带零吸收项的变步长l0范数归一化最小均方误差算法

doi:10.3969/j.issn.1000-1093.2016.11.027

兵工学报 ›› 2016, Vol. 37 ›› Issue (11): 2170-2176.doi: 10.3969/j.issn.1000-1093.2016.11.027

• 研究简报 • 上一篇

带零吸收项的变步长l₀范数归一化最小均方误差算法

管四海¹, 李智¹，黄辉²，王哲³

(1.西安电子科技大学机电工程学院, 陕西西安 710071；2. 西安电子科技大学电子工程学院，陕西西安 710071；3.西安航天动力测控技术研究所，陕西西安 710025)

收稿日期:2016-01-06 修回日期:2016-01-06 上线日期:2016-12-30
通讯作者: 管四海 E-mail:gcihey@sina.cn
作者简介:管四海（1990—），男，博士研究生
基金资助:
国家自然科学基金项目（61074120）；高等学校博士学科点专项科研基金项目(2011020311004)

Modified Zero-Attracting l₀-NLMS Algorithm

GUAN Si-hai¹， LI Zhi¹, HUANG Hui², WANG Zhe³

(1.School of Mechano-Electronic Engineering, Xidian University, Xi'an 710071, Shaanxi, China;2.School of Electronic Engineering, Xidian University, Xi'an 710071, Shaanxi, China;3.Xi'an Aerospace Power Measurement and Control Technology Institute, Xi'an 710025, Shaanxi, China)

Received:2016-01-06 Revised:2016-01-06 Online:2016-12-30
Contact: GUAN Si-hai E-mail:gcihey@sina.cn

摘要/Abstract

摘要： 针对稀疏系统的识别问题，提出一种带零吸收项的变步长l₀范数约束归一化最小均方误差 (l₀-NLMS)算法。在此改进的l₀-NLMS算法中,通过箕舌函数来调整步长的变化,理论推导了此l₀-NLMS算法在均值和均方差下的收敛条件以及均方误差和均方偏移量的表达式。设计实验分别比较在不同输入信号时算法的步长和稳态偏移量的变化,通过仿真验证该算法在识别稀疏信道模型上是有效的。分析结果表明：当处于相对高的信噪比、低的信噪比、输入不相关信号和输入相关信号时,该算法具有较快的收敛速度，能很好地进行稀疏系统的模型识别。针对稀疏系统的识别问题，提出一种带零吸收项的变步长l₀范数约束归一化最小均方误差 (l₀-NLMS)算法。在此改进的l₀-NLMS算法中,通过箕舌函数来调整步长的变化,理论推导了此l₀-NLMS算法在均值和均方差下的收敛条件以及均方误差和均方偏移量的表达式。设计实验分别比较在不同输入信号时算法的步长和稳态偏移量的变化,通过仿真验证该算法在识别稀疏信道模型上是有效的。分析结果表明：当处于相对高的信噪比、低的信噪比、输入不相关信号和输入相关信号时,该算法具有较快的收敛速度，能很好地进行稀疏系统的模型识别。

关键词: 信息处理技术, 稀疏系统, l₀范数约束归一化最小均方误差算法, 变步长, 系统噪声, 箕舌函数

Abstract: A new zero-attracting variable step size l₀-NLMS algorithm is proposed for recognition of sparse system. Step size of l₀-NLMS algorithm is changed by the versiera function. The convergence and convergence conditions, and the mean square error (MSE) and mean square deviation (MSD) of the proposed algorithm are derived. Simulation experiments with different signal-to-noise ratios (SNR) and different levels of autocorrelation of input signal are performed to compare the step size and MSD. The experimental simulation results show that the proposed algorithm can achieve faster convergence rate and good performance of pattern recognition even when the input signal is correlated, and can identify the sparse systems effectively.

Key words: information processing technology, sparse system, l₀-NLMS algorithm, variable step size, system noise, versiera function

中图分类号:

TN911.72

管四海, 李智，黄辉，王哲. 带零吸收项的变步长l₀范数归一化最小均方误差算法[J]. 兵工学报, 2016, 37(11): 2170-2176.

GUAN Si-hai， LI Zhi, HUANG Hui, WANG Zhe. Modified Zero-Attracting l₀-NLMS Algorithm[J]. Acta Armamentarii, 2016, 37(11): 2170-2176.

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带零吸收项的变步长l₀范数归一化最小均方误差算法

Modified Zero-Attracting l₀-NLMS Algorithm

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