改进的双曲正切函数的变步长LMS算法

doi:10.11959/j.issn.1000-436x.2020224

通信学报 ›› 2020, Vol. 41 ›› Issue (11): 116-123.doi: 10.11959/j.issn.1000-436x.2020224

改进的双曲正切函数的变步长LMS算法

章坚武¹,余皓¹,章谦骅²()

¹ 杭州电子科技大学通信工程学院，浙江杭州 310018
² 之江实验室智能网络研究中心，浙江杭州 311121

修回日期:2020-09-17 出版日期:2020-11-25 发布日期:2020-12-19
作者简介:章坚武（1961- ），男，博士，浙江杭州人，杭州电子科技大学教授、博士生导师，主要研究方向为移动通信、多媒体信号处理与人工智能、通信网络与信息安全等|余皓（1995- ），男，安徽黄山人，杭州电子科技大学硕士生，主要研究方向为自适应信号处理、同时同频自干扰信号消除等|章谦骅（1990- ），男，浙江杭州人，浙江大学博士生，之江实验室智能网络研究中心工程师，主要研究方向为无线网络、物联网、智慧城市等
基金资助:
工信部2019年产业技术基础公共服务平台基金资助项目(2019-00891-2-1)

Improved variable step-size LMS algorithm based on hyperbolic tangent function

Jianwu ZHANG¹,Hao YU¹,Qianhua ZHANG²()

¹ School of Communication Engineering,Hangzhou Electronic Science and Technology University,Hangzhou 310018,China
² Research Center for Intelligent Networks,Zhejiang Lab,Hangzhou 311121,China

Revised:2020-09-17 Online:2020-11-25 Published:2020-12-19
Supported by:
The Project of Industrial Technology Basic Public Service Platform of the Ministry of Industry and Information Technology in 2019(2019-00891-2-1)

摘要/Abstract

摘要：

为了解决定步长 LMS 算法不能同时满足快速收敛和低稳态误差的问题，提出了一种基于改进双曲正切函数的变步长LMS算法（IVSSLMS）。该算法利用步长反馈因子的二范数和误差信号的相关值来调节步长，克服了定步长算法收敛速度慢及抗噪声能力差的问题；并从理论上分析了算法的性能，给出了参数的取值方法。仿真实验结果表明，在高/低信噪比条件下，IVSSLMS 算法比已有变步长算法的收敛速度更快、稳态误差更小、系统跟踪能力更优。

关键词: 最小均方算法, 双曲正切函数, 稳态误差, 归一化

Abstract:

In order to improve that the LMS algorithm for determining step size cannot satisfy both rapid convergence and low steady-state misalignment errors,a variable step size algorithm (IVSSLMS) based on an improved hyperbolic tangent function was proposed.The step size feedback factor and the correlation value of the error signal were used to adjust the step size,and the problems of slow convergence speed and poor anti-noise ability of the fixed-step size algorithm was overcame.The performance and parameters settings of the proposed algorithm were analyzed.The simulation results show that IVSSLMS has a faster convergence rate,lower steady-state error and better system tracking capability than the existing variable step size algorithms under high and low SNR conditions.

Key words: LMS algorithm, hyperbolic tangent function, steady state misalignment error, normalization

中图分类号:

TN927

章坚武,余皓,章谦骅. 改进的双曲正切函数的变步长LMS算法[J]. 通信学报, 2020, 41(11): 116-123.

Jianwu ZHANG,Hao YU,Qianhua ZHANG. Improved variable step-size LMS algorithm based on hyperbolic tangent function[J]. Journal on Communications, 2020, 41(11): 116-123.

图/表 7

图1

图2

图3

图4

图5

表1

几种变步长算法对比"

算法	变步长算法流程	参数	参数取值（SNR=30 dB）	参数取值（SNR=15 dB）
	$J (n) = k J (n - 1) + e (n) X (n)$
IVSSLMS算法	$μ (n) = α (1 - \frac{m + 1}{m + \exp (β \| e (n) e (n - 1) \| {‖ J (n) ‖}^{2})})$	α,β	0.85，3 500	0.55，4 000
	$W (n + 1) = W (n) + \frac{2 μ (n) e (n) X (n)}{φ + X^{T} (n) X (n)}$	m,k	15，0.9	10，0.9
文献[18]	$μ (n) = α (1 - \frac{m + n}{m + n \exp (β \| e (n) e (n - 1) \| + λ \| e (n) \|)})$	α,β	0.85，2 000	0.65，2 000
		m,n	1 000，500	700，500
	$W (n + 1) = W (n) + 2 μ (n) e (n) X (n)$	λ	0.01	0.01
文献[19]	$J (n) = 1 - \frac{m}{m + \exp (β \| e (n) e (n - 1) \| + λ \| e (n) \| - 1}$	α,β	0.85，10	0.65，100
	$μ (n) = α μ (n - 1) + (1 - α) J (n)$	m,λ	100，0.01	10，0.01
	$W (n + 1) = W (n) + 2 μ (n) e (n) X (n)$
文献[20]	$μ (n) = \frac{λ}{φ + X^{T} (n) X (n)} atan (β ‖ e (n) X (n) ‖)$	λ,φ	0.85，0.001	0.65，0.001
	$W (n + 1) = W (n) + 2 μ (n) e (n) X (n)$	β	10	10
	$p (n + 1) = α p (n) + γ e^{2} (n)$
文献[21]	$μ (n) = {\begin{cases} μ_{max}, p (n + 1) < μ_{max} \\ μ_{min}, p (n + 1) > μ_{max} \\ p (n + 1), 其他 \end{cases}$	α,β	0.57，5	0.27，8
		λ,b	0.01，0.65	0.35，1.65
		μ_max	0.8	0.6
	$q (n) = \frac{sign (W (n))}{1 + b \| W (n) \| + b^{2} {‖ W (n) ‖}^{2}}$	μ_min	0.01	0.01
	$W (n + 1) = W (n) + 2 μ (n) e (n) X (n) - λ μ (n) q (n)$

表1

图6

参考文献 21

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改进的双曲正切函数的变步长LMS算法

Improved variable step-size LMS algorithm based on hyperbolic tangent function

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