基于韦伯分布函数的低复杂度变步长符号算法

doi:10.11959/j.issn.1000-0801.2018223

摘要/Abstract

摘要：

针对OFDM系统中传统信道估计算法在冲击噪声环境中性能急剧下降的问题，提出了一种基于韦伯分布函数的顽健型变步长符号算法进行信道估计。在深入研究冲击噪声特性及韦伯分布函数性质的基础上，提出了采用估计误差绝对值的韦伯分布函数控制步长的低复杂度变步长符号算法。该算法在利用传统符号算法顽健性的基础上，采用估计误差的韦伯分布函数动态地改变迭代符号算法的步长，从而能够以较低的复杂度提高变步长符号算法在冲击噪声环境中的收敛速度。算法复杂度分析及仿真结果表明，在冲击噪声环境下所提算法相较于传统自适应滤波信道估计算法能够以更低的复杂度、更快的收敛速度达到相同的信道估计均方误差。

关键词: 冲击噪声, 信道估计, 韦伯分布函数, 变步长, 符号算法

Abstract:

The performance of the traditional second-order statistics based channel estimation methods degrade seriously in the presence of impulsive noises.In order to deal with this problem,a Weibull distribution function based variable step-size sign algorithm for channel estimation under impulsive noises was proposed.The proposed method was robust against impulsive noises and it could improve the convergence speed of the sign algorithm with the Weibull distribution function based variable step-size method.Computational complexity analysis and simulation results demonstrate that the proposed algorithm can achieve the same steady-state estimation error with faster convergence speed and lower computational complexity.

Key words: impulsive noise, channel estimation, Weibull distribution function, variable step-size, sign algorithm

张瑞,史故臣,刘半藤,陈友荣. 基于韦伯分布函数的低复杂度变步长符号算法[J]. 电信科学, 2018, 34(9): 87-96.

Rui ZHANG,Guchen SHI,Banteng LIU,Yourong CHEN. Low-complexity variable step-size sign algorithm based on Weibull distribution function[J]. Telecommunications Science, 2018, 34(9): 87-96.

图/表 7

图1

图2

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表1

各种算法步长更新计算式及复杂度"

算法	步长更新计算式	算法复杂度
DSA^[18]	$μ_{i} = {\begin{matrix} sign (e_{i}), \| e_{i} \| \leq τ \\ η sign (e_{i}), \| e_{i} \| > τ \end{matrix}$	2L+1
APSA^[19]	$μ_{i} = \frac{μ}{\sqrt{sign (e_{i}^{T}) X_{i}^{T} X_{i} sign (e_{i})}}$	(M+3)L
VSSA^[20]	${\begin{matrix} {\hat{p}}_{i} = θ {\hat{p}}_{i - 1} + (1 - θ) s i g n (e_{i}) X_{i} \\ \begin{matrix} \begin{matrix} \begin{matrix} μ_{i} = φ μ_{i - 1} + γ_{s} {‖ {\hat{p}}_{i} ‖}^{2} \end{matrix} \end{matrix} \end{matrix} \end{matrix}$	5L+4
提出算法	$μ_{i} = θ μ_{i - 1} + (1 - θ) \frac{k}{λ} {(\frac{\| e_{i} \|}{λ})}^{k - 1} \exp (- {(\frac{\| e_{i} \|}{λ})}^{k})$	2L+k+5

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表2

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算法	Alpha稳定分布噪声n ～ S (1.2,0,0.1,0)	高斯噪声n ～ S (2,0,0.1,0)
SA^[17]	μ=0.000 5	μ=0.000 5
DSA^[18]	μ₁=0.001、μ₂=0.000 1	μ₁=0.001 5、μ₂=0.000 5
APSA^[19]	μ=0.004、M=10	μ=0.004、M=10
VSSA^[20]	θ=0.995、φ=0.99、γ_s=0.000 1	θ=0.99、φ=0.99、γ_s=0.000 04
提出的算法	k=4、λ=10、θ=0.995	k=3、λ=5、θ=0.99