一种稀疏系统辨识的子带自适应滤波算法
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摘要
利用改进的多带结构子带自适应滤波(IMSAF)算法辨识具有稀疏特性的未知系统。代价函数引入加权的l_1范数作为附加约束,并结合次梯度分析方法推导出新的更新方程。根据加权矩阵选取的不同,提出了两个l_1范数约束的IMSAF算法:l_1-IMSAF和l_1-RIMSAF。仿真结果表明,在未知系统具备稀疏特性的条件下,相较于传统的IMSAF算法,两个新算法的收敛性能具有显著提高。
The improved multiband-structured subband adaptive filter( IMSAF) algorithm is used to identify unknown system with sparse characteristics. A l_1-norm of the filter taps is introduced into the cost function. And then the new update equation is derived by using a subgradient analysis. According to the different weighting matrices,two kinds of the l_1-norm IMSAF are proposed. Simulation results prove that under sparse system conditions,two proposed methods have a significant improvement in both convergence rate and steady-state misadjustment compared with the standard IMSAF algorithm.
The improved multiband-structured subband adaptive filter( IMSAF) algorithm is used to identify unknown system with sparse characteristics. A l_1-norm of the filter taps is introduced into the cost function. And then the new update equation is derived by using a subgradient analysis. According to the different weighting matrices,two kinds of the l_1-norm IMSAF are proposed. Simulation results prove that under sparse system conditions,two proposed methods have a significant improvement in both convergence rate and steady-state misadjustment compared with the standard IMSAF algorithm.
引文
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[7]YANG F R,WU M,JI P F,et al.Low-complexity implementation of the improved multiband-structured subband adaptive filter algorithm[J].IEEE Transactions on Signal Processing,2015,63(19):5133-5148.
[8]BERTSEKAS D P,NEDI A,OZDAGLAR A E.Convex analysis and optimization[J].Athena scientific,Cambridge,MA USA,2003.
[9]CANDES E J,WAKIN M B,BOYD S P.Enhancing sparsity by reweighted1minimization[J].Journal of Fourier analysis and applications,2008,14(5-6):877-905.
[2]LEE K A,GAN W S.Improving convergence of the NLMS algorithm using constrained subband updates[J].IEEE signal processing letters,2004,11(9):736-739.
[3]YANG F R,WU M,JI P F,et al.An improved multiband-structured subband adaptive filter algorithm[J].IEEE Signal Processing Letters,2012,19(10):647-650.
[4]OZEKI K,UMEDA T.An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties[J].Electronics and Communications in Japan(Part I:Communications),1984,67(5):19-27.
[5]CHEN Y,GU Y,HERO A O.Sparse LMS for system identification[C]i/Proc.IEEE International Conference on Acoustics,Speech and Signal Processing,2009:3125-3128.
[6]SHI K,SHI P.Convergence analysis of sparse LMS algorithms with l1-norm penalty based on white input signal[J].Signal Processing,2010,90(12):3289-3293.
[7]YANG F R,WU M,JI P F,et al.Low-complexity implementation of the improved multiband-structured subband adaptive filter algorithm[J].IEEE Transactions on Signal Processing,2015,63(19):5133-5148.
[8]BERTSEKAS D P,NEDI A,OZDAGLAR A E.Convex analysis and optimization[J].Athena scientific,Cambridge,MA USA,2003.
[9]CANDES E J,WAKIN M B,BOYD S P.Enhancing sparsity by reweighted1minimization[J].Journal of Fourier analysis and applications,2008,14(5-6):877-905.