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Variable Step-Size Widely Linear Complex-Valued Affine Projection Algorithm and Performance Analysis
IEEE Transactions on Signal Processing ( IF 5.4 ) Pub Date : 2020-01-01 , DOI: 10.1109/tsp.2020.3029884 Long Shi , Haiquan Zhao , Yuriy Zakharov , Badong Chen , Yaoru Yang
IEEE Transactions on Signal Processing ( IF 5.4 ) Pub Date : 2020-01-01 , DOI: 10.1109/tsp.2020.3029884 Long Shi , Haiquan Zhao , Yuriy Zakharov , Badong Chen , Yaoru Yang
In this paper, a variable step-size widely linear complex-valued affine projection algorithm (VSS-WLCAPA) is proposed for processing noncircular signals. The variable step-size (VSS) is derived by minimizing the power of the augmented noise-free a posteriori error vector, which speeds up the convergence and reduces the steady-state misalignment. By exploiting the evolution of the covariance matrix of the weight error vector, we provide insight into the theoretical behavior of the VSS-WLCAPA algorithm. In the analysis, we take into account the dependency between the weight error vector and the noise vector, which is useful for accuracy of the theoretical prediction. To evaluate the mean step-size, the probability density function of the magnitude of the error is derived by employing polar coordinate transformation. Moreover, a special case when the projection order reduces to one is analysed in detail. The presented theoretical analysis is different from existing methodologies for analyzing affine projection algorithms due to the use of the Kronecker product. Simulation results for system identification scenarios demonstrate the merits of the proposed algorithm and verify the accuracy of the theoretical analysis. Wind prediction experiments support the superiority of the proposed VSS-WLCAPA as well.
中文翻译:
可变步长宽线性复值仿射投影算法及性能分析
在本文中,提出了一种用于处理非圆形信号的可变步长宽线性复值仿射投影算法(VSS-WLCAPA)。可变步长 (VSS) 是通过最小化增强的无噪声后验误差向量的功率来推导出来的,这可以加快收敛速度并减少稳态失准。通过利用权重误差向量的协方差矩阵的演化,我们深入了解 VSS-WLCAPA 算法的理论行为。在分析中,我们考虑了权重误差向量和噪声向量之间的依赖关系,这对理论预测的准确性很有用。为了评估平均步长,通过采用极坐标变换导出误差幅度的概率密度函数。而且,详细分析了投影阶数减少到一个的特殊情况。由于使用 Kronecker 产品,所提出的理论分析不同于现有的用于分析仿射投影算法的方法。系统识别场景的仿真结果证明了所提出算法的优点,并验证了理论分析的准确性。风预测实验也支持所提出的 VSS-WLCAPA 的优越性。
更新日期:2020-01-01
中文翻译:
可变步长宽线性复值仿射投影算法及性能分析
在本文中,提出了一种用于处理非圆形信号的可变步长宽线性复值仿射投影算法(VSS-WLCAPA)。可变步长 (VSS) 是通过最小化增强的无噪声后验误差向量的功率来推导出来的,这可以加快收敛速度并减少稳态失准。通过利用权重误差向量的协方差矩阵的演化,我们深入了解 VSS-WLCAPA 算法的理论行为。在分析中,我们考虑了权重误差向量和噪声向量之间的依赖关系,这对理论预测的准确性很有用。为了评估平均步长,通过采用极坐标变换导出误差幅度的概率密度函数。而且,详细分析了投影阶数减少到一个的特殊情况。由于使用 Kronecker 产品,所提出的理论分析不同于现有的用于分析仿射投影算法的方法。系统识别场景的仿真结果证明了所提出算法的优点,并验证了理论分析的准确性。风预测实验也支持所提出的 VSS-WLCAPA 的优越性。