A Full Mean Square Analysis of CLMS for Second-Order Noncircular Inputs
A Full Mean Square Analysis of CLMS for Second-Order Noncircular Inputs
复制标题
二阶非循环输入的 CLMS 全均方分析
DOI：
10.1109/tsp.2017.2739098
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发表时间：
2017-11
影响因子：
5.4
通讯作者：
ic Danilo P.
中科院分区：
文献类型：
--
作者：
Xia Yili;M;ic Danilo P.
针对一般二阶非圆(广义)高斯输入的严格线性估计，给出了复数最小均方(CLMS)算法的全均方暂态和稳态分析。为此，我们还考虑了根据CLMS的加权误差向量的互补均方误差(CMSE)和互补协方差(伪协方差)矩阵的演化来评估性能。这使得能够测量由于系统输入和系统噪声的二阶非圆性(不适当)而产生的输出误差和加权误差向量的非圆度。然后利用最近引入的近似不相关变换，该变换允许输入协方差矩阵和互补协方差矩阵的联合直接对角化和单个奇异值分解，以得到关于步长的统一界，从而保证标准均方误差和所提出的CMSE的收敛。综合考虑标准均方性能分析和所提出的互补性能分析，对于二阶非圆(不适当)高斯输入数据，CLMS的暂态和稳态性能提供了完全二阶、闭合形式的统计描述。在系统识别设置中的仿真支持该分析。
A full mean square transient and steady-state analysis of the complex least mean square (CLMS) algorithm is provided for strictly linear estimation of general second-order noncircular (improper) Gaussian inputs. To this end, we also consider the performance assessment in terms of the evolution of the complementary mean square error (CMSE) and the complementary covariance (pseudocovariance) matrix of the weight error vector of CLMS. This makes it possible to measure the degrees of noncircularity of the output error and the weight error vector, which arise due to second-order noncircularity (improperness) of the system input and system noise. The recently introduced approximate uncorrelating transform, which allows for joint direct diagonalization of both the input covariance and complementary covariance matrices with a single singular value decomposition, is then employed in order to derive a unified bound on the step-size, which guarantees the convergence of both the standard MSE and the proposed CMSE. A joint consideration of the standard mean square performance analysis and the proposed complementary performance analysis is shown to provide full second order, closed form, statistical descriptions of both the transient and steady state performances of CLMS for second-order noncircular (improper) Gaussian input data. Simulations in the system identification setting support the analysis.
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DOI：
10.1109/82.365348
发表时间：
1995-02
期刊：
IEEE Transactions on Circuits and Systems Ii: Analog and Digital Signal Processing
影响因子：
--
作者：
S. Douglas
通讯作者：
S. Douglas
DOI：
10.1007/978-1-4757-3637-3_2
发表时间：
2002
期刊：
--
影响因子：
--
作者：
P. S. Ramirez
通讯作者：
P. S. Ramirez
DOI：
10.1007/978-1-4614-4106-9_2
发表时间：
2019-11
期刊：
Adaptive Filtering
影响因子：
--
作者：
P. Diniz
通讯作者：
P. Diniz
影响因子：
5.4
作者：
T. Fusco;M. Tanda
通讯作者：
T. Fusco;M. Tanda
影响因子：
14.9
作者：
Xia, Yili;Douglas, Scott C.;Mandic, Danilo P.
通讯作者：
Mandic, Danilo P.