispersion compensator using two independent feedback signals enabling separation of principal states of polarization and differential group delay controls", Opt. Express, vol.20, Issue4, pp.3541-3549(2012).
[10]Y. Zheng, B.-J. Yang, and X.-G. Zhang, "Three-stage polarization mode dispersion compensator capable of compensating second-order polarization mode dispersion", IEEE Photon. Technol. Lett., vol.14, Issue10, pp.1412-1414(2002).
[11]H. Miao and C. Yang, "Scheme for Feed-Forward Polarization Mode Dispersion Compensation," Appl. Opt. vol.43, pp.1577-1582 (2004).
[12]L. Yan, Yao. X. S, Hauer. M.C, and A. E. Willner, "Practical solutions to polarization-mode-dispersion emulation and compensation", Journal of Lightwave Technology. vol.24, Issue 11,pp.3992-4005(2006).
[13]T. Do, H. Dong, and P. Shum, "Measurement of the complex polarization mode dispersion vector using Jones matrix analysis," Appl. Opt. vol.46, pp.916-921 (2007).
[14]J. Kim, H. Yoon, N. Park, and B. Lee, "Polarization-Mode-Dispersion Compensator Using a Polarization Beam Splitter and Quarter-Wave Plates," Appl. Opt. vol.40, pp.4473-4475 (2001).
[15]S. J. Savory, "Digital filters for coherent optical receivers", Opt. Express, vol.16, Issue2, pp.804-817(2008).
[16]S. J. Savory, "Digital coherent optical receivers:algorithms and subsystems", IEEE J Sel Top Quant, vol.16, Issue.5, pp.1164-1179(2010).
[17]N. Mantzoukis, et al., "Performance comparison of electronics PMD equalizers for coherent PDM QPSK systems", Journal of Lightwave Technology, vol.29, Issue 11(2011).
[18]P. Serena and A. Bononi, "Nonlinear phase noise mitigation by polarization mode dispersion in dispersion managed coherent PDM-QPSK systems", ECOC2009, paperP4.12.
[19]C. Xia, et al., "PMD-induced nonlinear penalty reduction in coherent polarization-multiplexed QPSK transmission", ECOC2010,paper.Th.10.E.5.
[20]X. Yi, J. Wu, Y. Li, W. Li, X. Hong, Y. Zuo, and J. Lin, "Nonlinear signal-noise interactions in dispersion managed coherent PM-QPSK systems in the presence of PMD", Opt. Express, vol.20, Issue.25, pp.27596-27602(2012).
[21]H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. vol.15, pp.320-322 (2003).
[22]A. Bononi, P. Serena, and N. Rossi, "Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats, " Opt. Fiber Technol.vol.16,Issue 2, pp.73-85 (2010).
[23]J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. vol.15, Issue 23, pp.1351-1353 (1990).
[24]X. Yi, Y. Li, J. Wu, K. Xu, and J. Lin, "Impact of nonlinear signal-noise interactions on symbol-aligned and -interleaved formats in dispersion managed coherent PM-QPSK systems," Opt. Express vol.20, Issue 15, pp.17183-17191 (2012).
[25]A. Bononi, P. Serena, N. Rossi, and D. Sperti, "Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?", ECOC2010, paper Th.10.E.1.
[26]A. Mecozzi and F. Matera, "Intrachannel nonlinearity enhancement in polarization multiplexed phase modulated systems with differential detection", Opt. Lett. vol.36, Issue 19,pp.3903-3905(2011).
[27]F. Curti. B. Daino, G. D. Marchis, and F. Matera, "Statistical treatment of the evolution of the principal states of polarization in single-mode fibers," J. Lightwave Technol. vol.8, Issue 8, pp.1162-1165 (1990).
[28]C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation," Opt. Express, vol.17, Issue.6, pp.4815-4823 (2009).
[29]H. Kim, "Nonlinear phase noise in phase-coded transmission," OFC2005, paper OThO3.
[30]P. Serena, N. Rossi, O. B. Pardo, J. Renaudier, A. Vannucci, and A. Bononi, "Intra- versus inter-channel PMD in linearly compensated coherent PDM-PSK nonlinear transmission," J. Lightwave Technol. vol.29, Issue.11, pp.1691-1700 (2011).
[31]C. Xie, "Dispersion management in WDM coherent PDM-QPSK systems", ECOC2009, paper.9.4.3.
[1]A. Hodzic, et.al, "Optimized filtering for 40-Gb/s/ch-based DWDM transmission systems over standard single-mode fiber', IEEE Photon. Technol. Lett. vol.15, Issue7, pp.1002-1004 (2003).
[2]C. J. Anderson and J. A. Lyle,"Technique for evaluation system performance using Q in numerical simulations exhibiting intersymbol interference", Electron. Lett., vol.30, Issue.1, pp.71-72(1994).
[3]G. Bosco, et.al, "On the use of NRZ, RZ, and CSRZ modulation at 40Gb/s with narrow DWDM channel spacing", J. Lightwave Technol. vol.20, Issue.9, pp.1694-1704(2002).
[4]P. J. Winzer and R.-J. Essiambre, "Advanced optical modulation formats", Proceddings of the IEEE, vol.94, Issue.5, pp.952-985(2006).
[5]L. Zong, J. Veselka, H. Sardesai, and M. Frankel, "Influence of filter shape and bandwidth on 44Gb/s DQPSK systems", OFC2009, paper JWA17.
[6]G. Bosco etal, "Investigation on the robustness of a Nyquist-WDM terabit superchannel to transmitter and receiver non-idealities", ECOC2010, paperTu.3.A.4.
[7]G. Bosco et.al, "On the performance of Nyquist-WDM terabit superchannels based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM subcarriers", J. Lightwave Technol. vol.29, Issue.1, pp.53-61(2011).
[8]G. Bosco et.al, "Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems", IEEE Photon. Technol. Lett. vol.22, Issue.15, pp.1129-1131 (2010).
[9]P. Poggiolini et al. "Analytical modeling of nonlinear propagation in uncompensated optical transmission links", IEEE Photon. Technol. Lett. vol.23, Issue.ll, pp.742-744 (2011).
[10]M. Nolle et al,"Transmission of 562Gbit/s DWDM coherent OFDM with a spectral efficiency of 7.2Bit/s/Hz using joint 64-QAM and 16-QAM modulation", OFC2010, paper.OMR4.
[11]O. Gaete, et al,"A digital subcarrier multiplexing technique for increased spectral efficiency in optical systems uding direct detection", OFC2010, paperOThM5.
[12]J.-X. Cai, "100G transmission over transoceanic distance with high spectral efficiency and large capacity", J. Lightwave Technol. vol.30, Issue.24, pp.3845-3856(2012).
[13]P. J. Winzer, "High-spectral-efficiency optical modulation formats", J. Lightwave Technol. vol.30, Issue.24, pp.3824-3835(2012).
[14]H. Takhashi, "Coherent OFDM transmission with high spectral efficiency", ECOC2009, paper.1.3.3.
[15]M. Pfennigbauer and P. J. Winzer, "Choice of MUX/DEMUX filter characteristics for NRZ, RZ, and CSRZ DWDM systems", J. Lightwave Technol. vol.24, Issue.4, pp.1689-1696(2006).
[16]P. Poggiolini, et al, "Performance dependence on channel baud-rate of PM-QPSK systems over uncompensated links", IEEE Photon. Technol. Lett. vol.23, Issue.1, pp.15-17(2011
[17]X. Yi, Yan Li, Jian Wu, Wei Li, Xiaobin Hong, Yong Zuo, and Jintong Lin, "Impact of filter shape and bandwidth on terabit polarization-multiplexed quadrature phase-shift keying transmission with baud-rate spacing" Opt. Engineering,51(10),105505(2012).
[1]G. Goldfard and G. Li, "BER estimation of QPSK ohomodyne detection with carrier phase estimation using digital signal processing", Opt. Express, vol.14, Issue.18, pp.8043-8053(2006).
[2]F. Zhang, et al, "Stochastic BER estimation for coherent QPSK transmission systems with digital carrier phase recovery", Opt. Express, vol.18, Issue.9, pp.9592-9599(2010).
[3]F. Zhang, et al, "Experimental comparison of different BER estimation methods for coherent optical QPSK transmission systems", IEEE Photon. Technol. Lett., vol.23, Issue18, pp.1343-1345(2011).
[4]E. Ciarameiia, et al, "BER estimation for performance monitoring in high-speed digital optical signals", J. Lightwave Technol. vol.30, Issue.13, pp.2117-2124 (2012).
[5]P. Serena, et al, "A stratified sampling Monte Carlo algorithm for efficient BER measurement and its application to DQPSK terrestrial systems", ECOC2008, paper.We.1.E.2
[6]廖延彪《偏振光学》北京：科学出版社2003.