面向实时通信系统的自适应回声消除算法研究
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摘要
实时语音通信所伴随的电子、声学回声现象极大地降低了通信质量。有效的解决方案是用线性滤波器以自适应算法辨识回声系统,滤波器输出作为回声信号的估计值,两者相减以抑制回声能量,提高通信质量。
归一化最小均方(Normalized Least Mean Square, NLMS)算法以其低计算复杂度与强鲁棒性而普遍应用于回声消除(Echo Cancellation, EC)领域,其主要缺点是收敛速度慢。随着处理器运算能力提高,计算复杂度更高、收敛速度更快的仿射投影算法(Affine Projection Algorithm, APA)开始应用于EC系统。但语音信号的非平稳性、强相关性严重减慢各种自适应算法的收敛速度。为消除输入信号强相关性对APA的影响,提出解相关APA (Decorrelation APA, DAPA)算法。DAPA利用实线性空间求内积的方法对输入信号矩阵进行预处理,解除不同时刻输入矩阵的相关性。与APA相比,DAPA计算复杂度适中,收敛速度有较大提高。
无参数变步长NLMS(Noparametric Variable Step Size NLMS, NPVSS-NLMS)算法可解决固定步长NLMS算法高收敛速度与低稳态失调的矛盾,其核心思想是从误差信号中恢复背景噪声,因此需要获得背景噪声功率(Background Noise Power, BNP)估计。为提高BNP估计的精度与可靠性,在分析BNP与失调噪声功率比后,提出一种在线的BNP估计改进算法,以提高BNP的估计精度、提高NPVSS-NLMS性能。为解决APA收敛速度与稳态失调的矛盾,通过强迫APA后验误差向量与背景噪声向量二次范数相等,推导得NPVSS-APA算法。分析APA算法失调比后,提出针对NPVSS-APA的改进BNP估计。
因回声延时的不确定性,在回声消除应用中,为保证充分建模,滤波器必须包含至少上千个系数。过长的滤波器将导致算法收敛速度减慢,计算复杂度增加等缺点。同时因延时效应,回声系统的冲激响应序列呈现稀疏性,即：序列大部分系数为零值系数以模拟延时。产生回声能量的活跃系数在时域上聚集,数量仅占系数总量极少一部分。
利用稀疏性提高自适应算法的工作效率成为EC系统实现的研究热点。本文通过两类算法,即Proportionate自适应算法(P算法)与延时检测-部分系数更新(Delay Estimate-Selective Partial Update, D-SPU)算法,对此进行讨论。
一、P算法按系数幅值为滤波器的不同系数赋以各异的收敛步长(Proportionate步长,P步长)以加快大系数收敛,达到加快滤波器整体收敛速度的目的。P算法收敛速度提高以计算复杂度增加为代价,且其P步长计算方式与目标系统系数幅值有关,实际应用时只能以滤波器系数当前幅值代替,引入误差。
本文利用独立性假设对P算法进行统计学建模,提出描述P算法滤波器各系数收敛曲线的理论公式,以该公式为基础,提出一种高效的P步长估计算法。新算法每隔若干步更新一次P步长,极大地降低算法计算复杂度。
为APA算法滤波器各系数指定相应的P步长,提出PAPA(Proportionate APA)算法。讨论PAPA算法的收敛性,并推导保证PAPA算法收敛的步长取值范围。
二、利用稀疏性最直接的方法是先用一延时检测滤波器估计延时(Delay Estimate),然后以滤波器峰值系数为中心,再用一个短的滤波器辨识活跃系数部分。因传统的延时检测算法需要用两个滤波器辨识目标系统,造成信息冗余。
部分系数更新(Selective Partial Update, SPU)算法用全长滤波器辨识系统,但每次只更新滤波器的一段系数以减小算法计算复杂度。传统的SPU算法未能充分利用回声路径稀疏性,造成算法性能下降。
提出D-SPU算法。D-SPU将SPU算法与回声路径稀疏性相结合,用移动窗积分扫描滤波器,以积分值最大区间为活跃系数位置。每次迭代均更新活跃系数,同时循环更新一段非活跃系数。更新活跃系数可精确辨识目标系统,更新一段非活跃系数可保证回声路径突变时算法的跟踪能力。D-SPU以一个滤波器同时完成延时检测与活跃系数辨识,避免传统延时检测算法的信息冗余。D-SPU计算复杂度低,收敛速度快,回声路径突变时跟踪能力强,有较高的实用价值。
本文主要对应用于EC系统的自适应算法进行研究,以达到加快系统收敛速度,提高系统稳定性的目的。此外,研究成果亦可丰富自适应理论,促进自适应算法的发展,其中某些范例可为其它自适应算法应用提供借鉴。
Network and Acoustic Echo impact the voice quality in the real-time audio communication equipment. An effective solution is to use an linear filter to identify the impulse response of echo path with adaptive algorithm. The filter outtput, which provides an electronic replica of the echo, is subtracted from the microphone signal to control the echo.
The Normalized Least Mean Square (NLMS) algorithm is the most popular adaptive algorithm in Echo Cancellation (EC) system for its robustness, simplicity and stability. Its main disadvantage is the slow convergence speed. With the improvement of processing power, the Affine Projection Algorithm (APA), which has higher computational complexity and convergences faster than the NLMS algorithm, begins to be deployed in EC system. However, the non-stationarity and auto-correlativity of speech signal significantly deteriorate the convergence speed of various adaptive algorithms. Decorrelation APA (DAPA) is proposed to eliminate the correlation of input matrices at different time instant with inner product defined in real linear space. It enhances the convergence speed of APA while its computational complexity is moderate.
Nonparametric Variable Step Size NLMS (NPVSS-NLMS) algorithm achieves both fast convergence and low misalignment, which are conflicting requirements in traditional adaptive algorithm. NPVSS-NLMS requires the Background Noise Power (BNP) estimate for recovering the background noise from error signal. After analyzing the power rate between background noise and misalignment noise, an on-line precise BNP estimate is obtained for NPVSS-NLMS to improve the accuracy and reliability of BNP estimate. In order to settle the conflicting requirements in APA, NPVSS-APA is proposed by making the2-Euclidian norms of error signal vector and background noise vector equal. After analyzing the misalignment rate in APA, a precise BNP estimate for NPVSS-APA is eventually achieved.
The bulk delay in the echo path varies significantly. Therefore, the adaptive filter used for EC system has to be equiped with at least thousands of coefficients to ensure exact modeling situation. The excessive length of the filter leads to slow convergnce and high computational complexity. On the other hand, the echo path is sparse in nature. Most of its coefficients are zero or unnoticeably smal value for bulk delay. Only a small portion of the coefficients, which are known as active coefficients, is significantly different from zero. They gather around in time domain to produce echo.
Exploiting the sparseness to improve the efficiency of adaptive algorithm has attracted more and more attentions. Two algorithms for sparseness, Proportionate algorithm (P algorithm) and Delay Estimate-Selective Partial Update (D-SPU) algorithm, are discussed in this thesis.
1) P algorithm assigns proportionate step-size to differenct coefficients based on the coefficient magnitude. The large coefficients obtaining large proportionate step-size convegence faster than the small coefficients, which leads to high overall convergence. However, P algorithm achieves fast convergence on the cost of computational complexity. Moreover, its proportionate step-size should be computed based on the coefficient magnitude of echo path. Due to the unavailable echo path, the current estimated magnitudes have to be used instead, which introduces error.
After analyzing the adaptation process of P algorithm with the stochastic approximation paradigm, a statistical model is obtained to describe the convergence process of each coefficient. Motivated by this result, an improved P algorithm is proposed whose proportionate step-size is based on the precise magnitude estimate. It saves computational complexity significantly by recomputing proportionate step-size every some iterations.
Proportionate APA (PAPA) is proposed by assigning proportionate step-sizes to each coefficients in APA. The convergence characteristic of PAPA is discussed. The range of the step-size which ensures the convergence of PAPA is derivated.
2) The most straightforward method in exploiting the sparseness of echo path is to estimate the bulk delay with an adaptive filter. Another short adaptive filter is then centered around this estimate to identify the active coefficients. Since the echo path is identified with two individual adaptive filters, this algorithm introduces information redundancy.
Selective Partial Update (SPU) algorithm identifies the whole system with an entire filter. However, it saves computational complexity by adapting a block of the filter coefficients rather than the entire filter at every iteration. However, the performance of tradional SPU is negative for it hasn't exploit the sparseness
Taking advantage of the sparseness with SPU algorithm, Delay-SPU (D-SPU) algorithm is proposed. D-SPU traverses the entire filter with slipping-window integrator. The block with the maximum integral indicates the location of active coefficients. Beside the active coefficients, D-SPU updates a block of the adaptive filter periodically at every iteration. The echo path is identified precisely by updating the active coefficients. Additionally, the algorithm is equipped with sensitive tracking capability by updating a block of adaptive filter irrespective of the active coefficients. D-SPU algorithm has both low computational complexity and high convergence speed, and it reacts instantaneously when the echo path changes. Consequently, it is practicable in real application.
The main contributions of this thesis lay in adaptive algorithm and the EC system implementation. It aims at improving the convergence speed and enhancing the stability of EC system. Beisdes, this reseach enriches adaptive theory and promotes the development of adaptive algorithm. Some of the examples in this thesis could offer object lessons for other adaptive applications.
归一化最小均方(Normalized Least Mean Square, NLMS)算法以其低计算复杂度与强鲁棒性而普遍应用于回声消除(Echo Cancellation, EC)领域,其主要缺点是收敛速度慢。随着处理器运算能力提高,计算复杂度更高、收敛速度更快的仿射投影算法(Affine Projection Algorithm, APA)开始应用于EC系统。但语音信号的非平稳性、强相关性严重减慢各种自适应算法的收敛速度。为消除输入信号强相关性对APA的影响,提出解相关APA (Decorrelation APA, DAPA)算法。DAPA利用实线性空间求内积的方法对输入信号矩阵进行预处理,解除不同时刻输入矩阵的相关性。与APA相比,DAPA计算复杂度适中,收敛速度有较大提高。
无参数变步长NLMS(Noparametric Variable Step Size NLMS, NPVSS-NLMS)算法可解决固定步长NLMS算法高收敛速度与低稳态失调的矛盾,其核心思想是从误差信号中恢复背景噪声,因此需要获得背景噪声功率(Background Noise Power, BNP)估计。为提高BNP估计的精度与可靠性,在分析BNP与失调噪声功率比后,提出一种在线的BNP估计改进算法,以提高BNP的估计精度、提高NPVSS-NLMS性能。为解决APA收敛速度与稳态失调的矛盾,通过强迫APA后验误差向量与背景噪声向量二次范数相等,推导得NPVSS-APA算法。分析APA算法失调比后,提出针对NPVSS-APA的改进BNP估计。
因回声延时的不确定性,在回声消除应用中,为保证充分建模,滤波器必须包含至少上千个系数。过长的滤波器将导致算法收敛速度减慢,计算复杂度增加等缺点。同时因延时效应,回声系统的冲激响应序列呈现稀疏性,即：序列大部分系数为零值系数以模拟延时。产生回声能量的活跃系数在时域上聚集,数量仅占系数总量极少一部分。
利用稀疏性提高自适应算法的工作效率成为EC系统实现的研究热点。本文通过两类算法,即Proportionate自适应算法(P算法)与延时检测-部分系数更新(Delay Estimate-Selective Partial Update, D-SPU)算法,对此进行讨论。
一、P算法按系数幅值为滤波器的不同系数赋以各异的收敛步长(Proportionate步长,P步长)以加快大系数收敛,达到加快滤波器整体收敛速度的目的。P算法收敛速度提高以计算复杂度增加为代价,且其P步长计算方式与目标系统系数幅值有关,实际应用时只能以滤波器系数当前幅值代替,引入误差。
本文利用独立性假设对P算法进行统计学建模,提出描述P算法滤波器各系数收敛曲线的理论公式,以该公式为基础,提出一种高效的P步长估计算法。新算法每隔若干步更新一次P步长,极大地降低算法计算复杂度。
为APA算法滤波器各系数指定相应的P步长,提出PAPA(Proportionate APA)算法。讨论PAPA算法的收敛性,并推导保证PAPA算法收敛的步长取值范围。
二、利用稀疏性最直接的方法是先用一延时检测滤波器估计延时(Delay Estimate),然后以滤波器峰值系数为中心,再用一个短的滤波器辨识活跃系数部分。因传统的延时检测算法需要用两个滤波器辨识目标系统,造成信息冗余。
部分系数更新(Selective Partial Update, SPU)算法用全长滤波器辨识系统,但每次只更新滤波器的一段系数以减小算法计算复杂度。传统的SPU算法未能充分利用回声路径稀疏性,造成算法性能下降。
提出D-SPU算法。D-SPU将SPU算法与回声路径稀疏性相结合,用移动窗积分扫描滤波器,以积分值最大区间为活跃系数位置。每次迭代均更新活跃系数,同时循环更新一段非活跃系数。更新活跃系数可精确辨识目标系统,更新一段非活跃系数可保证回声路径突变时算法的跟踪能力。D-SPU以一个滤波器同时完成延时检测与活跃系数辨识,避免传统延时检测算法的信息冗余。D-SPU计算复杂度低,收敛速度快,回声路径突变时跟踪能力强,有较高的实用价值。
本文主要对应用于EC系统的自适应算法进行研究,以达到加快系统收敛速度,提高系统稳定性的目的。此外,研究成果亦可丰富自适应理论,促进自适应算法的发展,其中某些范例可为其它自适应算法应用提供借鉴。
Network and Acoustic Echo impact the voice quality in the real-time audio communication equipment. An effective solution is to use an linear filter to identify the impulse response of echo path with adaptive algorithm. The filter outtput, which provides an electronic replica of the echo, is subtracted from the microphone signal to control the echo.
The Normalized Least Mean Square (NLMS) algorithm is the most popular adaptive algorithm in Echo Cancellation (EC) system for its robustness, simplicity and stability. Its main disadvantage is the slow convergence speed. With the improvement of processing power, the Affine Projection Algorithm (APA), which has higher computational complexity and convergences faster than the NLMS algorithm, begins to be deployed in EC system. However, the non-stationarity and auto-correlativity of speech signal significantly deteriorate the convergence speed of various adaptive algorithms. Decorrelation APA (DAPA) is proposed to eliminate the correlation of input matrices at different time instant with inner product defined in real linear space. It enhances the convergence speed of APA while its computational complexity is moderate.
Nonparametric Variable Step Size NLMS (NPVSS-NLMS) algorithm achieves both fast convergence and low misalignment, which are conflicting requirements in traditional adaptive algorithm. NPVSS-NLMS requires the Background Noise Power (BNP) estimate for recovering the background noise from error signal. After analyzing the power rate between background noise and misalignment noise, an on-line precise BNP estimate is obtained for NPVSS-NLMS to improve the accuracy and reliability of BNP estimate. In order to settle the conflicting requirements in APA, NPVSS-APA is proposed by making the2-Euclidian norms of error signal vector and background noise vector equal. After analyzing the misalignment rate in APA, a precise BNP estimate for NPVSS-APA is eventually achieved.
The bulk delay in the echo path varies significantly. Therefore, the adaptive filter used for EC system has to be equiped with at least thousands of coefficients to ensure exact modeling situation. The excessive length of the filter leads to slow convergnce and high computational complexity. On the other hand, the echo path is sparse in nature. Most of its coefficients are zero or unnoticeably smal value for bulk delay. Only a small portion of the coefficients, which are known as active coefficients, is significantly different from zero. They gather around in time domain to produce echo.
Exploiting the sparseness to improve the efficiency of adaptive algorithm has attracted more and more attentions. Two algorithms for sparseness, Proportionate algorithm (P algorithm) and Delay Estimate-Selective Partial Update (D-SPU) algorithm, are discussed in this thesis.
1) P algorithm assigns proportionate step-size to differenct coefficients based on the coefficient magnitude. The large coefficients obtaining large proportionate step-size convegence faster than the small coefficients, which leads to high overall convergence. However, P algorithm achieves fast convergence on the cost of computational complexity. Moreover, its proportionate step-size should be computed based on the coefficient magnitude of echo path. Due to the unavailable echo path, the current estimated magnitudes have to be used instead, which introduces error.
After analyzing the adaptation process of P algorithm with the stochastic approximation paradigm, a statistical model is obtained to describe the convergence process of each coefficient. Motivated by this result, an improved P algorithm is proposed whose proportionate step-size is based on the precise magnitude estimate. It saves computational complexity significantly by recomputing proportionate step-size every some iterations.
Proportionate APA (PAPA) is proposed by assigning proportionate step-sizes to each coefficients in APA. The convergence characteristic of PAPA is discussed. The range of the step-size which ensures the convergence of PAPA is derivated.
2) The most straightforward method in exploiting the sparseness of echo path is to estimate the bulk delay with an adaptive filter. Another short adaptive filter is then centered around this estimate to identify the active coefficients. Since the echo path is identified with two individual adaptive filters, this algorithm introduces information redundancy.
Selective Partial Update (SPU) algorithm identifies the whole system with an entire filter. However, it saves computational complexity by adapting a block of the filter coefficients rather than the entire filter at every iteration. However, the performance of tradional SPU is negative for it hasn't exploit the sparseness
Taking advantage of the sparseness with SPU algorithm, Delay-SPU (D-SPU) algorithm is proposed. D-SPU traverses the entire filter with slipping-window integrator. The block with the maximum integral indicates the location of active coefficients. Beside the active coefficients, D-SPU updates a block of the adaptive filter periodically at every iteration. The echo path is identified precisely by updating the active coefficients. Additionally, the algorithm is equipped with sensitive tracking capability by updating a block of adaptive filter irrespective of the active coefficients. D-SPU algorithm has both low computational complexity and high convergence speed, and it reacts instantaneously when the echo path changes. Consequently, it is practicable in real application.
The main contributions of this thesis lay in adaptive algorithm and the EC system implementation. It aims at improving the convergence speed and enhancing the stability of EC system. Beisdes, this reseach enriches adaptive theory and promotes the development of adaptive algorithm. Some of the examples in this thesis could offer object lessons for other adaptive applications.
引文
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