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Article(id=1251505538253668823, tenantId=1146029695717560320, journalId=1251233954884272221, issueId=1251505536634667461, articleNumber=null, orderNo=null, doi=10.13682/j.issn.2095-6533.2025.06.003, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1737561600000, receivedDateStr=2025-01-23, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1776311772168, onlineDateStr=2026-04-16, pubDate=1762704000000, pubDateStr=2025-11-10, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1776311772168, onlineIssueDateStr=2026-04-16, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1776311772168, creator=13701087609, updateTime=1776311772168, updator=13701087609, issue=Issue{id=1251505536634667461, tenantId=1146029695717560320, journalId=1251233954884272221, year='2025', volume='30', issue='6', pageStart='1', pageEnd='130', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1776311771782, creator=13701087609, updateTime=1776311824541, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1251505758014226723, tenantId=1146029695717560320, journalId=1251233954884272221, issueId=1251505536634667461, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1251505758014226724, tenantId=1146029695717560320, journalId=1251233954884272221, issueId=1251505536634667461, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=21, endPage=30, ext={EN=ArticleExt(id=1251505538434023901, articleId=1251505538253668823, tenantId=1146029695717560320, journalId=1251233954884272221, language=EN, title=Adaptive equilibrium processing optimization algorithm for optical fiber channel damage, columnId=null, journalTitle=Journal of Xi'an University of Posts and Telecommunications, columnName=null, runingTitle=null, highlight=null, articleAbstract=

A cascaded Kalman filter fiber channel damage adaptive equalization processing optimization algorithm，which is based on the multiple input multiple output constant module algorithm（MIMO-CMA）is proposed to address the issues of excessive rotation of state of polarization（RSOP）speed，polarization mode dispersion（PMD），residual chromatic dispersion，polarization dependent loss（PDL），residual carrier frequency offset（CFO），and carrier phase noise（CPN）that seriously affect communication quality in extreme conditions of optical fiber polarized light signals.Firstly，the quadrature phase shift keying（QPSK）signal containing various optical fiber channel impairments is balanced using MIMO-CMA to achieve residual dispersion and preliminary polarization effect related impairments.Then，the Kalman filter is adopted to balance the residual RSOP damage，CFO，and CPN.Simulation results show that the constellation recovery effect of the input signal after the equalization of the optimization algorithm is good，and the trackable RSOP speed can reach over 9Mrad·s-1，and can effectively reduce the computational complexity of the algorithm.

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针对极端条件下光纤偏振光信号的偏振态旋转（Rotation of State of Polarization，RSOP）速度过快，以及本身存在的偏振模色散（Polarization Mode Dispersion，PMD）、残余色散、偏振相关损耗（Polarization Dependent Loss，PDL）、残余载波频率偏移（Carrier Frequency Offset，CFO）和载波相位噪声损伤（Carrier Phase Noise，CPN）严重影响通信质量的问题，提出一种基于多输入多输出系统盲均衡算法（Multiple Input Multiple Output-Constant Modulus Algorithm，MIMO-CMA）级联卡尔曼滤波器光纤信道损伤自适应均衡处理优化算法。首先，将包含各种光纤信道损伤的正交相移键控（Quadrature Phase Shift Keying，QPSK）信号使用MIMO-CMA完成残余色散与初步的偏振效应相关损伤均衡，再使用卡尔曼滤波器均衡残余的RSOP损伤、CFO及CPN。仿真结果表明，经过优化算法均衡后的输入信号，其星座图恢复效果良好，且能追踪的RSOP转速可以达到9Mrad·s-1以上，有效降低了算法的计算复杂度。

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赵尔乐（1998-），男，四川广元人，西安邮电大学硕士研究生，主要研究方向为相干光通信中的DSP技术。E-mail:

山蕊（1986-），女，陕西咸阳人，博士，西安邮电大学副教授，主要研究方向为集成电路系统设计。E-mail:

丁洋（1990-），男，陕西渭南人，武汉飞思灵微电子西安研发中心工程师，主要研究方向为相干光通信中DSP技术。E-mail:

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赵尔乐（1998-），男，四川广元人，西安邮电大学硕士研究生，主要研究方向为相干光通信中的DSP技术。E-mail:

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赵尔乐（1998-），男，四川广元人，西安邮电大学硕士研究生，主要研究方向为相干光通信中的DSP技术。E-mail:

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山蕊（1986-），女，陕西咸阳人，博士，西安邮电大学副教授，主要研究方向为集成电路系统设计。E-mail:

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山蕊（1986-），女，陕西咸阳人，博士，西安邮电大学副教授，主要研究方向为集成电路系统设计。E-mail:

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丁洋（1990-），男，陕西渭南人，武汉飞思灵微电子西安研发中心工程师，主要研究方向为相干光通信中DSP技术。E-mail:

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参数数值
载波频偏Δfc/MHz200
相位噪声θc106
光的波长λ/m1.55×10-6
学习率μ10-3
残余色散/（ps·nm-1）200
状态矢量初值S=[a，b，c，d，θ][1，0，0，0，0]
过程方程初值Adiag（[1，1，1，1，1]）
误差协方差初值Pdiag（[1，1，1，1，1]）
过程噪声协方差初值Qdiag（[10-6，10-6，10-6，10-6，10-4]）
测量噪声协方差初值Rdiag（[10-5，10-5]）
光信噪比/dB15
RSOP正常环境转速（κ，ζ，η）/（krad·s-1）30
RSOP极端环境转速（κ，ζ，η）/（Mrad·s-1）5
JPDL的ρ值0.5
光纤长度/km100
PMD矢量分量τ1/ps5×10-12
PMD矢量分量τ2/ps5×10-12
PMD矢量分量τ3/ps7×10-12
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参数说明和默认值设置

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参数数值
载波频偏Δfc/MHz200
相位噪声θc106
光的波长λ/m1.55×10-6
学习率μ10-3
残余色散/（ps·nm-1）200
状态矢量初值S=[a，b，c，d，θ][1，0，0，0，0]
过程方程初值Adiag（[1，1，1，1，1]）
误差协方差初值Pdiag（[1，1，1，1，1]）
过程噪声协方差初值Qdiag（[10-6，10-6，10-6，10-6，10-4]）
测量噪声协方差初值Rdiag（[10-5，10-5]）
光信噪比/dB15
RSOP正常环境转速（κ，ζ，η）/（krad·s-1）30
RSOP极端环境转速（κ，ζ，η）/（Mrad·s-1）5
JPDL的ρ值0.5
光纤长度/km100
PMD矢量分量τ1/ps5×10-12
PMD矢量分量τ2/ps5×10-12
PMD矢量分量τ3/ps7×10-12
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算法乘法器加法器
“MIMO-CMA+IMA+BPS”算法36NCMA1+（12+5F）NIMP+4F+2B（NBPS+8）+2924NCMA1+（6+4F）NIMP+F+26B+8
EKF两阶段级联算法954+88N749+56N
所提算法36NCMA2+56N+50N/P+824NCMA2+32N+42N/P
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算法复杂度分析

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算法乘法器加法器
“MIMO-CMA+IMA+BPS”算法36NCMA1+（12+5F）NIMP+4F+2B（NBPS+8）+2924NCMA1+（6+4F）NIMP+F+26B+8
EKF两阶段级联算法954+88N749+56N
所提算法36NCMA2+56N+50N/P+824NCMA2+32N+42N/P
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光纤信道损伤自适应均衡处理优化算法
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赵尔乐 1 , 山蕊 1 , 丁洋 2
西安邮电大学学报 | 通信与电子 2025,30(6): 21-30
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西安邮电大学学报 | 通信与电子 2025, 30(6): 21-30
光纤信道损伤自适应均衡处理优化算法
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赵尔乐1 , 山蕊1 , 丁洋2
作者信息
  • 1.西安邮电大学电子工程学院，陕西西安 710121
  • 2.武汉飞思灵微电子西安研发中心，陕西西安 710121

    • 赵尔乐（1998-），男，四川广元人，西安邮电大学硕士研究生，主要研究方向为相干光通信中的DSP技术。E-mail:

    山蕊（1986-），女，陕西咸阳人，博士，西安邮电大学副教授，主要研究方向为集成电路系统设计。E-mail:

    丁洋（1990-），男，陕西渭南人，武汉飞思灵微电子西安研发中心工程师，主要研究方向为相干光通信中DSP技术。E-mail:

Adaptive equilibrium processing optimization algorithm for optical fiber channel damage
Erle ZHAO1 , Rui SHAN1 , Yang DING2
Affiliations
  • 1.School of Electronic Engineering，Xi'an University of Posts and Telecommunications，Xi'an 710121，China
  • 2.Xi'an R&D Center，Wuhan Fisilink Microelectronics，Xi'an 710121，China
出版时间: 2025-11-10 doi: 10.13682/j.issn.2095-6533.2025.06.003
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摘要
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针对极端条件下光纤偏振光信号的偏振态旋转（Rotation of State of Polarization，RSOP）速度过快，以及本身存在的偏振模色散（Polarization Mode Dispersion，PMD）、残余色散、偏振相关损耗（Polarization Dependent Loss，PDL）、残余载波频率偏移（Carrier Frequency Offset，CFO）和载波相位噪声损伤（Carrier Phase Noise，CPN）严重影响通信质量的问题，提出一种基于多输入多输出系统盲均衡算法（Multiple Input Multiple Output-Constant Modulus Algorithm，MIMO-CMA）级联卡尔曼滤波器光纤信道损伤自适应均衡处理优化算法。首先，将包含各种光纤信道损伤的正交相移键控（Quadrature Phase Shift Keying，QPSK）信号使用MIMO-CMA完成残余色散与初步的偏振效应相关损伤均衡，再使用卡尔曼滤波器均衡残余的RSOP损伤、CFO及CPN。仿真结果表明，经过优化算法均衡后的输入信号，其星座图恢复效果良好，且能追踪的RSOP转速可以达到9Mrad·s-1以上，有效降低了算法的计算复杂度。

光纤偏振光信号  /  偏振态旋转  /  偏振模色散  /  残余色散  /  偏振相关损耗  /  多输入多输出系统盲均衡算法  /  卡尔曼滤波

A cascaded Kalman filter fiber channel damage adaptive equalization processing optimization algorithm，which is based on the multiple input multiple output constant module algorithm（MIMO-CMA）is proposed to address the issues of excessive rotation of state of polarization（RSOP）speed，polarization mode dispersion（PMD），residual chromatic dispersion，polarization dependent loss（PDL），residual carrier frequency offset（CFO），and carrier phase noise（CPN）that seriously affect communication quality in extreme conditions of optical fiber polarized light signals.Firstly，the quadrature phase shift keying（QPSK）signal containing various optical fiber channel impairments is balanced using MIMO-CMA to achieve residual dispersion and preliminary polarization effect related impairments.Then，the Kalman filter is adopted to balance the residual RSOP damage，CFO，and CPN.Simulation results show that the constellation recovery effect of the input signal after the equalization of the optimization algorithm is good，and the trackable RSOP speed can reach over 9Mrad·s-1，and can effectively reduce the computational complexity of the algorithm.

optical fiber polarized light signal  /  rotation of state of polarization  /  polarization mode dispersion  /  residual chromatic dispersion  /  polarization dependent loss  /  multiple input multiple output-blind equalization algorithm  /  Kalman filter
赵尔乐, 山蕊, 丁洋. 光纤信道损伤自适应均衡处理优化算法. 西安邮电大学学报, 2025 , 30 (6) : 21 -30 . DOI: 10.13682/j.issn.2095-6533.2025.06.003
Erle ZHAO, Rui SHAN, Yang DING. Adaptive equilibrium processing optimization algorithm for optical fiber channel damage[J]. Journal of Xi'an University of Posts and Telecommunications, 2025 , 30 (6) : 21 -30 . DOI: 10.13682/j.issn.2095-6533.2025.06.003
正文
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光纤通信凭借其高带宽、高安全性和灵活性等特点，在光通信领域已经成为最常用的传输技术。该技术已被广泛应用于电信、互联网、云计算、数据中心和医疗保健等领域，促进了该领域技术与应用的进步和创新[1-2]。随着网络流量数据需求的增加，相干光偏振分复用系统已成为提高系统容量的一种有前景的技术。该系统通过允许在同一光载波的两个独立和正交偏振态上传输信息信号，表现出将光谱效率加倍的能力[3]。但是，信号在系统的光纤传输过程中会受到偏振效应相关影响而产生偏振效应相关损伤，包含偏振态旋转（Rotation of State of Polarization，RSOP）、偏振模色散（Polarization Mode Dispersion，PMD）以及偏振相关损耗（Polarization Dependent Loss，PDL）损伤。除此之外，还存在如色散、载波频率偏移（Carrier Frequency Offset，CFO）和载波相位噪声损伤（Carrier Phase Noise，CPN）等其他损伤[4-5]。当在极端的环境下通信时，偏振效应相关损伤会更加明显地导致信号延迟或失真，极大降低了光纤通信质量[6]，因此解决光纤通信相关损伤均衡问题得到越来越多研究者的关注。
近年来，由于相干检测技术以及数字信号处理（Digital Signal Processing，DSP）技术模块的集成化，已经广泛应用到光纤通信系统并对各类损伤做自适应均衡处理，以提高通信质量和系统的抗干扰能力。文献[7]提出了一种可用多输入多输出系统盲均衡算法（Multiple Input Multiple Output-Constant Modulus Algorithm，MIMO-CMA）均衡光纤偏振效应相关损伤的经典算法。该算法以恒模为目标函数，通过梯度下降法不断估计并更新4个滤波器的抽头系数，以实现对偏振相关效应损伤的补偿，但其存在奇异值的缺点。正常情况下RSOP转速通常只有10～100krad·s-1，在遇到雷电等天气条件时，RSOP转速将达到2～8Mrad·s-1。在此极端条件下，MIMO-CMA对输入信号的均衡效果会变差，且无法直接均衡CFO与CPN。因此，文献[8]提出了一种采用MIMO-CMA、改进次方（Improved Mth Power，IMP）以及盲相位搜索（Blind Phase Search，BPS）相结合的算法，即“MIMO-CMA+IMP+BPS”算法，通过该算法对输入信号做自适应均衡处理。该算法虽然可以有效均衡上述的所有损伤，但其采用了3种不同的结构进行硬件设计时会造成资源浪费，对超快转速的RSOP损伤的均衡效果也没有得到有效改善。针对该问题，文献[9]提出了一种基于扩展卡尔曼滤波器（Extended Kalman Filter，EKF）的两阶段级联均衡算法，可以有效跟踪超快速的RSOP损伤。但是，如果要完成全部损伤的均衡，至少需要用到两个甚至更多的EKF，这使得计算复杂度加大，硬件不利于实现。
针对在极端场景下光纤通信系统存在的偏振效应相关损伤、残余色散、CFO与CPN问题，拟提出一种MIMO-CMA级联卡尔曼滤波器光纤信道损伤自适应均衡处理优化算法。首先，通过数学模型依次建模各种光纤信道损伤及光信噪比（Optical Signal-to-Noise Ratio，OSNR），并依次加入到正交相移键控（Quadrature Phase Shift Keying，QPSK）信号。同时，仿真观察进入MIMO-CMA均衡器前包含各种损伤的输入信号星座图，再通过MIMO-CMA对信号进行第一轮均衡，以完成对基本的偏振效应相关损伤及残余色散的补偿。然后，通过卡尔曼滤波器完成对超快速RSOP损伤、CFO以及CPN的均衡。接着，通过仿真对残余色散的容忍度、误码率与光纤长度的影响关系进行分析，对比分析所提算法与经典的“MIMO-CMA+IMP+BPS”算法在正常和极端环境下的均衡性能、对超快速RSOP损伤的追踪效率，最后比较所提算法、经典算法以及EKF均衡算法的计算复杂度。
1　系统网络架构
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光纤通信系统通常采用相干检测技术实现光纤信道各种损伤从光域系统到电域系统的转换。同时，可通过DSP技术完成各类损伤的自适应均衡处理[10]。常见的相干光通信系统主要由发射模块、光纤信道、接收模块3部分组成。其中，在光纤信道方面，相干光通信系统可利用光的偏振态进行偏振复用，以此提高系统的传输容量，而DSP技术主要存在于接收端。设I、Q分别表示基带复信号的实部与虚部，P/2表示90°相位偏移，x与y分别表示在x偏振与y偏振上传输的调制信号，得到的具体相干光通信系统网络架构示意图[11-12]如图1所示。
1.1　数字信号处理
在光纤通信系统中，接收到的光信号经历偏振分集相干探测、信号放大、采样等步骤被转换成数字电信号，之后DSP模块会对信号损伤进行均衡处理。然而，在模数转换采样过程中，本地时钟与发射端时钟之间的时钟差异会导致时钟不同步问题[13]。因此，在一般情况下，首先需要进行时钟校准，防止偏差对后续工作的影响。若将非线性效应造成的影响排除在外，DSP工作的第一步就是补偿色度色散[14-16]。色散模块通常工作量大且复杂，再加上受光纤色散值波动以及补偿算法的影响，补偿后的信号仍然存在一定的残余色散。因此，下一步在做偏振相关效应损伤均衡时还需要考虑残余色散。此外，发射端激光器与接收端本振光源的频率不一致和激光器自身具有的线宽效应导致的CFO与CPN，也都需要做均衡处理[17-19]。若不进行偏振效应相关损伤的均衡，接收到的两路信号会混叠在一起。为了更精确地对每个信号进行恢复，将对CFO与CPN的补偿放在偏振效应相关损伤均衡之后。最后，可以对信号进行判决和解码，大致得到原始数据，并进行误码统计。具体的数字信号处理过程[20]如图2所示。
1.2　偏振效应相关损伤数学模型的建立
RSOP与PMD损伤产生的原因均是光纤的双折射效应，但方式不同，而PDL损伤产生的原因一般是因为光学元器件导致的x路与y路偏振态衰减不一致[21-22]。由于RSOP、PMD与PDL这3种损伤产生的机理都不相同，因此每种损伤建立所需用到的数学模型也存在着较大的差异。
1.2.1　RSOP损伤数学模型的建立
在实验中常采用两参量的Jones矩阵建立RSOP损伤数学模型，但两参量Jones矩阵不能模拟任意状态的偏振态。为了使得RSOP运动轨迹布满整个庞加莱球，可以采用三参量Jones矩阵建立RSOP损伤。RSOP损伤的表达式[23]为
式中：κ、ζ及η表示3个自由度，其中，κ表示方位旋转角，ζ和η表示相位旋转角；j表示虚数单位。
1.2.2　PMD损伤数学模型的建立
对PMD而言，当只考虑一阶偏振模色散时，常在斯托克斯空间中描述PMD损伤。假设斯托克斯空间中的PMD矢量为=（τ1，τ2，τ3）T，其中，τ1，τ2，τ3分别是PMD矢量的3个分量，都是ps量级。由此可获得PMD在对应琼斯空间中的频域矩阵，文献[24]给出了斯托克斯空间到琼斯空间的详细推导过程。PMD损伤的表达式[25-26]为
其中，
式中：Δτ表示PMD的大小，也是PMD矢量的模值，可用差分群时延（Differential Group Delay，DGD）表示PMD大小；φ=ωΔτ，ω表示角频率；为泡利矩阵，σ→=（σ1，σ2，σ3），其中σ1=，σ2=，σ3=。
1.2.3　PDL损伤数学模型的建立
RSOP与PMD损伤并不会改变系统的能量损耗，但PDL会导致两路信号的能量损耗不一致，输出信号的偏振态也随之变化。PDL损伤的表达式[27]为
式中：ρ表示偏振相关损耗参量，其范围为0＜ρ＜1。
2　自适应均衡优化算法
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将所有损伤全部置入QPSK信号中，考虑到传统的MIMO-CMA无法均衡极端条件下超快速旋转的RSOP、CFO、CPN，以及采用基于EKF两阶段级联算法计算复杂度较大的问题，因此选用MIMO-CMA级联卡尔曼滤波器解决。
2.1　全部损伤模型的建立
在光纤信道中的上述所有损伤中，时域损伤包括RSOP、PDL、CFO与CPN，频域损伤包括PMD与残余色散。t时刻CFO、CPN损伤及残余色散的数学公式分别表示为
式中：ΔFc与θc分别表示CFO和CPN的值；β2=-λ2D/2πc，其中，λ表示波长，c表示光在真空中的传播速度。
假设J表示损伤，则JRSOP表示RSOP损伤，JPMD表示PMD损伤，JPDL表示PDL损伤。假设x（t）表示QPSK信号，则将RSOP损伤，CFO、CPN损伤加入QPSK信号的表达式为
式中：表示傅里叶变换。
接着再将PDL损伤、残余色散及PMD损伤代入到式（6），得到的数学公式为
式中：-1表示傅里叶逆变换[26，28]。
2.2　MIMO-CMA级联卡尔曼滤波器算法
将光纤信道损伤建立完成之后，根据光纤通信系统接收端DSP过程与优化算法的基本原理，可以得到光纤信道损伤均衡过程如图3所示。
在图3中，MIMO-CMA级联卡尔曼滤波器算法先经过MIMO-CMA均衡偏振效应相关损伤以及残余色散，再使用卡尔曼滤波器跟踪未均衡好的超快速旋转的RSOP损伤及CFO与CPN。
2.2.1　MIMO-CMA
光纤通信中常采用的系统是MIMO系统。该系统由4个有限长脉冲响应（Finite Impulse Response，Fir）滤波器构成，并呈现出蝶形滤波器结构。周期用T表示，则经过T/2插值采样后，使用MIMO-CMA完成对偏振效应相关损伤的自适应均衡[27]。蝶形Fir滤波器结构如图4所示。
MIMO-CMA是CMA利用QPSK或者其他信号对应的半径信息完成对相关损伤的自适应均衡，其核心是完成对抽头系数的自适应调整。更新抽头系数常采用的方法是最小均方算法，其均衡公式为
式中：k表示时间索引；Ex，in与Ey，in分别为输入信号；Ex，out与Ey，out分别为均衡之后的信号；hxx、hxy、hyx、hyy分别表示4个Fir滤波器的抽头系数。
根据随机梯度算法，4个Fir滤波器的更新公式分别表示[29]为
式中：p表示延迟偏移；μ表示学习率；εx、εy分别表示x路信号、y路信号和与其对应的原始信号间的误差函数，表达式分别为
式中：r表示信号星座点的模值，对于QPSK信号而言，r取值为1。
2.2.2　卡尔曼滤波器
经过MIMO-CMA均衡后的信号，不仅剩下的超快速旋转的RSOP损伤还需要通过卡尔曼滤波器做进一步的跟踪与补偿，而且CFO与CPN也需要得到有效均衡。卡尔曼滤波器分为预测模块与矫正模块，其中预测模块的状态矢量的先验估计与在第i个时刻的先验误差协方差矩阵的表达式[30-32]分别为
式中：Si-1表示状态矢量的后验估计，用于预测下一时刻的状态向量Si，包含旋转偏振角、CFO与CPN；A表示过程方程，用于描述状态如何随时间演化；Q表示过程噪声协方差；Pi-1表示在第i-1个时刻的后验误差协方差矩阵。
在卡尔曼滤波器的矫正模块中，第i个时刻的卡尔曼增益Ki、状态的更新Si以及后验误差协方差矩阵Pi的表达式分别[32-33]为
其中，
式中：R表示测量噪声协方差；Z表示有效的最近星座符号；a、b、c及d用于描述偏振旋转的幅度和方向，其中a和b控制主偏振态的旋转，c和d描述交叉耦合，并满足约束条件a2+b2+c2+d2=1，这一酉性约束是为了保证偏振旋转不改变光功率；交叉项如jax-bx+jcy-dy反映偏振旋转引起的信号干涉；相位项ejθ中θ包含CFO的线性累积和CPN的随机波动，卡尔曼滤波器通过状态变量θ动态跟踪两者。CFO和CPN导致接收信号的相位偏移可通过复数运算捕获这种效应。
Jones矩阵直接对应x、y两路输入信号RSOP旋转，ejθ同时引入CFO与CPN共同造成的相位偏移，最终生成含损伤的观测信号供卡尔曼滤波器与实际接收信号比较。根据卡尔曼滤波器相关物理参数与损伤的映射意义，设状态矢量为S=[a，b，c，d，θ]T。
3　仿真结果及分析
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为了验证通信系统的有效性，首先，通过星座图直观展示所提算法对QPSK信号的均衡效果。然后，利用仿真曲线分析优化算法对残余色散的容忍度，同时探讨误码率与光纤长度之间的关系，进一步分析系统的性能变化趋势。为了全面评估所提算法，将其与经典的“MIMO-CMA+IMP+BPS”算法在两种典型环境下进行对比分析，接着观察误码率随RSOP的变化情况，并对通信系统性能做具体分析。最后，为了全面评估所提算法的实际应用潜力，将其与经典的“MIMO-CMA+IMP+BPS”算法、基于EKF的两阶段级联算法在计算复杂度方面进行对比分析。通过对仿真结果的分析，为光纤通信系统的优化提供理论依据和实践指导。
3.1　仿真环境及参数设置
仿真环境为Matlab r2021a以及VPI Design Suite 11.1，由于色散补偿光纤的成本较高，因此采用的光纤为标准单模光纤。仿真所用到的默认参数设置如表1所示，若没有特殊说明，表1中的参数值在仿真过程中保持不变。
3.2　星座图分析
3.2.1　含全部损伤QPSK信号模型分析
若系统中含有各种光纤信道损伤，会导致在光纤通信系统接收端接收到的QPSK信号发生较大变化，具体体现在星座点的位置变化上。通过Matlab仿真可以观察到正常的QPSK调制信号星座图与在极端环境下经过T/2插值采样后进入MIMO-CMA之前含各种损伤的信号星座图的变化情况，具体结果分别如图5、图6与图7所示。由图5可知，正常QPSK信号的调制星座点均分布在模值为1且横纵坐标绝对值相等的4个点附近。但是，由图6和图7可以看出，含多种损伤的QPSK信号不管是x路还是y路，星座点都随机遍布在很大一片区域，说明QPSK信号在加入了光纤信道损伤之后发生了极大的改变，导致接收端难以直接接收到正常的QPSK信号。
3.2.2　MIMO-CMA分析
将输入信号经过MIMO-CMA算法均衡后，分别在极端与正常两种环境下得到信号星座图，分别如图8和图9所示。
由图8可以看出，在极端环境下经过MIMO-CMA均衡后的传输信号形成的环较为模糊，点分布很乱，说明除了CFO与CPN不能有效均衡外，超快速旋转的RSOP损伤也未能得到有效补偿。由图9可以看出，在正常环境下经过MIMO-CMA均衡后的传输信号呈现出一定的环形，说明除了CFO与CPN未得到有效均衡外，RSOP、PMD及PDL均得到有效均衡。
3.2.3　卡尔曼滤波器分析
卡尔曼滤波器可以进一步对RSOP损伤进行追踪，以及对CFO、CPN作补偿。由于正常环境下MIMO-CMA对输入信号的均衡效果良好，因此选择极端环境作为观察卡尔曼滤波器对经过MIMO-CMA均衡后的输入信号恢复效果的仿真条件。该信号再次经过卡尔曼滤波器均衡后的星座图如图10所示。
由图10可以看出，经卡尔曼滤波器均衡后的信号星座点明显又大多集中到了QPSK信号对应4个星座点的位置。说明除了超快转速的RSOP损伤得到了有效跟踪与补偿外，CFO与CPN也得到了有效均衡。
3.3　系统性能相关参数分析
基于EKF两阶段级联算法是在假设色度色散补偿效果完美的情况下进行的，但实际上在对信号做了色度色散补偿之后仍然会留下一定的残余色散，若不做补偿处理，在传输过程中会不断累加，最终降低通信质量。因此，针对残余色散需要拥有一定程度的容忍度。星座图可以直观地反映MIMO-CMA对光纤信道的均衡效果，但判定算法均衡成功的指标是误码率。经过仿真之后，得到的MIMO-CMA的误码率与残余色散的关系如图11所示。通信质量良好的标准为误码率低于0.02。因此，由图11可以看出，MIMO-CMA对残余色散的容忍度达到了正负500ps·nm-1，说明该算法可以完成一定程度的残余色散补偿。
光纤越长，在传输时可能会放大偏振动态性和相位噪声的累积效应，对通信质量的影响也就会越大。通过仿真得到的极端环境下，所提算法的误码率与光纤长度的关系如图12所示。
由图12可以看出，在极端环境下，光纤长度即使达到了300km，误码率依然低于0.02，通信质量较好。
OSNR也是影响光纤通信质量的关键因素。分别在正常环境与极端环境下仿真所提算法与经典的“MIMO-CMA+IMP+BPS”算法的误码率随OSNR的变化情况，具体如图13所示。
由图13可以看出，正常条件下，两种算法均可以完成对各种光纤信道损伤的自适应均衡。但是，所提算法的误码率在OSNR为10dB时先于“MIMO-CMA+IMP+BPS”算法降到0.02以下，且误码率一直低于“MIMO-CMA+IMP+BPS”算法，说明所提算法的抗干扰能力更强。在极端条件下，“MIMO-CMA+IMP+BPS”算法的损伤均衡效果非常不理想，而所提算法在OSNR达到10dB时，误码率依然低于0.02，说明所提算法是可行的。
假设除RSOP与PMD外无其他损伤，OSNR为15dB，分别仿真MIMO-CMA与所提算法之间的误码率与RSOP转速的关系，并观察两种算法对超快速RSOP损伤的跟踪效果。误码率与RSOP转速的关系如图14所示。
由图14可以看出，MIMO-CMA只要在极端条件下，其误码率就一直远高于0.02，不能直接用于通信，而所提算法对RSOP的跟踪效果达到了9Mrad·s-1以上。因此，所提算法相对于MIMO-CMA能更有效地完成对极端环境下光纤信道损伤的自适应均衡。
3.4　复杂度分析
算法复杂度在硬件实现中亦是一个极为重要的性能指标。仿真中，经典算法与所提算法中的MIMO-CMA抽头系数分别为NCMA1和NCMA2。在“MIMO-CMA+IMP+BPS”算法中，NIMP表示IMP算法平滑滤波器长度，F表示IMP算法测试频率的数量，NBPS表示BPS算法平滑滤波器的长度，B表示BPS算法测试相位的数量，在基于EKF两阶段级联算法中，N表示CFO的符号数[26]。在所提算法中，P表示双偏振并行处理。所提算法、“MIMO-CMA+IMP+BPS”算法与基于EKF两阶段级联算法的计算复杂度如表2所示。
在仿真中，NCMA1为35，NCMA2为17，NIMP为1024，F为500，NBPS为31，B为32，N为1024，P为2，得到“MIMO-CMA+IMP+BPS”算法所需的乘法器个数为2578073个，加法器个数为2056324个。基于EKF两阶段级联算法所需的乘法器个数为91066个，加法器个数为58093个。所提算法所需乘法器个数为83564个，所需加法器个数为54680个。因此，所提算法的计算复杂度是三者当中最低的。
4　结语
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针对光纤通信中存在的光纤信道损伤自适应均衡问题，提出了一种基于MIMO-CMA级联卡尔曼滤波器的优化算法。先对QPSK信号建立极快转速的RSOP以及PMD等其他各种损伤，然后将信号作为输入信号输入到MIMO-CMA中进行第一轮自适应均衡，完成PDL、残余色散、PMD及基本的RSOP损伤均衡，再通过卡尔曼滤波器补偿残余的RSOP损伤，并均衡CFO与CPN。仿真结果表明，相较于其他算法，所提算法既能完成对超快速旋转的RSOP、PMD和其他损伤的跟踪与均衡，又能减少计算复杂度，有利于硬件的实现，比如在现场可编程门阵列上能够满足超高速光通信实时处理要求的高吞吐率。
文献
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2025年第30卷第6期
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doi: 10.13682/j.issn.2095-6533.2025.06.003
  • 接收时间：2025-01-23
  • 首发时间：2026-04-16
  • 出版时间：2025-11-10
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  • 收稿日期：2025-01-23
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    1.西安邮电大学电子工程学院，陕西西安 710121
    2.武汉飞思灵微电子西安研发中心，陕西西安 710121
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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