偏振复用系统中解复用技术的研究
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摘要
随着通信业务的急速增长,系统容量的提升势在必行。偏振复用技术利用光在单模光纤中传输的偏振特性,将传输波长的两个独立且相互正交的偏振态作为独立信道分别传输两路信号,成倍提高了系统容量、增加了频谱利用率。该技术可在已铺设光纤网络的基础上极大的提升系统容量,实现快速、低成本的系统升级。由于两个偏振态在传输过程中会受到偏振模色散、偏振相关损耗以及输入信号非正交等因素的影响,使得偏振态发生变化形成相互之间的串扰。因此,对于偏振复用技术而言,在接收端实现信号的解复用是该技术亟待解决的难题。依据偏振复用的技术原理,针对偏振复用系统的特点,研究和寻找有效的偏振解复用方法是本文的主要工作。
本文在前人的基础上进一步研究了偏振解复用技术。建立了偏振复用系统的仿真模型。首先研究了基于恒模算法(CMA)实现偏振解复用的方法,针对偏振复用系统传输矩阵的特点,改进了递归最小二乘恒模算法(RLS-CMA)并对该算法的解复用效果进行了分析。为了得到更稳定的基于CMA的解复用算法,本文首次采用基于正交三角分解(QR-decomposition)的RLS-CMA算法(QR-RLS-CMA)对偏振混合信号解复用,该算法对初始值的选取不敏感,具有更高的稳定性。还研究了基于独立成分分析(ICA)实现偏振解复用的方法,针对偏振复用系统的特点,首次采用复数域内基于负熵最大化的不动点算法对偏振混合信号进行解复用,该算法只需调整非线性函数便可实现不同调制格式信号的解复用,该方法不需要求解信道矩阵的逆从而降低了系统硬件实现的复杂度。本文的具体工作主要包含以下内容:
首先,根据偏振复用技术的基本原理,利用Optisystem 9.0光纤通信系统仿真软件搭建了偏振复用系统的仿真模型。通过MATLAB编程实现了系统所需的信号处理模块,对系统各组成部分的结构和原理进行了详细介绍。分析了偏振模色散和偏振相关损耗的成因,研究了偏振复用系统中信号串扰产生的原因。从理论上分析了偏振解复用的原理,得出了解复用的实质就是求解分离矩阵(传输矩阵的逆矩阵)的结论,为后续解复用算法的实现做了充分的准备。
其次,利用CMA实现偏振解复用。对基于随机梯度下降的恒模算法(SGD-CMA)、RLS-CMA算法和QR-RLS-CMA算法进行了数学推导,并以表格的形式给出了这些算法的主要步骤以及变量初值的设定。针对偏振复用系统传输矩阵的特点,改进了RLS-CMA算法,首次使用QR-RLS-CMA算法进行解复用。利用星座图和眼图分析了这三种算法的解复用效果,并对它们的收敛性能进行研究,通过分析得到了QR-RLS-CMA算法稳定性最强的结论。
再次,利用ICA实现偏振解复用。介绍了复数ICA的基本概念和估计准则,分析了复数ICA解复用技术在偏振复用系统中的可行性。使用MATLAB开发出了适用于偏振复用系统的基于负熵最大化的不动点算法(T-CMN),并以表格的形式给出了渐进正则化T-CMN算法和对称正则化T-CMN算法的主要步骤。对对称正则化T-CMN算法的解复用效果进行了仿真,从多个方面与基于张量的ICA算法相比较,结果显示对称正则化T-CMN算法不需要求解信道矩阵的逆从而降低了系统复杂度。利用眼图分析了T-CMN算法的解复用效果,结果显示T-CMN算法的解复用效果较好。
最后,利用Viterbi-Viterbi算法对解复用后的信号进行相位估计,还原出QPSK调制的源信号,然后通过门限判决的方法得到接收比特序列,利用误码率测试模块将接收比特序列与发送比特序列直接比较得到系统误码率,经测量系统无误码。
With the growth of people’s demand for communication services, enhancing system capacity is imperative. Using the polarization property of optics transmitted in a single mode fiber, Polarization multiplexing (PM) technique aims at creating two independent communication channels over the transmission wavelength by using the independent and mutually orthogonal polarization, which can double the capacity of optical fiber communication system and increase spectrum efficiency. This technique can upgrade system rapidly and economically on the existing optical network. The two polarizations can be affected by polarization mode dispersion, polarization dependent loss etc., which will cause crosstalk between each other. The most important problem to be solved in polarization multiplexing system is eliminating the crosstalk between the received signals, which can be called polarization de-multiplexing. According to the principle of polarization multiplexing technology and characteristics of polarization multiplexing system, the major work of this paper is studying and finding a suitable method for polarization de-multiplexing. This paper has done a lot of further work of polarization multiplexing technology on the basis of previous research. In order to verify the validity of polarization de-multiplexing algorithm, we establish the simulation model of polarization multiplexing system. First of all, we research on the polarization de-multiplexing method carried out by using constant modulus algorithm (CMA).
The Recursive Least Squares constant modulus algorithm (RLS-CMA) is modified based on feature of transmission matrix in polarization multiplexing system, and then we show the de-multiplexing results of this algorithm. In order to get a more robust de-multiplexing algorithm based on the CMA, it is the first time to use RLS-CMA algorithm based on QR decomposition (QR-RLS-CMA) as the de-multiplexing algorithm in polarization multiplexing system. This algorithm is not sensitive about initial values, furthermore it has strong robustness. Moreover, we research on the polarization de-multiplexing method carried out by using independent component analysis (ICA). According to characteristics of polarization multiplexing system, a fixed-point algorithm based on complex maximization of negentropy is used as the de-multiplexing method in polarization multiplexing system for the first time. This algorithm can realize de-multiplexing of different modulation format just by adjusting nonlinear function. It doesn’t need solving inverse of channel matrix, which can significantly reduce complexity while guaranteeing the de-multiplexing performance. The works in this paper are as follows:
Firstly, a simulation model of the polarization multiplexing system based on the principle of polarization multiplexing technology has been established by using Optisystem 9.0 fiber communication software. The signal processing module requiring for de-multiplexing is realized by MATLAB programming. Each part of the system has been introduced in detail. The origins of polarization mode dispersion and polarization dependent loss have been analyzed; in addition, the causes of crosstalk have been researched. As the principle of polarization de-multiplexing has been analyzed from the theoretical, we get the conclusion that the essence of de-multiplexing is solving the separating matrix.
Secondly, polarization de-multiplexing is carried out by using CMA. We focus on the Stochastic Gradient Descent constant modulus algorithm (SGD-CMA), RLS-CMA algorithm and QR-RLS-CMA algorithm, giving the mathematical deduction of these algorithms. The main steps and initial value of these algorithms have been given in table. The RLS-CMA algorithm is modified based on feature of transmission matrix in polarization multiplexing system, and QR-RLS-CMA algorithm used as the de-multiplexing method in polarization multiplexing system at the first time. De-multiplexing results of these algorithms have been analyzed by using constellations diagram and eye diagram, comparing the convergence among these algorithms, and then we get the conclusion that QR-RLS-CMA algorithm has the best performance among these algorithms.
Thirdly, polarization de-multiplexing is carried out by using ICA. The basic conception of complex ICA and the estimation principle are introduced in detail, and then the feasibility of the de-multiplexing of polarization multiplexing system with complex ICA is analyzed. The fixed-point algorithm based on complex maximization of negentropy (T-CMN) is developed by MATLAB programming. The main steps of deflationary regularization T-CMN algorithm and symmetric regularization T-CMN algorithm are given in table, and then we show the de-multiplexing results of symmetric regularization T-CMN algorithm by simulation. The symmetric regularization T-CMN algorithm and tensor based ICA algorithm have been compared in several aspects, the results shows that symmetric regularization T-CMN algorithm doesn’t need solving inverse of channel matrix, which can significantly reduce complexity while guaranteeing the de-multiplexing performance. Comparing de-multiplexing performance between CMA and T-CMN algorithm by using eye diagram, the result shows that T-CMN algorithm has better robustness.
Finally, we use Viterbi-Viterbi algorithm to estimate signal phase to recover the original signal, and then we get the received bit sequence by using threshold judgment. System bit error ratio can be tested through bit error test module by comparing the bit sequence between transmitted bits and received bits. After measurement of bit error rate, the result shows that this system is error-free.
本文在前人的基础上进一步研究了偏振解复用技术。建立了偏振复用系统的仿真模型。首先研究了基于恒模算法(CMA)实现偏振解复用的方法,针对偏振复用系统传输矩阵的特点,改进了递归最小二乘恒模算法(RLS-CMA)并对该算法的解复用效果进行了分析。为了得到更稳定的基于CMA的解复用算法,本文首次采用基于正交三角分解(QR-decomposition)的RLS-CMA算法(QR-RLS-CMA)对偏振混合信号解复用,该算法对初始值的选取不敏感,具有更高的稳定性。还研究了基于独立成分分析(ICA)实现偏振解复用的方法,针对偏振复用系统的特点,首次采用复数域内基于负熵最大化的不动点算法对偏振混合信号进行解复用,该算法只需调整非线性函数便可实现不同调制格式信号的解复用,该方法不需要求解信道矩阵的逆从而降低了系统硬件实现的复杂度。本文的具体工作主要包含以下内容:
首先,根据偏振复用技术的基本原理,利用Optisystem 9.0光纤通信系统仿真软件搭建了偏振复用系统的仿真模型。通过MATLAB编程实现了系统所需的信号处理模块,对系统各组成部分的结构和原理进行了详细介绍。分析了偏振模色散和偏振相关损耗的成因,研究了偏振复用系统中信号串扰产生的原因。从理论上分析了偏振解复用的原理,得出了解复用的实质就是求解分离矩阵(传输矩阵的逆矩阵)的结论,为后续解复用算法的实现做了充分的准备。
其次,利用CMA实现偏振解复用。对基于随机梯度下降的恒模算法(SGD-CMA)、RLS-CMA算法和QR-RLS-CMA算法进行了数学推导,并以表格的形式给出了这些算法的主要步骤以及变量初值的设定。针对偏振复用系统传输矩阵的特点,改进了RLS-CMA算法,首次使用QR-RLS-CMA算法进行解复用。利用星座图和眼图分析了这三种算法的解复用效果,并对它们的收敛性能进行研究,通过分析得到了QR-RLS-CMA算法稳定性最强的结论。
再次,利用ICA实现偏振解复用。介绍了复数ICA的基本概念和估计准则,分析了复数ICA解复用技术在偏振复用系统中的可行性。使用MATLAB开发出了适用于偏振复用系统的基于负熵最大化的不动点算法(T-CMN),并以表格的形式给出了渐进正则化T-CMN算法和对称正则化T-CMN算法的主要步骤。对对称正则化T-CMN算法的解复用效果进行了仿真,从多个方面与基于张量的ICA算法相比较,结果显示对称正则化T-CMN算法不需要求解信道矩阵的逆从而降低了系统复杂度。利用眼图分析了T-CMN算法的解复用效果,结果显示T-CMN算法的解复用效果较好。
最后,利用Viterbi-Viterbi算法对解复用后的信号进行相位估计,还原出QPSK调制的源信号,然后通过门限判决的方法得到接收比特序列,利用误码率测试模块将接收比特序列与发送比特序列直接比较得到系统误码率,经测量系统无误码。
With the growth of people’s demand for communication services, enhancing system capacity is imperative. Using the polarization property of optics transmitted in a single mode fiber, Polarization multiplexing (PM) technique aims at creating two independent communication channels over the transmission wavelength by using the independent and mutually orthogonal polarization, which can double the capacity of optical fiber communication system and increase spectrum efficiency. This technique can upgrade system rapidly and economically on the existing optical network. The two polarizations can be affected by polarization mode dispersion, polarization dependent loss etc., which will cause crosstalk between each other. The most important problem to be solved in polarization multiplexing system is eliminating the crosstalk between the received signals, which can be called polarization de-multiplexing. According to the principle of polarization multiplexing technology and characteristics of polarization multiplexing system, the major work of this paper is studying and finding a suitable method for polarization de-multiplexing. This paper has done a lot of further work of polarization multiplexing technology on the basis of previous research. In order to verify the validity of polarization de-multiplexing algorithm, we establish the simulation model of polarization multiplexing system. First of all, we research on the polarization de-multiplexing method carried out by using constant modulus algorithm (CMA).
The Recursive Least Squares constant modulus algorithm (RLS-CMA) is modified based on feature of transmission matrix in polarization multiplexing system, and then we show the de-multiplexing results of this algorithm. In order to get a more robust de-multiplexing algorithm based on the CMA, it is the first time to use RLS-CMA algorithm based on QR decomposition (QR-RLS-CMA) as the de-multiplexing algorithm in polarization multiplexing system. This algorithm is not sensitive about initial values, furthermore it has strong robustness. Moreover, we research on the polarization de-multiplexing method carried out by using independent component analysis (ICA). According to characteristics of polarization multiplexing system, a fixed-point algorithm based on complex maximization of negentropy is used as the de-multiplexing method in polarization multiplexing system for the first time. This algorithm can realize de-multiplexing of different modulation format just by adjusting nonlinear function. It doesn’t need solving inverse of channel matrix, which can significantly reduce complexity while guaranteeing the de-multiplexing performance. The works in this paper are as follows:
Firstly, a simulation model of the polarization multiplexing system based on the principle of polarization multiplexing technology has been established by using Optisystem 9.0 fiber communication software. The signal processing module requiring for de-multiplexing is realized by MATLAB programming. Each part of the system has been introduced in detail. The origins of polarization mode dispersion and polarization dependent loss have been analyzed; in addition, the causes of crosstalk have been researched. As the principle of polarization de-multiplexing has been analyzed from the theoretical, we get the conclusion that the essence of de-multiplexing is solving the separating matrix.
Secondly, polarization de-multiplexing is carried out by using CMA. We focus on the Stochastic Gradient Descent constant modulus algorithm (SGD-CMA), RLS-CMA algorithm and QR-RLS-CMA algorithm, giving the mathematical deduction of these algorithms. The main steps and initial value of these algorithms have been given in table. The RLS-CMA algorithm is modified based on feature of transmission matrix in polarization multiplexing system, and QR-RLS-CMA algorithm used as the de-multiplexing method in polarization multiplexing system at the first time. De-multiplexing results of these algorithms have been analyzed by using constellations diagram and eye diagram, comparing the convergence among these algorithms, and then we get the conclusion that QR-RLS-CMA algorithm has the best performance among these algorithms.
Thirdly, polarization de-multiplexing is carried out by using ICA. The basic conception of complex ICA and the estimation principle are introduced in detail, and then the feasibility of the de-multiplexing of polarization multiplexing system with complex ICA is analyzed. The fixed-point algorithm based on complex maximization of negentropy (T-CMN) is developed by MATLAB programming. The main steps of deflationary regularization T-CMN algorithm and symmetric regularization T-CMN algorithm are given in table, and then we show the de-multiplexing results of symmetric regularization T-CMN algorithm by simulation. The symmetric regularization T-CMN algorithm and tensor based ICA algorithm have been compared in several aspects, the results shows that symmetric regularization T-CMN algorithm doesn’t need solving inverse of channel matrix, which can significantly reduce complexity while guaranteeing the de-multiplexing performance. Comparing de-multiplexing performance between CMA and T-CMN algorithm by using eye diagram, the result shows that T-CMN algorithm has better robustness.
Finally, we use Viterbi-Viterbi algorithm to estimate signal phase to recover the original signal, and then we get the received bit sequence by using threshold judgment. System bit error ratio can be tested through bit error test module by comparing the bit sequence between transmitted bits and received bits. After measurement of bit error rate, the result shows that this system is error-free.
引文
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