大容量光纤通信系统中PMD理论与补偿控制算法的研究
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摘要
在高速光纤通信系统中,随时间随机变化的偏振模色散(Polarization mode dispersion PMD)是限制系统比特速率和传输距离的重要因素之一。作为当前PMD问题理想的解决方式,动态补偿的技术与应用前景极为广阔,PMD补偿技术及相关理论的研究已经成为当前光纤通信领域的研究热点之一。本课题的研究工作主要包括以下几方面:
分析光纤中PMD现象的实质,由单模光纤中光传输的基本方程出发,得出描述PMD效应的非线性Schr?ndinger方程;在斯托克斯空间中,推导了一阶、二阶和更高阶PMD矢量模型,并由此分析PMD所引起的脉冲展宽,在多种情况下进行讨论,得到简化模型。通过输入光脉冲信号的自相关函数建立起差分群时延(Differential group delay DGD)与偏振度(Degree of polarization DOP)的关系模型。
针对PMD在线监测的问题,采用偏振扰动和正交偏振分束探测来实现,采用差动式测量方案的设计来提高DOP测量的灵敏度,通过对比电域补偿、光域补偿和光电混合补偿三大PMD补偿方案,选取偏振控制器(Polarization controller PC)加可变(或固定)时延线的光域补偿方案来设计PMD补偿单元。
在PMD补偿系统搜索算法的设计中,将原标准粒子群优化(Particle swarm optimization PSO)算法进行了改进,通过动态改变惯性权重,用影响算法性能的两个主要因素——粒子聚集度和全局最优值变化的速度来构建惯性权重调整的策略,同时在PSO算法中引入免疫克隆原理来保持种群的多样性,从而提高了算法的全局搜索能力而不至于陷入局部最优解。通过算法测试可以发现,改进PSO的全局寻优能力明显优于原标准PSO算法。
为了在多维空间中准确、快速、实时地跟踪最佳补偿点的随机变化,在跟踪算法的设计中,采用局部搜索算法——改进的单纯形法(Simplex method SM)对PMD的微小变化进行局部精细搜索。在反射操作中,除了基于最差点和剩下点的重心进行反射操作外,还加上了剔除最好点,并基于最好点和剩下点的重心进行反射操作,从以上两个反射方向上选择一个有利的方向进行反射和扩张,从而使迭代运算过程很快地逼近极值点;用单纯形映射操作代替原有的顶点代换操作,从而可使单纯形在迭代过程中不发生退化现象。
在跟踪算法设计的基础上,提出基于改进SM与改进PSO算法的串行算法作为反馈控制算法的总体设计方案。整个算法由IC-PSO算法、改进SM和个体迁移操作三部分组成,通过设置适当的个体迁移条件,改进的SM利用IC-PSO算法跳出局部最优,IC-PSO算法依靠改进的SM迅速找到问题的最优解,从而做到广度探索和深度开发的均衡。
通过搭建以DOP为反馈控制信号的PMD自适应补偿系统,将本文所提出的搜索算法和跟踪算法作为补偿系统的反馈控制算法,对DOP进行寻优,调整光纤时延线和PC的波片使得DOP不断趋近全局最优值,并根据PMD的随机波动情况对补偿单元进行动态调整,将基于改进SM和改进PSO的串行算法应用于实验获得了良好的效果,搜索算法的响应时间约为71 ms,跟踪算法的信号恢复时间小于12 ms。实验证明,该反馈控制算法具有很好的抗噪声能力,且能够有效避开局部最大值,找到全局最佳补偿点。由眼图和误码率(Bit error rate BER)的监测统计结果,可以发现,通过反馈控制算法对DOP的寻优,系统的PMD大大降低,信号传输质量明显改善,BER最低可达3.59e-16,达到了动态自适应PMD补偿的要求。
In high-speed optical fiber systems, polarization mode dispersion (PMD) can spread optical signal, and is acknowledged as one of the serious degradation factors limiting the bit rate and the transmission distance, since it is a statistical quantity and leads to random broadening of optical transmitting signal. As an ideal solution to the severe effect of PMD on system performance, dynamic PMD compensation has an irreplaceable wide technical and application foreground. Accordingly, the relative PMD compensating theories and technologies have been one of the most significant topics in recent researches related to high-speed and long-haul optical communication system. The main work includes:
The essential of PMD effect has been analyzed, and from the foundamental equation of optical signal transmission in single mode fiber, the nonlinear Schr?ndinger equation describing PMD can be obtained, from which pulse broadening due to PMD can be deduced. Various discussions have been made in different situations, by which can approximate module be obtained. The relationship between differential group delay (DGD) and degree of polarization (DOP) can be established using self-relative function of input optical signal.
In order to solve the problem of online PMD detection, the schieme combing polarization scrambing with perpendicular polarization splitting detection has been proposed, in which the differential design can be used to increase the measurement sensitivity. Through the comparison between the three compensation schemes, electrical domain compensation, optical domain compensation and optoelectronic compensation, the design solution combing polarization controller with variable (or fixed) delay line has been chosen to realize PMD compensation.
In the thesis, partical swarm optimization (PSO) has been deeply studied and adopted to design the searching algorithm. An improved PSO algorithm has been proposed. Two main factors influencing the properties of the algorithm, the degree of aggregation and the changing velocity of global optimum for the particles, have been considered to establish the stratedy of changing the inertia weight dynamically. Besides, the immune clone principle has been adopted to maintain the diversity of the swarm. From the algorithm test, the global searching ability is obviously better than the standard PSO algorithm.
In order to track the random fluctuation of the global optimum accurately and quickly, an improved simplex method (SM) has been proposed to search accurately in a local domain. Where, in the reflection operation, besides the reflection operation based on the worst vertex point and the center of gravity for the other nodes, the reflection operation based on the best vertex point and the center of gravity for the other nodes has been added. A better direction can be chosen to perform reflection operation and expansion operation, which can reach the optimum rapidly. The mapping operation has been adopted to replace the vertex point substitution operation, which can avoid the degeneration in the procedure of iteration.
Based on the searching algorithm and the tracking algorithm, the general design scheme for the feedback control algorithm has been proposed. The whole algorithm includes IC-PSO algorithm, improved SM, and agent migration operation. Through the combination of IC-PSO and improved SM, the balance between global exploration and local deep development can be realized.
The adaptive PMD compensation system has been established, in which the searching algorithm and the tracking algorithm proposed above has been used to search and track the optimum of DOP. From the experimental results, the response time is about 71 ms, and the recovering time is less than 12 ms. It has been demonstrated that the feedback algorithm has perfect ability to avoid local optimum and reach the global best compensation point. Compared the eye diagram before and after compensation, the opening of the eye diagram has been improved obviously. And from the statistic results for the bit error rate (BER), the BER of the system has been reduced increasingly, and the minimum can be attained to 3.59e-16. The quality of transmission signal has been improved obviously, which can meet the requirement of dynamic adaptive PMD compensation.
分析光纤中PMD现象的实质,由单模光纤中光传输的基本方程出发,得出描述PMD效应的非线性Schr?ndinger方程;在斯托克斯空间中,推导了一阶、二阶和更高阶PMD矢量模型,并由此分析PMD所引起的脉冲展宽,在多种情况下进行讨论,得到简化模型。通过输入光脉冲信号的自相关函数建立起差分群时延(Differential group delay DGD)与偏振度(Degree of polarization DOP)的关系模型。
针对PMD在线监测的问题,采用偏振扰动和正交偏振分束探测来实现,采用差动式测量方案的设计来提高DOP测量的灵敏度,通过对比电域补偿、光域补偿和光电混合补偿三大PMD补偿方案,选取偏振控制器(Polarization controller PC)加可变(或固定)时延线的光域补偿方案来设计PMD补偿单元。
在PMD补偿系统搜索算法的设计中,将原标准粒子群优化(Particle swarm optimization PSO)算法进行了改进,通过动态改变惯性权重,用影响算法性能的两个主要因素——粒子聚集度和全局最优值变化的速度来构建惯性权重调整的策略,同时在PSO算法中引入免疫克隆原理来保持种群的多样性,从而提高了算法的全局搜索能力而不至于陷入局部最优解。通过算法测试可以发现,改进PSO的全局寻优能力明显优于原标准PSO算法。
为了在多维空间中准确、快速、实时地跟踪最佳补偿点的随机变化,在跟踪算法的设计中,采用局部搜索算法——改进的单纯形法(Simplex method SM)对PMD的微小变化进行局部精细搜索。在反射操作中,除了基于最差点和剩下点的重心进行反射操作外,还加上了剔除最好点,并基于最好点和剩下点的重心进行反射操作,从以上两个反射方向上选择一个有利的方向进行反射和扩张,从而使迭代运算过程很快地逼近极值点;用单纯形映射操作代替原有的顶点代换操作,从而可使单纯形在迭代过程中不发生退化现象。
在跟踪算法设计的基础上,提出基于改进SM与改进PSO算法的串行算法作为反馈控制算法的总体设计方案。整个算法由IC-PSO算法、改进SM和个体迁移操作三部分组成,通过设置适当的个体迁移条件,改进的SM利用IC-PSO算法跳出局部最优,IC-PSO算法依靠改进的SM迅速找到问题的最优解,从而做到广度探索和深度开发的均衡。
通过搭建以DOP为反馈控制信号的PMD自适应补偿系统,将本文所提出的搜索算法和跟踪算法作为补偿系统的反馈控制算法,对DOP进行寻优,调整光纤时延线和PC的波片使得DOP不断趋近全局最优值,并根据PMD的随机波动情况对补偿单元进行动态调整,将基于改进SM和改进PSO的串行算法应用于实验获得了良好的效果,搜索算法的响应时间约为71 ms,跟踪算法的信号恢复时间小于12 ms。实验证明,该反馈控制算法具有很好的抗噪声能力,且能够有效避开局部最大值,找到全局最佳补偿点。由眼图和误码率(Bit error rate BER)的监测统计结果,可以发现,通过反馈控制算法对DOP的寻优,系统的PMD大大降低,信号传输质量明显改善,BER最低可达3.59e-16,达到了动态自适应PMD补偿的要求。
In high-speed optical fiber systems, polarization mode dispersion (PMD) can spread optical signal, and is acknowledged as one of the serious degradation factors limiting the bit rate and the transmission distance, since it is a statistical quantity and leads to random broadening of optical transmitting signal. As an ideal solution to the severe effect of PMD on system performance, dynamic PMD compensation has an irreplaceable wide technical and application foreground. Accordingly, the relative PMD compensating theories and technologies have been one of the most significant topics in recent researches related to high-speed and long-haul optical communication system. The main work includes:
The essential of PMD effect has been analyzed, and from the foundamental equation of optical signal transmission in single mode fiber, the nonlinear Schr?ndinger equation describing PMD can be obtained, from which pulse broadening due to PMD can be deduced. Various discussions have been made in different situations, by which can approximate module be obtained. The relationship between differential group delay (DGD) and degree of polarization (DOP) can be established using self-relative function of input optical signal.
In order to solve the problem of online PMD detection, the schieme combing polarization scrambing with perpendicular polarization splitting detection has been proposed, in which the differential design can be used to increase the measurement sensitivity. Through the comparison between the three compensation schemes, electrical domain compensation, optical domain compensation and optoelectronic compensation, the design solution combing polarization controller with variable (or fixed) delay line has been chosen to realize PMD compensation.
In the thesis, partical swarm optimization (PSO) has been deeply studied and adopted to design the searching algorithm. An improved PSO algorithm has been proposed. Two main factors influencing the properties of the algorithm, the degree of aggregation and the changing velocity of global optimum for the particles, have been considered to establish the stratedy of changing the inertia weight dynamically. Besides, the immune clone principle has been adopted to maintain the diversity of the swarm. From the algorithm test, the global searching ability is obviously better than the standard PSO algorithm.
In order to track the random fluctuation of the global optimum accurately and quickly, an improved simplex method (SM) has been proposed to search accurately in a local domain. Where, in the reflection operation, besides the reflection operation based on the worst vertex point and the center of gravity for the other nodes, the reflection operation based on the best vertex point and the center of gravity for the other nodes has been added. A better direction can be chosen to perform reflection operation and expansion operation, which can reach the optimum rapidly. The mapping operation has been adopted to replace the vertex point substitution operation, which can avoid the degeneration in the procedure of iteration.
Based on the searching algorithm and the tracking algorithm, the general design scheme for the feedback control algorithm has been proposed. The whole algorithm includes IC-PSO algorithm, improved SM, and agent migration operation. Through the combination of IC-PSO and improved SM, the balance between global exploration and local deep development can be realized.
The adaptive PMD compensation system has been established, in which the searching algorithm and the tracking algorithm proposed above has been used to search and track the optimum of DOP. From the experimental results, the response time is about 71 ms, and the recovering time is less than 12 ms. It has been demonstrated that the feedback algorithm has perfect ability to avoid local optimum and reach the global best compensation point. Compared the eye diagram before and after compensation, the opening of the eye diagram has been improved obviously. And from the statistic results for the bit error rate (BER), the BER of the system has been reduced increasingly, and the minimum can be attained to 3.59e-16. The quality of transmission signal has been improved obviously, which can meet the requirement of dynamic adaptive PMD compensation.
引文
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