稀疏冲激响应的自适应滤波算法及其应用研究
|
摘要
信息技术的进步正影响着人们生活的方方面面,为人类社会带来了深刻的变化。如何更便捷高效地获取、分析和利用信息,是现代信息技术的核心。数字信号处理技术利用离散时间系统的特性对输入信号进行加工处理,其中自适应信号处理是信号处理领域的一个非常重要的分支,已经广泛应用于通信、控制等众多领域。自适应滤波器能使用特定的算法动态地调整滤波器系数,从而能处理系统特性事先不能准确知道或时变的系统。
近年来,随着需求的不断提高,自适应滤波器的长度成倍地增长,传统的自适应滤波算法面临着新的挑战。首先,自适应滤波器的收敛速度随着滤波器长度的增长而降低了。其次,自适应滤波算法的计算复杂度急速增长,不能适应资源有限的应用,和实时性要求很高的应用。第三,自适应滤波器的收敛精度下降了。为了解决这些伺题,研究者已经提出了很多方法。最近,一种新的观点和新的自适应方法,即系数比例自适应(Proportionate adaptation),获得了研究者的重视和深入研究。这种方法基于这些长滤波器本质上是稀疏的这一事实,即,虽然这种滤波器具有成百上千个系数,但是只有很少的系数有显著的值而其他的系数都是零或者很小的值。本文致力于对系数比例自适应算法及其应用进行研究,从收敛速度、收敛精度和计算复杂度三个方面对系数比例自适应算法进行改善。
首先,对MPNLMS算法进行了优化。本论文给出了MPNLMS算法的一个简化的推导过程,提出了一个确定其收敛标准的方法。基于这个收敛标准,提出了一个更好地逼近mu律曲线的分段函数,来保持MPNLMS算法的收敛速度。然后,对系数比例自适应算法的计算复杂度就行了分析和简化,通过省略一些冗余操作,在不影响算法收敛性能的情况下,减低了算法的计算复杂度。系数比例自适应算法主要对稀疏冲激响应有效,在目标冲激响应的稀疏程度随环境变化的应用中,算法的性能不能保证。本论文提出,将冲激响应的稀疏度引入算法,随着目标冲激响应稀疏度的变化调整算法的参数,使算法处理各种稀疏度的冲激响应时收敛速度都很快。
其次,通过使用分块的方法对系数比例自适应算法的收敛过程进行了分析,为理解系数比例自适应过程提供了一种新视角,得出了一种确定比例步长参数的新方法。现有的系数比例算法利用目标冲激响应的形状来确定比例步长参数,这种方法虽然在初始阶段很有效,但是算法收敛到一定程度后,该方法却导致小的滤波器系数不能获得足够的比例步长参数,延缓了算法的整体收敛。分析揭示出,最优比例步长参数应该根据目标冲激响应与自适应滤波器的当前估计值之间的差来确定。这个发现提供了一种新的途径寻求收敛速更快的系数比例自适应算法。本论文提出用自适应滤波器的当前估计值与过去某个时刻的估计值之间的差来确定比例步长参数。在初始阶段,新算法与原有算法具有相同行为,保持了原有算法极快的收敛速度。之后,新算法为每个滤波器系数分配了相对均等的步长增益,加快了小系数的收敛速度,从而提高了算法的整体收敛速度。新算法不但对稀疏冲激响应有效,而且在无须调整算法参数的情况下对非稀疏的冲激响应也是有效的。
最后,为了提高算法的收敛精度,将变步长技术引入到系数比例自适应算法中,使自适应滤波器保持很快的收敛速度的同时,稳态失调尽可能小。步长参数是自适应滤波算法最重要的参数之一,对算法的收敛速度和稳态失调有极大的影响。但是,对一个固定全局步长参数的自适应算法,快收敛速度和低稳态失调是一对矛盾的需求。固定步长算法必须在算法开始之前折中选择一个步长参数以满足应用在这两方面的需求。本论文提出可变全局步长参数的系数比例自适应算法,很好地解决了这个问题。这种方法将干扰信号的影响考虑进算法的自适应过程,在每一步迭代中,使后验误差等于干扰信号(而不是像通常的强迫后验误差等于零),建立了一个获得可变的全局步长参数的标准。利用这个标准,推导出了适用于系数比例归一化最小均方(NLMS)算法的可变全局步长方法。所提方法在滤波器输出误差较大时,使用较大的全局步长参数使算法以很快的速度收敛；当算法收敛到一定程度后,滤波器输出误差变小,全局步长参数相应变小,使算法获得很低的稳态失调。对于输入信号为语音信号等相关信号时,仿射投影算法(APA)比NLMS收敛速度快。所提的可变全局步长方法被进一步扩展到了系数比例仿射投影算法(PAPA)。此时,引入一个可变全局步长参数的对角矩阵,通过使后验误差向量等于干扰信号向量,推导出了适用于PAPA的可变步长方法。仿真实验结果验证了这种方法的有效性。
Advances in information technology have influnced every apsect of humman being's life. They have changed our socity profoundly. How to conviniently and efficiently retrieve, analyze and use information is a key problem of morden information technology. Digital signal processing technology processes the input signals using the characteristics of time discret system in order to use the information included in the signals. The adaptive signal processing technology is one of the important aspects of digital signal processing technology and has widely applied in many fields such as communication, control, etc. Adaptive filter dynamically adjusts its coefficients according to a certain adaptive algorithm so it can deal with the systems where the exact system characteristic is unknow in advance, or the system is time-varying.
In recent years, with the increase of demand, the length of adaptive filter was doubled. As a result, traditional adaptive algorithms encounter many new challenges. First, the convergence speed of adaptive filter becomes slow with the increase of the filter length. Second, computational complexity of adaptive algorithm becomes too heavy to be implemented in resource-limited applications or in real-time applications. Third, convergence accuracy of adaptive filter is degraded. Many approaches have been proposed to solve these problems. Recently, a new perspective of adaptation process, proportionate adaptation, was developed and investigated widely. This new method is based on a fact, that long adaptive filters are sparse in nature. That is, although these filters have hundereds or thousands coefficients, only a small portion of them have noticeable value while most of the others are zeros. This dissertation is engaged to sduty the various proportionate adaptive algorithms, in order to improve theire convergence speed, convergence accuracy and computational complexity.
First, the MPNLMS algorithm is improved. A simplified derivation of MPNLMS algorithm is provided in a concise process. A method is proposed to determine its convergence criterion. Based on this criterion, a new segment function is proposed to approximate the mu-law function. Consequently the fast convergence speed of MPNLMS algorithm is retained. Then, computational complexity of proportionate adaptive algorithms is reduced by removing some redundant operations, while the convergence speed is not degraded. The original proportionate adaptive algorithms are only effective for sparse impulse responses. In an application where the sparsity of target impulse response varies with the environment, the performance of proportionate adaptive algorithms is not guaranteed. This dissertation proposes to introduce the measure of the sparsity into the algorithms. It then adjusts the related parameters of proportionate adaptive algorithms according to the sparsity. The convergence speed of the related algorithms is improved for any impulse response with different sparsity.
Second, by analyzing the convergence process of proportionate adaptive algorithm using a block method, a new perspective is provided for proportionate adaptation. Then, a new method is proposed to determine the proportionate step size. All existing proportionate adaptive algorithms exploit the shape of target impulse response to determine their proportionate step size. This method is effective in the initial period of adaptation. But after the adaptive filter has converged to certain degree, this method will result in slow convergence of the small coefficients because they cannot obtain reseonable step size. Consequently, the convergence speed in the second period is degraded. The analysis reveals that, the optimal proportionate step gain should be determined according to the difference between the target impulse response and the current estimate of adaptive filter. This discovery implies a new way to pursuit faster proportionate adaptive algorithms. In this dissertation, it is proposed to determine the proportionate step gain according to the coefficients difference between the current estimate and a past estimate. In the initial period, this method is identical to the original proportionate algorithms. Thereafter, this method can assign similar proportionate step gain for all the coefficients so the overall convergence is improved. This method is not only effective for sparse impulse response, but also for non-sparse impulse response and it is unnecessary to adjust any parameter.
Third, a variable step-size method is proposed for proportionate adaptive algorithms in order to improve their convergence accuracy. This method can keep fast convergence speed of proportionate adaptive algorithms, and it can achieve very low steady-state misalignment at the same time. The step-size parameter is one of the most important parameters of adaptive algorithms. It has great influence on convergence speed and the steady-state misalignment of adaptive algorithms. However, the requirements of fast convergence and low steady-state misalignment are conflict for constant step-size adaptive algorithms. For a constant global step-size algorithm, a step-size parameter has to be selected before start of algorithm, by compromising these two conflict requirements. In this dissertation, a variable step-size is proposed for proportionate adaptive algorithms to solve this problem. By taking into account the disturbance signal, it is proposed to force the a posterior error to be the disturbance signal, instead of to be zero. Then, a new optimization criterion is established. Based on this criterion, a step-size control approach for proportionate NLMS algorithm is proposed. This method uses a large global step-size when the output error is large to accuralate the convergence speed. After the adaptive filter has converged to certain degree, the output error becomes small, so the global step-size becomes small to achieve low steady-state misalignment. For the the correlated input signal, for example, speech signals, affine projection algorithm (APA) has faster convergence speed than the NLMS algorithm. The proposed variable step-size method is then extended to the proportionate APA. In this case, it is necessary to introduce a diagonal variable step-size matrix. By forcing the the a posterior error vector to be the disturbance signal vector, after the similar process, a variable step-size method is achieved for PAPA. Simulation results verify the effectiveness of the proposed algorithms.
近年来,随着需求的不断提高,自适应滤波器的长度成倍地增长,传统的自适应滤波算法面临着新的挑战。首先,自适应滤波器的收敛速度随着滤波器长度的增长而降低了。其次,自适应滤波算法的计算复杂度急速增长,不能适应资源有限的应用,和实时性要求很高的应用。第三,自适应滤波器的收敛精度下降了。为了解决这些伺题,研究者已经提出了很多方法。最近,一种新的观点和新的自适应方法,即系数比例自适应(Proportionate adaptation),获得了研究者的重视和深入研究。这种方法基于这些长滤波器本质上是稀疏的这一事实,即,虽然这种滤波器具有成百上千个系数,但是只有很少的系数有显著的值而其他的系数都是零或者很小的值。本文致力于对系数比例自适应算法及其应用进行研究,从收敛速度、收敛精度和计算复杂度三个方面对系数比例自适应算法进行改善。
首先,对MPNLMS算法进行了优化。本论文给出了MPNLMS算法的一个简化的推导过程,提出了一个确定其收敛标准的方法。基于这个收敛标准,提出了一个更好地逼近mu律曲线的分段函数,来保持MPNLMS算法的收敛速度。然后,对系数比例自适应算法的计算复杂度就行了分析和简化,通过省略一些冗余操作,在不影响算法收敛性能的情况下,减低了算法的计算复杂度。系数比例自适应算法主要对稀疏冲激响应有效,在目标冲激响应的稀疏程度随环境变化的应用中,算法的性能不能保证。本论文提出,将冲激响应的稀疏度引入算法,随着目标冲激响应稀疏度的变化调整算法的参数,使算法处理各种稀疏度的冲激响应时收敛速度都很快。
其次,通过使用分块的方法对系数比例自适应算法的收敛过程进行了分析,为理解系数比例自适应过程提供了一种新视角,得出了一种确定比例步长参数的新方法。现有的系数比例算法利用目标冲激响应的形状来确定比例步长参数,这种方法虽然在初始阶段很有效,但是算法收敛到一定程度后,该方法却导致小的滤波器系数不能获得足够的比例步长参数,延缓了算法的整体收敛。分析揭示出,最优比例步长参数应该根据目标冲激响应与自适应滤波器的当前估计值之间的差来确定。这个发现提供了一种新的途径寻求收敛速更快的系数比例自适应算法。本论文提出用自适应滤波器的当前估计值与过去某个时刻的估计值之间的差来确定比例步长参数。在初始阶段,新算法与原有算法具有相同行为,保持了原有算法极快的收敛速度。之后,新算法为每个滤波器系数分配了相对均等的步长增益,加快了小系数的收敛速度,从而提高了算法的整体收敛速度。新算法不但对稀疏冲激响应有效,而且在无须调整算法参数的情况下对非稀疏的冲激响应也是有效的。
最后,为了提高算法的收敛精度,将变步长技术引入到系数比例自适应算法中,使自适应滤波器保持很快的收敛速度的同时,稳态失调尽可能小。步长参数是自适应滤波算法最重要的参数之一,对算法的收敛速度和稳态失调有极大的影响。但是,对一个固定全局步长参数的自适应算法,快收敛速度和低稳态失调是一对矛盾的需求。固定步长算法必须在算法开始之前折中选择一个步长参数以满足应用在这两方面的需求。本论文提出可变全局步长参数的系数比例自适应算法,很好地解决了这个问题。这种方法将干扰信号的影响考虑进算法的自适应过程,在每一步迭代中,使后验误差等于干扰信号(而不是像通常的强迫后验误差等于零),建立了一个获得可变的全局步长参数的标准。利用这个标准,推导出了适用于系数比例归一化最小均方(NLMS)算法的可变全局步长方法。所提方法在滤波器输出误差较大时,使用较大的全局步长参数使算法以很快的速度收敛；当算法收敛到一定程度后,滤波器输出误差变小,全局步长参数相应变小,使算法获得很低的稳态失调。对于输入信号为语音信号等相关信号时,仿射投影算法(APA)比NLMS收敛速度快。所提的可变全局步长方法被进一步扩展到了系数比例仿射投影算法(PAPA)。此时,引入一个可变全局步长参数的对角矩阵,通过使后验误差向量等于干扰信号向量,推导出了适用于PAPA的可变步长方法。仿真实验结果验证了这种方法的有效性。
Advances in information technology have influnced every apsect of humman being's life. They have changed our socity profoundly. How to conviniently and efficiently retrieve, analyze and use information is a key problem of morden information technology. Digital signal processing technology processes the input signals using the characteristics of time discret system in order to use the information included in the signals. The adaptive signal processing technology is one of the important aspects of digital signal processing technology and has widely applied in many fields such as communication, control, etc. Adaptive filter dynamically adjusts its coefficients according to a certain adaptive algorithm so it can deal with the systems where the exact system characteristic is unknow in advance, or the system is time-varying.
In recent years, with the increase of demand, the length of adaptive filter was doubled. As a result, traditional adaptive algorithms encounter many new challenges. First, the convergence speed of adaptive filter becomes slow with the increase of the filter length. Second, computational complexity of adaptive algorithm becomes too heavy to be implemented in resource-limited applications or in real-time applications. Third, convergence accuracy of adaptive filter is degraded. Many approaches have been proposed to solve these problems. Recently, a new perspective of adaptation process, proportionate adaptation, was developed and investigated widely. This new method is based on a fact, that long adaptive filters are sparse in nature. That is, although these filters have hundereds or thousands coefficients, only a small portion of them have noticeable value while most of the others are zeros. This dissertation is engaged to sduty the various proportionate adaptive algorithms, in order to improve theire convergence speed, convergence accuracy and computational complexity.
First, the MPNLMS algorithm is improved. A simplified derivation of MPNLMS algorithm is provided in a concise process. A method is proposed to determine its convergence criterion. Based on this criterion, a new segment function is proposed to approximate the mu-law function. Consequently the fast convergence speed of MPNLMS algorithm is retained. Then, computational complexity of proportionate adaptive algorithms is reduced by removing some redundant operations, while the convergence speed is not degraded. The original proportionate adaptive algorithms are only effective for sparse impulse responses. In an application where the sparsity of target impulse response varies with the environment, the performance of proportionate adaptive algorithms is not guaranteed. This dissertation proposes to introduce the measure of the sparsity into the algorithms. It then adjusts the related parameters of proportionate adaptive algorithms according to the sparsity. The convergence speed of the related algorithms is improved for any impulse response with different sparsity.
Second, by analyzing the convergence process of proportionate adaptive algorithm using a block method, a new perspective is provided for proportionate adaptation. Then, a new method is proposed to determine the proportionate step size. All existing proportionate adaptive algorithms exploit the shape of target impulse response to determine their proportionate step size. This method is effective in the initial period of adaptation. But after the adaptive filter has converged to certain degree, this method will result in slow convergence of the small coefficients because they cannot obtain reseonable step size. Consequently, the convergence speed in the second period is degraded. The analysis reveals that, the optimal proportionate step gain should be determined according to the difference between the target impulse response and the current estimate of adaptive filter. This discovery implies a new way to pursuit faster proportionate adaptive algorithms. In this dissertation, it is proposed to determine the proportionate step gain according to the coefficients difference between the current estimate and a past estimate. In the initial period, this method is identical to the original proportionate algorithms. Thereafter, this method can assign similar proportionate step gain for all the coefficients so the overall convergence is improved. This method is not only effective for sparse impulse response, but also for non-sparse impulse response and it is unnecessary to adjust any parameter.
Third, a variable step-size method is proposed for proportionate adaptive algorithms in order to improve their convergence accuracy. This method can keep fast convergence speed of proportionate adaptive algorithms, and it can achieve very low steady-state misalignment at the same time. The step-size parameter is one of the most important parameters of adaptive algorithms. It has great influence on convergence speed and the steady-state misalignment of adaptive algorithms. However, the requirements of fast convergence and low steady-state misalignment are conflict for constant step-size adaptive algorithms. For a constant global step-size algorithm, a step-size parameter has to be selected before start of algorithm, by compromising these two conflict requirements. In this dissertation, a variable step-size is proposed for proportionate adaptive algorithms to solve this problem. By taking into account the disturbance signal, it is proposed to force the a posterior error to be the disturbance signal, instead of to be zero. Then, a new optimization criterion is established. Based on this criterion, a step-size control approach for proportionate NLMS algorithm is proposed. This method uses a large global step-size when the output error is large to accuralate the convergence speed. After the adaptive filter has converged to certain degree, the output error becomes small, so the global step-size becomes small to achieve low steady-state misalignment. For the the correlated input signal, for example, speech signals, affine projection algorithm (APA) has faster convergence speed than the NLMS algorithm. The proposed variable step-size method is then extended to the proportionate APA. In this case, it is necessary to introduce a diagonal variable step-size matrix. By forcing the the a posterior error vector to be the disturbance signal vector, after the similar process, a variable step-size method is achieved for PAPA. Simulation results verify the effectiveness of the proposed algorithms.
引文
[1]B. Widrow and S.D. Steams, Adaptive signal processing, Prentice-Hall, Upper Saddle River, NJ,1985.
[2]P.S.R. Diniz, Adaptive filtering:algorithms and practical implementation, Kluwer Academic Publishers, Norwell, MA, USA,1997.
[3]P.S.R. Diniz(著).刘郁林,景晓军,谭刚兵(译).自适应滤波算法与实现,第二版.北京：电子工业出版社,2004
[4]S. Haykin, Adaptive Filter Theory,4th ed, Prentice-Hall, Upper Saddle River, NJ, 2003.
[5]西蒙-霍金(著).郑宝玉等(译).自适应滤波器原理,第四版,北京：电子工业出版社,2006.
[6]何振亚.自适应信号处理.北京：科学出版社,2003.
[7]张贤达,保铮.通信信号处理.北京：国防工业出版社,2000.
[8]A.H. Sayed, Fundamentals of Adaptive Filtering, Wiley, New York,2003.
[9]Y. Huang, J. Benesty, and J. Chen, Acoustic MIMO Signal Processing (Signals and Communication Technology), Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2006.
[10]J. Benesty, T. Gansler, D. Morgan, M. Sondhi, and S. Gay, Eds., Advances in Network and Acoustic Echo Cancellation, Springer, Boston, Mass, USA,2001.
[11]S. Haykin and B. Widrow Eds. Advances in LMS Filters, Wiley,2005.
[12]ITU-T recommendation G168:Digital network echo cancellers,2007.
[13]P. Loganathan, A.W.H. Khong, and P. A. A. Nay lor, Sparseness controlled proportionate algorithm for acoustic echo cancellation, Proc. European Signal Processing Conference (EUSIPCO'08), Lausanne, Switzerland, pp.1-5, Aug 2008.
[14]Y. Huang, J. Benesty, and J. Chen, Sparse Adaptive Filters, in Acoustic MIMO Signal Processing., ch.4, Springer-Verlag New York Inc., Secaucus, NJ, USA,2005.
[15]Z. Chen, S. L. Gay, and S. Haykin, Proportionate Adaptation:New Paradigms in Adaptive Filters, in S. Haykin and B. Widrow Eds. Advances in LMS Filters, ch.8. Wiley,2005.
[16]D.L. Duttweiler, Proportionate normalized least-mean-squares adaptation in echo cancelers, IEEE Trans. Speech Audio Processing, vol.8, no.5, pp.508-518, Sept.2000.
[17]R.K. Martin, W.A. Sethares, R.C. Williamson, and C.R. Johnson Jr., Exploiting sparsity in adaptive filters, IEEE Trans. Signal Processing, vol.50, no.8, pp. 1883-1894, Aug.2002.
[18]D.L. Duttweiler, Subsampling to estimate delay with application to echo canceling, IEEE Trans. Acoust., Speech, Signal Processing, vol.31, no.5, pp.1090-1099, Oct. 1983.
[19]0. Tanrikulu, Method and apparatus for fast network bulk delay and span estimation for line echo cancellation, Aug.2004.
[20]J. Homer, Detection guided NLMS estimation of sparsely parameterized channels, IEEE Trans. Circuits Syst. II, vol.47, no.12, pp.1437-1442, Dec.2000.
[21]J. Homer, I. Mareels, and C. Hoang, Enhanced detection-guided NLMS estimation of sparse FIR-modeled signal channels, IEEE Trans. Circuits Syst. I, vol.53, no.8, pp. 1783-1791, Aug.2006.
[22]Y. Jennifer, J. Homer, G. Rombouts, and M. Moonen, Detection-Guided Fast Affine Projection Channel Estimator for Speech Applications, EURASIP J. Audio, Speech, and Music Process., Volume 2007, Article ID 71495,13 pages, doi:10.1155/2007/71495,2007.
[23]Y. Cheng and D.M. Etter, Analysis of an adaptive technique for modeling sparse systems, IEEE Trans. Acoust., Speech, Signal Processing, vol.37, no.2, pp.254-263, Feb.1989.
[24]S.L Gay, An efficient, fast converging adaptive filter for network echo cancellation, Proc. of the 32nd Asilomar Conference on Signals, Systems and Computers (ACSSC'98), Pacific Grove, Calif, USA, pp.394-398, Nov.1998.
[25]M. Nekuii and M. Atarodi, A fast converging algorithm for network echo cancellation, IEEE Signal Processing Lett., vol.11, no.4, pp.427-430, Apr.2004.
[26]J. Benesty and S.L. Gay, An improved PNLMS algorithm, Proc. IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP'02), Orlando, USA, pp.1881-1884, May.2002.
[27]J. Cui, P. Naylor, and D. Brown, An improved IPNLMS algorithm for echo cancellation in packet-switched networks, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'04), Montreal, Quebec, Canada, pp.141-144, May.2004.
[28]H. Deng and M. Doroslovacki, Improving convergence of the PNLMS algorithm for sparse impulse response identification, IEEE Signal Processing Lett., vol.12, no.3, pp. 181-184, Mar.2005.
[29]H. Deng and M. Doroslovacki, Proportionate adaptive algorithms for network echo cancellation, IEEE Trans. Signal Processing, vol.54, no.5, pp.1794-1803, May.2006.
[30]H. Deng, Adaptive algorithms of sparse impulse response identification, D.SC dissertation, Dept. of Electrical and Computer Engineering, George Washington University, Washington, DC, Mar.2005.
[31]田磊,汪小志,刘志刚.自适应滤波算法及应用研究.电子测试,2008,(160)1：5-9.
[32]耿妍,张端金.自适应滤波算法综述.信息与电子工程,2008,(6)4：315-320
[33]詹望,杨福生.基于累积量的递归最小二乘算法研究.信号处理,1999,(15)3：240-248
[34]高鹰,谢胜利.基于矩阵广义逆递推的自适应滤波算法,电子学报,2002,(30)7：1032-1034.
[35]高鹰,谢胜利.基于相关函数的递推最小二乘算法及其在回波消除中的应用.通信学报,2002,23(9)：114-118.
[36]胡春风,高立,张筱华,王德隽.一种改进的RLS自适应滤波器算法.通信学,1998,(19)8：67-71
[37]赵知劲.一种新的基于高阶统计量的自适应滤波方法.电子学报,2000,28(12)：83-84,51.
[38]S. Gay and S. Tavathia, The fast affine projection algorithm, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'95), Detroit, Michigan, pp.3023-3026, May.1995.
[39]M. Tanaka, Y. Kaneda, S. Makino, and J. Kojima, Fast projection algorithm and its step size control, Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'95), Washington, DC, USA, pp.945-948, IEEE Computer Society,1995.
[40]M. Tanaka, Y. Kaneda, S. Makino, and J. Kojima, A fast projection algorithm for adaptive filtering, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., vol.E78-A, no.10,pp.1355-1361, Oct.1995.
[41]S.L. Gay, The fast affine projection algorithm, in Acoustic signal processing for telecommunication, pp.23-46, Kluwer Academic Publishers, Hingham, MA, USA, 2000.
[42]S. Gay and S. Douglas, Normalized natural gradient adaptive filtering for sparse and non-sparse systems, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'02), Orlando, USA, pp.1405-1408, May.2002.
[43]B. Jelfs and D. Mandic, A unifying approach to the derivation of the class of PNLMS algorithms, Proc.15th International Conference on Digital Signal Processing (DSP'07), London, UK, pp.35-38, Jul.2007.
[44]M. Doroslovacki and H. Deng, On convergence of proportionate-type NLMS adaptive algorithms, Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'06), Toulouse, Franc, pp.105-108, Mar.2006.
[45]A.W.H. Khong, P.A. Naylor, and J. Benesty, A low delay and fast converging improved proportionate algorithm for sparse system identification, EURASIP J. Audio Speech Music Process., Volume 2007, Article ID 84376,8 pages, doi:10.1155/2007/84376,2007.
[46]H. Deng and M. Doroslovacki, Wavelet-based MPNLMS adaptive algorithm for network echo cancellation, EURASIP J. Audio Speech Music Process., Volume 2007, Article ID 96101,5 pages doi:10.1155/2007/96101,2007.
[47]M.R. Petraglia and G Barboza, Improved PNLMS algorithm employing wavelet transform and sparse filters, Porc.16th European Signal Processing Conference (EUSIPCO'08), Lausanne, Switzerland, pp.1-5, Aug.2008.
[48]M. Yukawa, Krylov-proportionate adaptive filtering techniques not limited to sparse systems, IEEE Trans. Signal Processing, vol.57, no.3, pp.927-943, Mar.2009.
[49]S. Douglas, Adaptive filters employing partial updates, IEEE Trans. Circuits Syst. II, vol.44, no.3, pp.209-216, Mar.1997.
[50]T. Aboulnasr and K. Mayya, Selective coefficient update of gradient-based adaptive algorithms, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'97), Munich, Germany, pp.1929-1932, Apr.1997.
[51]T. Schertler, Selective block update of NLMS type algorithms, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'98), Seattle, WA, pp.1717-1720, May.1998.
[52]T. Aboulnasr and K. Mayyas, Complexity reduction of the NLMS algorithm via selective coefficient update, IEEE Trans. Signal Processing, vol.47, no.5, pp. 1421-1427, May.1999.
[53]K. Dogancay and 0. Tanrkulu, Selective-partial-update NLMS and affine projection algorithms for acoustic echo cancellation, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), Istanbul, Turkey, pp. 448-451, Jun.2000.
[54]K. Dogancay and O. Tanrikulu, Adaptive filtering algorithms with selective partial updates, IEEE Trans. Circuits Syst. II, vol.48, no.8, pp.762-769, Aug.2001.
[55]K. Dogancay and O. Tanrikulu, Selective-partial-update NLMS and affine projection algorithms for acoustic echo cancellation, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), pp.448-451, May.2000.
[56]A. Tandon, M.N.S. Swamy, and M.O. Ahmad, Partial-update Loo-norm based algorithms, IEEE Trans. Circuits Syst. I, vol.54, no.2, pp.411-419, Feb.2007.
[57]S. Gollamudi, S. Nagaraj, S. Kapoor, and Y.F. Huang, Set-membership filtering and a set-membership normalized LMS algorithm with an adaptive step size, IEEE Signal Processing Lett., vol.5, no.5, pp.111-114, May.1998.
[58]S. Gollamudi, S. Nagaraj, S. Kapoor, and Y.F. Huang, Set-membership adaptive equalization and updator-shared implementation for multiple channel communications systems, IEEE Trans. Signal Processing, vol.46, no.9, pp.2372-2384, Sep.1998.
[59]P.S.R. Diniz and S. Werner, Set-membership binormalized data-reusing algorithms, IEEE Trans. Signal Processing, vol.51, no.l, pp.124-134, Jan.2003.
[60]S. Werner, M.L.R. de Campos, and J.A. Apolinario, Data-selective constrained affine projection algorithm, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, (ICASSP'01), Salt Lake City, Uta, pp.3745-3748, May.2001.
[61]S. Werner and P.S.R. Diniz, Set-membership affine projection algorithm, IEEE Signal Processing Lett., vol.8, no.8, pp.231-235, Aug.2001.
[62]S. Werner, C.R. Johnson Jr., M.L.R. de Campos, and P.S.R. Diniz, Low-complexity constrained affine projection algorithms, IEEE Trans. Signal Processing, vol.53, no.12, pp.4545-4555, Dec.2005.
[63]O. Tanrikulu and K. Dogancay, Selective-partial-update proportionate normalized least-mean-squares algorithm for network echo cancellation, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'02), Orlando, FL, USA, pp.1889-1892, May.2002.
[64]J.D. Gordy, T. Aboulnasr, and M. Bouchard, Reduced-complexity proportionate NLMS employing block-based selective coefficient updates, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'08), Las Vegas, USA, pp.233-236, Mar.2008.
[65]S. Werner, J.A. Apolinario, and P.S.R. Diniz, Set-membership proportionate affine projection algorithms, EURASIP J. Audio, Speech, and Music Process., Volume 2007, Article ID 34242,10 pages, doi:10.1155/2007/34242,2009.
[66]H. Deng and M. Doroslovacki, New sparse adaptive algorithms using partial update, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'04), pp.845-848, May.2004.
[67]T. Gansler, J. Benesty, S.L. Gay, and M.M. Sondhi, A robust proportionate affine projection algorithm for network echo cancellation, Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), pp.793-796, May 2000.
[68]P.O. Hoyer, Non-negative matrix factorization with sparseness constraints, J. Mach. Learn. Res., vol.5, pp.1457-1469,2004.
[69]T. Gansler, J. Benesty, M.M. Sondhi, and S.L. Gay, Dynamic resource allocation for network echo cancellation, Proc. IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP'01), Salt Lake City, UT, USA, pp.3233-3236, May. 2001.
[70]A.W.H. Khong and P.A.A. Naylor, Efficient use of sparse adaptive filters, Proc.40th Asilomar Conf. on Signals, Systems and Computers (ACSSC'06), Pacific Grove, Calif, USA, pp.1375-1379, Oct-Nov 2006.
[71]K. Dogancay and P.A.A. Naylor, Recent advances in partial update and sparse adaptive filters, Proc.14th European Signal Processing Conference (EUSIPCO'05), Antalya, Turkey, pp.1-4 Sep.2005.
[72]R. Kwong and E. Johnston, A variable step size LMS algorithm, IEEE Trans. Signal Processing, vol.40, no.7, pp.1633-1642, Jul.1992.
[73]A.I. Sulyman and A. Zerguine, Convergence and steady-state analysis of a variable step-size NLMS algorithm, Signal Processing, vol.83, no.6, pp.1255-1273, Jun.2003.
[74]A. Mader, H. Puder, and G.U. Schmidt, Step-size control for acoustic echo cancellation filter-an overview, Signal Processing, vol.80, no.9, pp.1697-1719, Sep. 2000.
[75]H.C. Shin, A.H. Sayed, and W.J. Song, Variable step-size NLMS and affine projection algorithms, IEEE Signal Processing Lett., vol.11, no.2, pp.132-135, Feb.2004.
[76]J. Benesty, H. Rey, L.R. Vega, and S. Tressens, A nonparametric VSS NLMS algorithm, IEEE Signal Processing Lett., vol.13, no.10, pp.581-584, Oct.2006.
[77]C. Paleologu, S. Ciochina, and J. Benesty, Variable step-size NLMS algorithm for under-modeling acoustic echo cancellation, IEEE Signal Processing Lett., vol.15, no.10,pp.5-8,Jan.2008.
[78]C. Paleologu, J. Benesty, and S. Ciochina, A variable step-size affine projection algorithm designed for acoustic echo cancellation, IEEE Trans. Acoust., Speech, Signal Processing, vol.16, no.8, pp.1466-1478, Nov.2008.
[79]叶华,吴伯修.变步长自适应滤波算法的研究.电子学报,1990,18(4)：63-69.
[80]覃景繁,欧阳景正.一种新的变步长自适应滤波算法.数据采集与处理,1997,12(3)：171-174.
[8l]高鹰,谢胜利.一种变步长LMS自适应滤波算法及分析.电子学报,2001,29(8)：1094·1097.
[82]O. Hoshuyama, R. Goubran, and A. Sugiyama, A generalized proportionate variable step-size algorithm for fast changing acoustic environments, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'04), Montreal, Quebec, Canada, pp.161-164, May.2004.
[83]P. Mahale, SVS-PNLMS algorithm for acoustic echo cancellation, Proc. of the 3rd International Conference on Information and Communication Technologies:From Theory to Applications (ICTTA'08), pp.1-6, Apr.2008.
[84]S. Saiki and M. Fukumoto, Improvement of the IPNLMS algorithm exploiting variable step size, IEICE Tech. Rep., vol.107, no.180, pp.25-28, Aug.2007.
[85]O. Tanrkulu, B. Baykal, A.G. Constantinides, and J.A. Chambers, Residual echo signal in critically sampled subband acoustic echo cancellers based on IIR and FIR filterbanks, IEEE Signal Processing Lett., vol.45, pp.901-912,1997.
[86]阎兆立,杜利民.电话语音回声消除的研究.电子学报,2002,(28)11：1726-1728.
[87]李挥,林茫茫等.VoIP回声消除器设计及算法研究.电子学报,2007,(35)9：1774-1778.
[88]王振力,张雄伟,杨吉斌,陈功.一种新的快速自适应滤波算法的研究.通信学报,2005,(26)11：1-6
[89]谢胜利,周元建.一种新自适应滤波快速算法及其在对路回波消除中的应用.电子学报,2003,(31)2：276-279.
[2]P.S.R. Diniz, Adaptive filtering:algorithms and practical implementation, Kluwer Academic Publishers, Norwell, MA, USA,1997.
[3]P.S.R. Diniz(著).刘郁林,景晓军,谭刚兵(译).自适应滤波算法与实现,第二版.北京：电子工业出版社,2004
[4]S. Haykin, Adaptive Filter Theory,4th ed, Prentice-Hall, Upper Saddle River, NJ, 2003.
[5]西蒙-霍金(著).郑宝玉等(译).自适应滤波器原理,第四版,北京：电子工业出版社,2006.
[6]何振亚.自适应信号处理.北京：科学出版社,2003.
[7]张贤达,保铮.通信信号处理.北京：国防工业出版社,2000.
[8]A.H. Sayed, Fundamentals of Adaptive Filtering, Wiley, New York,2003.
[9]Y. Huang, J. Benesty, and J. Chen, Acoustic MIMO Signal Processing (Signals and Communication Technology), Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2006.
[10]J. Benesty, T. Gansler, D. Morgan, M. Sondhi, and S. Gay, Eds., Advances in Network and Acoustic Echo Cancellation, Springer, Boston, Mass, USA,2001.
[11]S. Haykin and B. Widrow Eds. Advances in LMS Filters, Wiley,2005.
[12]ITU-T recommendation G168:Digital network echo cancellers,2007.
[13]P. Loganathan, A.W.H. Khong, and P. A. A. Nay lor, Sparseness controlled proportionate algorithm for acoustic echo cancellation, Proc. European Signal Processing Conference (EUSIPCO'08), Lausanne, Switzerland, pp.1-5, Aug 2008.
[14]Y. Huang, J. Benesty, and J. Chen, Sparse Adaptive Filters, in Acoustic MIMO Signal Processing., ch.4, Springer-Verlag New York Inc., Secaucus, NJ, USA,2005.
[15]Z. Chen, S. L. Gay, and S. Haykin, Proportionate Adaptation:New Paradigms in Adaptive Filters, in S. Haykin and B. Widrow Eds. Advances in LMS Filters, ch.8. Wiley,2005.
[16]D.L. Duttweiler, Proportionate normalized least-mean-squares adaptation in echo cancelers, IEEE Trans. Speech Audio Processing, vol.8, no.5, pp.508-518, Sept.2000.
[17]R.K. Martin, W.A. Sethares, R.C. Williamson, and C.R. Johnson Jr., Exploiting sparsity in adaptive filters, IEEE Trans. Signal Processing, vol.50, no.8, pp. 1883-1894, Aug.2002.
[18]D.L. Duttweiler, Subsampling to estimate delay with application to echo canceling, IEEE Trans. Acoust., Speech, Signal Processing, vol.31, no.5, pp.1090-1099, Oct. 1983.
[19]0. Tanrikulu, Method and apparatus for fast network bulk delay and span estimation for line echo cancellation, Aug.2004.
[20]J. Homer, Detection guided NLMS estimation of sparsely parameterized channels, IEEE Trans. Circuits Syst. II, vol.47, no.12, pp.1437-1442, Dec.2000.
[21]J. Homer, I. Mareels, and C. Hoang, Enhanced detection-guided NLMS estimation of sparse FIR-modeled signal channels, IEEE Trans. Circuits Syst. I, vol.53, no.8, pp. 1783-1791, Aug.2006.
[22]Y. Jennifer, J. Homer, G. Rombouts, and M. Moonen, Detection-Guided Fast Affine Projection Channel Estimator for Speech Applications, EURASIP J. Audio, Speech, and Music Process., Volume 2007, Article ID 71495,13 pages, doi:10.1155/2007/71495,2007.
[23]Y. Cheng and D.M. Etter, Analysis of an adaptive technique for modeling sparse systems, IEEE Trans. Acoust., Speech, Signal Processing, vol.37, no.2, pp.254-263, Feb.1989.
[24]S.L Gay, An efficient, fast converging adaptive filter for network echo cancellation, Proc. of the 32nd Asilomar Conference on Signals, Systems and Computers (ACSSC'98), Pacific Grove, Calif, USA, pp.394-398, Nov.1998.
[25]M. Nekuii and M. Atarodi, A fast converging algorithm for network echo cancellation, IEEE Signal Processing Lett., vol.11, no.4, pp.427-430, Apr.2004.
[26]J. Benesty and S.L. Gay, An improved PNLMS algorithm, Proc. IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP'02), Orlando, USA, pp.1881-1884, May.2002.
[27]J. Cui, P. Naylor, and D. Brown, An improved IPNLMS algorithm for echo cancellation in packet-switched networks, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'04), Montreal, Quebec, Canada, pp.141-144, May.2004.
[28]H. Deng and M. Doroslovacki, Improving convergence of the PNLMS algorithm for sparse impulse response identification, IEEE Signal Processing Lett., vol.12, no.3, pp. 181-184, Mar.2005.
[29]H. Deng and M. Doroslovacki, Proportionate adaptive algorithms for network echo cancellation, IEEE Trans. Signal Processing, vol.54, no.5, pp.1794-1803, May.2006.
[30]H. Deng, Adaptive algorithms of sparse impulse response identification, D.SC dissertation, Dept. of Electrical and Computer Engineering, George Washington University, Washington, DC, Mar.2005.
[31]田磊,汪小志,刘志刚.自适应滤波算法及应用研究.电子测试,2008,(160)1：5-9.
[32]耿妍,张端金.自适应滤波算法综述.信息与电子工程,2008,(6)4：315-320
[33]詹望,杨福生.基于累积量的递归最小二乘算法研究.信号处理,1999,(15)3：240-248
[34]高鹰,谢胜利.基于矩阵广义逆递推的自适应滤波算法,电子学报,2002,(30)7：1032-1034.
[35]高鹰,谢胜利.基于相关函数的递推最小二乘算法及其在回波消除中的应用.通信学报,2002,23(9)：114-118.
[36]胡春风,高立,张筱华,王德隽.一种改进的RLS自适应滤波器算法.通信学,1998,(19)8：67-71
[37]赵知劲.一种新的基于高阶统计量的自适应滤波方法.电子学报,2000,28(12)：83-84,51.
[38]S. Gay and S. Tavathia, The fast affine projection algorithm, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'95), Detroit, Michigan, pp.3023-3026, May.1995.
[39]M. Tanaka, Y. Kaneda, S. Makino, and J. Kojima, Fast projection algorithm and its step size control, Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'95), Washington, DC, USA, pp.945-948, IEEE Computer Society,1995.
[40]M. Tanaka, Y. Kaneda, S. Makino, and J. Kojima, A fast projection algorithm for adaptive filtering, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., vol.E78-A, no.10,pp.1355-1361, Oct.1995.
[41]S.L. Gay, The fast affine projection algorithm, in Acoustic signal processing for telecommunication, pp.23-46, Kluwer Academic Publishers, Hingham, MA, USA, 2000.
[42]S. Gay and S. Douglas, Normalized natural gradient adaptive filtering for sparse and non-sparse systems, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'02), Orlando, USA, pp.1405-1408, May.2002.
[43]B. Jelfs and D. Mandic, A unifying approach to the derivation of the class of PNLMS algorithms, Proc.15th International Conference on Digital Signal Processing (DSP'07), London, UK, pp.35-38, Jul.2007.
[44]M. Doroslovacki and H. Deng, On convergence of proportionate-type NLMS adaptive algorithms, Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'06), Toulouse, Franc, pp.105-108, Mar.2006.
[45]A.W.H. Khong, P.A. Naylor, and J. Benesty, A low delay and fast converging improved proportionate algorithm for sparse system identification, EURASIP J. Audio Speech Music Process., Volume 2007, Article ID 84376,8 pages, doi:10.1155/2007/84376,2007.
[46]H. Deng and M. Doroslovacki, Wavelet-based MPNLMS adaptive algorithm for network echo cancellation, EURASIP J. Audio Speech Music Process., Volume 2007, Article ID 96101,5 pages doi:10.1155/2007/96101,2007.
[47]M.R. Petraglia and G Barboza, Improved PNLMS algorithm employing wavelet transform and sparse filters, Porc.16th European Signal Processing Conference (EUSIPCO'08), Lausanne, Switzerland, pp.1-5, Aug.2008.
[48]M. Yukawa, Krylov-proportionate adaptive filtering techniques not limited to sparse systems, IEEE Trans. Signal Processing, vol.57, no.3, pp.927-943, Mar.2009.
[49]S. Douglas, Adaptive filters employing partial updates, IEEE Trans. Circuits Syst. II, vol.44, no.3, pp.209-216, Mar.1997.
[50]T. Aboulnasr and K. Mayya, Selective coefficient update of gradient-based adaptive algorithms, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'97), Munich, Germany, pp.1929-1932, Apr.1997.
[51]T. Schertler, Selective block update of NLMS type algorithms, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'98), Seattle, WA, pp.1717-1720, May.1998.
[52]T. Aboulnasr and K. Mayyas, Complexity reduction of the NLMS algorithm via selective coefficient update, IEEE Trans. Signal Processing, vol.47, no.5, pp. 1421-1427, May.1999.
[53]K. Dogancay and 0. Tanrkulu, Selective-partial-update NLMS and affine projection algorithms for acoustic echo cancellation, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), Istanbul, Turkey, pp. 448-451, Jun.2000.
[54]K. Dogancay and O. Tanrikulu, Adaptive filtering algorithms with selective partial updates, IEEE Trans. Circuits Syst. II, vol.48, no.8, pp.762-769, Aug.2001.
[55]K. Dogancay and O. Tanrikulu, Selective-partial-update NLMS and affine projection algorithms for acoustic echo cancellation, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), pp.448-451, May.2000.
[56]A. Tandon, M.N.S. Swamy, and M.O. Ahmad, Partial-update Loo-norm based algorithms, IEEE Trans. Circuits Syst. I, vol.54, no.2, pp.411-419, Feb.2007.
[57]S. Gollamudi, S. Nagaraj, S. Kapoor, and Y.F. Huang, Set-membership filtering and a set-membership normalized LMS algorithm with an adaptive step size, IEEE Signal Processing Lett., vol.5, no.5, pp.111-114, May.1998.
[58]S. Gollamudi, S. Nagaraj, S. Kapoor, and Y.F. Huang, Set-membership adaptive equalization and updator-shared implementation for multiple channel communications systems, IEEE Trans. Signal Processing, vol.46, no.9, pp.2372-2384, Sep.1998.
[59]P.S.R. Diniz and S. Werner, Set-membership binormalized data-reusing algorithms, IEEE Trans. Signal Processing, vol.51, no.l, pp.124-134, Jan.2003.
[60]S. Werner, M.L.R. de Campos, and J.A. Apolinario, Data-selective constrained affine projection algorithm, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, (ICASSP'01), Salt Lake City, Uta, pp.3745-3748, May.2001.
[61]S. Werner and P.S.R. Diniz, Set-membership affine projection algorithm, IEEE Signal Processing Lett., vol.8, no.8, pp.231-235, Aug.2001.
[62]S. Werner, C.R. Johnson Jr., M.L.R. de Campos, and P.S.R. Diniz, Low-complexity constrained affine projection algorithms, IEEE Trans. Signal Processing, vol.53, no.12, pp.4545-4555, Dec.2005.
[63]O. Tanrikulu and K. Dogancay, Selective-partial-update proportionate normalized least-mean-squares algorithm for network echo cancellation, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'02), Orlando, FL, USA, pp.1889-1892, May.2002.
[64]J.D. Gordy, T. Aboulnasr, and M. Bouchard, Reduced-complexity proportionate NLMS employing block-based selective coefficient updates, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'08), Las Vegas, USA, pp.233-236, Mar.2008.
[65]S. Werner, J.A. Apolinario, and P.S.R. Diniz, Set-membership proportionate affine projection algorithms, EURASIP J. Audio, Speech, and Music Process., Volume 2007, Article ID 34242,10 pages, doi:10.1155/2007/34242,2009.
[66]H. Deng and M. Doroslovacki, New sparse adaptive algorithms using partial update, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'04), pp.845-848, May.2004.
[67]T. Gansler, J. Benesty, S.L. Gay, and M.M. Sondhi, A robust proportionate affine projection algorithm for network echo cancellation, Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), pp.793-796, May 2000.
[68]P.O. Hoyer, Non-negative matrix factorization with sparseness constraints, J. Mach. Learn. Res., vol.5, pp.1457-1469,2004.
[69]T. Gansler, J. Benesty, M.M. Sondhi, and S.L. Gay, Dynamic resource allocation for network echo cancellation, Proc. IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP'01), Salt Lake City, UT, USA, pp.3233-3236, May. 2001.
[70]A.W.H. Khong and P.A.A. Naylor, Efficient use of sparse adaptive filters, Proc.40th Asilomar Conf. on Signals, Systems and Computers (ACSSC'06), Pacific Grove, Calif, USA, pp.1375-1379, Oct-Nov 2006.
[71]K. Dogancay and P.A.A. Naylor, Recent advances in partial update and sparse adaptive filters, Proc.14th European Signal Processing Conference (EUSIPCO'05), Antalya, Turkey, pp.1-4 Sep.2005.
[72]R. Kwong and E. Johnston, A variable step size LMS algorithm, IEEE Trans. Signal Processing, vol.40, no.7, pp.1633-1642, Jul.1992.
[73]A.I. Sulyman and A. Zerguine, Convergence and steady-state analysis of a variable step-size NLMS algorithm, Signal Processing, vol.83, no.6, pp.1255-1273, Jun.2003.
[74]A. Mader, H. Puder, and G.U. Schmidt, Step-size control for acoustic echo cancellation filter-an overview, Signal Processing, vol.80, no.9, pp.1697-1719, Sep. 2000.
[75]H.C. Shin, A.H. Sayed, and W.J. Song, Variable step-size NLMS and affine projection algorithms, IEEE Signal Processing Lett., vol.11, no.2, pp.132-135, Feb.2004.
[76]J. Benesty, H. Rey, L.R. Vega, and S. Tressens, A nonparametric VSS NLMS algorithm, IEEE Signal Processing Lett., vol.13, no.10, pp.581-584, Oct.2006.
[77]C. Paleologu, S. Ciochina, and J. Benesty, Variable step-size NLMS algorithm for under-modeling acoustic echo cancellation, IEEE Signal Processing Lett., vol.15, no.10,pp.5-8,Jan.2008.
[78]C. Paleologu, J. Benesty, and S. Ciochina, A variable step-size affine projection algorithm designed for acoustic echo cancellation, IEEE Trans. Acoust., Speech, Signal Processing, vol.16, no.8, pp.1466-1478, Nov.2008.
[79]叶华,吴伯修.变步长自适应滤波算法的研究.电子学报,1990,18(4)：63-69.
[80]覃景繁,欧阳景正.一种新的变步长自适应滤波算法.数据采集与处理,1997,12(3)：171-174.
[8l]高鹰,谢胜利.一种变步长LMS自适应滤波算法及分析.电子学报,2001,29(8)：1094·1097.
[82]O. Hoshuyama, R. Goubran, and A. Sugiyama, A generalized proportionate variable step-size algorithm for fast changing acoustic environments, Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'04), Montreal, Quebec, Canada, pp.161-164, May.2004.
[83]P. Mahale, SVS-PNLMS algorithm for acoustic echo cancellation, Proc. of the 3rd International Conference on Information and Communication Technologies:From Theory to Applications (ICTTA'08), pp.1-6, Apr.2008.
[84]S. Saiki and M. Fukumoto, Improvement of the IPNLMS algorithm exploiting variable step size, IEICE Tech. Rep., vol.107, no.180, pp.25-28, Aug.2007.
[85]O. Tanrkulu, B. Baykal, A.G. Constantinides, and J.A. Chambers, Residual echo signal in critically sampled subband acoustic echo cancellers based on IIR and FIR filterbanks, IEEE Signal Processing Lett., vol.45, pp.901-912,1997.
[86]阎兆立,杜利民.电话语音回声消除的研究.电子学报,2002,(28)11：1726-1728.
[87]李挥,林茫茫等.VoIP回声消除器设计及算法研究.电子学报,2007,(35)9：1774-1778.
[88]王振力,张雄伟,杨吉斌,陈功.一种新的快速自适应滤波算法的研究.通信学报,2005,(26)11：1-6
[89]谢胜利,周元建.一种新自适应滤波快速算法及其在对路回波消除中的应用.电子学报,2003,(31)2：276-279.