学科门类： 工 学 单位代码：90006 中图分类号：TN911 密 级：公开
硕士研究生学位论文
DMT系统有色噪声下均衡理论的研究
一级学科：信息与通信工程 学科专业：通信与信息系统 研究方向：宽 带 接 入 技 术 培养院所：通信工程学院 研 究 生：伍 云 指导教师： 柯赓 教授
DMT系统有色噪声下均衡理论的研究
摘 要
在数字传输系统中，均衡器是接收机的一个必不可少的模块，在接收滤波器和抽样判决器之间插入一种滤波器来校正或补偿系统特性，减小码间串绕的影响。因此，均衡是数字通信的关键技术之一和研究热点，有大量的理论和实际问题有待解决。
论文首先介绍DSL的历史和发展未来，特别是ADSL的性能，然后介绍本课题的研究背景。对DMT传输系统进行分析，给出通信性能的评测标准，并对该系统的重要部分重点分析，建立了完整的用于研究DMT均衡算法的MATLAB仿真系统。
其次介绍研究均衡算法的主要数学背景，用统一的公式对均衡器的现有算法进行分类，分析总结现有的均衡算法，并且比较各自的优缺点。然后又研究了MMSE、MSSNR、MERRY算法中的对称性，通过对称性的分析来简化算法的复杂度得到Sym-MMSE、Sym-MSSNR、Sym-MERRY算法，并通过仿真分别给出原算法和对称性算法的性能比较。
接着通过分析比较得出PTEQ是最佳适合本研究背景的算法，并针对其计算量大的缺点设计改进算法，并仿真比较性能。
最后，本文对已做工作进行了简明归纳，并对下一步研究进行了展望。
关键词：数字用户环路 DMT 均衡 串扰 对称性
Abstract
In a digital transmission system, Equalization is an essential receiver function in order to compensate for the channel's dispersion in the time domain and the channel's distortion in the frequency domain of the transmitted waveform.. Many new research productions about equalization can drive the DMT to use in practice. In the sequel, equalization is the one of the key technique in digital communication system, and there are a mass of theory and practice problems to be solved.
Firstly, the paper introduces the history and future of DSL, especially the performance of ADSL, then analyses the parts of the DMT system, especially the important part, finally establishes the matlab simulate environment.
Secondly, A conventional ADSL equalizer consists of a time-domain equalizer and a frequency domain equalizer. Almost all of the algorithms fit into the same formulation: the maximization of a generalized Rayleigh quotient or a product of generalized Rayleigh quotients. The paper summarizes the existing TEQ algorithm using the formulation, and compares respective good and bad points. Then, studies well-known properties of the eigenvectors of symmetric centrosymmetric matrices, and extends these properties to MMSE, MSSNR and MERRY to get Sym-MMSE, Sym-MSSNR, Sym-MERRY, and compares respective performance.
Thirdly, the thesis studies the results of matlab simulation and proposes a practical PTEQ algorithm for the actual system, and compares its performance by simulation.
Finally, all works that have been done are summarized, and the works that will be done next are proposed at the end of this thesis.
Wu yun（Commnunication and Information System） Directed by Professor Ke-geng
Key words:Digital Subscriber Line (DSL) DMT Equalization Crosstalk Rayleigh quotient Symmetry .
目 录
第一章绪论 ................................................................................................................... 1 1.1
DSL的历史和未来 ......................................................................................... 1
DSL的历史 .............................................................................................. 1 DSL的未来 .............................................................................................. 2 传输媒质及回路频响............................................................................... 3 噪声........................................................................................................... 4
1.1.1. 1.1.2. 1.2 1.2.1 1.2.2 1.3 1.4 1.5
ADSL的用户线性能及工作环境 .................................................................. 2
课题的提出...................................................................................................... 6 主要工作........................................................................ 错误！未定义书签。 论文的内容安排.............................................................................................. 7
第二章 DMT系统和仿真模型 ................................................................................... 8 2.1
DMT简介 ........................................................................................................ 8
调制的基本概念....................................................................................... 8
2.1.1
2.1.2 DMT传输 .................................................................................................... 8 2.1.3 DMT的应用 .............................................................................................. 13 2.2 2.3
通信性能评测................................................................................................ 13 主要仿真环境模块........................................................................................ 14
测试线路模块......................................................................................... 14 噪声环境模块......................................................................................... 15
2.3.1 2.3.2
第三章 时域均衡算法分析 ....................................................................................... 17 3.1
数学背景........................................................................................................ 17
广义Rayleigh商 .................................................................................... 18 通用公式................................................................................................. 20
3.1.1 Rayleigh商 ................................................................................................. 17 3.1.2 3.1.3
3.2 单个RAYLEIGH商情况 ..................................................................................... 21 3.2.1 MMSE .......................................................................................................... 21 3.2.2 MSSNR ...................................................................................................... 25 3.2.3 Min-ISI ....................................................................................................... 29 3.2.4 MERRY ...................................................................................................... 32 3.2.5 MDS最小时延算法 .................................................................................. 33 3.3
多个滤波器，每个都是单个RAYLEIGH商情况 ......................................... 34 3.3.1 PTEQ（每信道均衡） .............................................................................. 34 3.3.2 TEQFB(TEQ滤波器组) ............................................................................ 36 3.4
多个RAYLEIGH商情况 ................................................................................. 38
最大几何信噪比算法MGSNR ............................................................. 38
3.4.1
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