lms算法毕业论文

lms算法毕业论文

LMS算法研究

专 业：通信工程

摘 要

因LMS算法具有低计算复杂度、在平稳环境中的收敛性好、其均值无偏地收敛到wiener解和利用有限精度实现算法时的稳定性等特性，使LMS算法成为自适应算法中应用最广泛的算法。对LMS算法及其改进算法进行了研究，探讨了步长因子??n?对各种算法收敛性、稳定性的影响。并用MATLAB对其学习曲线、收敛速度等进行了仿真分析。结果表明，变步长??n?的取值尤为重要，如果μ（n）取较大值则具有较快的收敛速度，如果μ（n）取值很小，则MLMS算法近似等效于LMS算法。它们的自适应过程较快，性能有了很大改进。

2

Abstract

Because of low computational complexity, stable environment in the convergence of good, unbiased and its mean converges to the wiener solution and implementation algorithms using finite precision stability and other characteristics, LMS algorithm as adaptive algorithm in the application of the most a wide range of algorithms.We have a detailed study on LMS algotithm and its complementary algotithm,disscused the step-size’s influent for the algorithm’s convergence speed and stability. And using MATLAB simulated the learning curve, convergence speed of LMS algotithm.The result observed that the value of variable step-size μ（n）is very important,if it is a bigger may have a fast convergence speed,but if not ,the NLMS algotithm can instead the LMS algotithm in the characteristics. In addition , they have a fast adaptive course and greatly progress in performance.

Keywords：LMS algorithm，Adaptive，NLMS algorithm，Variable step，MATLAB simulation.

3

目 录

第一章 绪论 .............................................................................. 6 1.1 自适应滤波理论的发展 ............................................................... 6 1.2 自适应LMS算法的发展 ............................................................... 7 1.2.1 LMS算法历史 .................................................................... 7 1.2.2 LMS算法的现状 .................................................................. 7 1.2.3 LMS算法的发展前景 .............................................................. 7 第二章 自适应LMS算法的研究 .............................................................. 9 2.1 概述 ............................................................................... 9 2.2 LMS算法 ........................................................................... 9 2.2.1自适应收敛性 ................................................................... 11 2.2.2平均MSE——学习曲线 ........................................................... 12 2.2.3 失调 .......................................................................... 14 2.2.4 缩短收敛过程的方法 ............................................................ 15 第三章LMS自适应滤波器的改进形式 ........................................................ 17 3.1归一化LMS算法 ..................................................................... 17 3.1.1 TDO-LMS算法 ................................................................... 19 3.1.2 MLMS算法 ...................................................................... 20 3.2 泄露LMS算法 ...................................................................... 21 3.3 极性LMS算法 ...................................................................... 22 3.4 LMS算法梯度估计的平滑 ............................................................. 22 3.5 解相关LMS算法 .................................................................... 23 3.6 性能比较 .......................................................................... 24 第五章 LMS算法的应用 .................................................................... 25 5.1 LMS类均衡器 ....................................................................... 25 5.1.1 解相关LMS（Decorrelation LMS,DLMS）均衡算法 ................................... 25 5.1.2 变化域解相关LMS均衡算法 ...................................................... 25 5.2 自适应信号分离器 .................................................................. 26 5.3 自适应陷波器 ...................................................................... 27 5.4系统辨识或系统建模 ................................................................. 27 第六章 仿真及其结果分析 ................................................................. 29 6.1仿真思路 ........................................................................... 29 6.2结果及分析 ......................................................................... 29 6.2.1 LMS及其改进算法 ............................................................... 29 6.2.2 LMS自适应均衡器 ............................................................... 32 6.2.3 自适应信号分离器 .............................................................. 34 6.2.4 自适应陷波器 .................................................................. 34 6.2.5系统辨识或系统建模 ............................................................. 34 结 论 ................................................................................ 36

4

参考文献 ................................................................................ 37 附录Ⅰ 英文原文及译文 ................................................................... 38 附录Ⅱ 仿真程序 ......................................................................... 51 致 谢 ................................................................................ 65

5