自适应滤波理论及其在回波消除中的应用研究
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摘要
自适应滤波器已经广泛应用于语音处理、回波消除、信道均衡、系统辨识、谱线增强、自适应阵列处理和生物医学信号处理等诸多领域中。而在调制解调器、长途电话、免提电话和电话会议系统中，回波消除技术占有极其重要的地位。但是，在声学回波消除应用中，往往需要上千个甚至更多的自适应滤波器系数才能达到回声消除的要求。这对自适应算法的计算负担提出了很高的要求。本论文主要研究了如何降低高阶自适应滤波器算法的计算复杂度及其在回波消除器中的应用。
当输入信号为有色信号时，快速仿射投影算法的收敛速度比NLMS算法快，但计算量接近NLMS算法。为了减小快速仿射投影算法的计算量，我们提出了两种简化的仿射投影算法。这两种简化算法均节省了一定的计算量，并具有与快速仿射投影算法十分相近的收敛性能。简化算法中的前置滤波器可以采用Leaky LMS算法和噪声LMS算法两种方法实现。在声学回波消除应用中，即使采用计算复杂度为O(N)量级的自适应滤波算法，其计算量仍然显得过大。在自适应滤波器中采用分组处理技术，可以大大减小算法的运算量。因此，我们提出了一种分组准确快速仿射投影算法和分组准确简化仿射投影算法。分组准确仿射投影算法在数学上与原始的仿射投影算法完全等价，因此收敛性能也一样。但是，分组准确仿射投影算法大大降低了计算复杂度。分组准确仿射投影算法可以采用较小的分组以获得较短的处理延迟。此外，我们还尝试对回波消除器中的残差进行听觉加权，从而改善回波消除的主观质量。
立体声回声消除可以看作是单路回声消除的直接推广。但是，在多路回声消除中，由于多路输入信号之间存在强相关性，消除多路回波出现了与单路回波消除不同的新问题。本文对各种立体声回声消除自适应算法进行了初步的研究，并提出了一种改进的非线性预处理方法，可以对多路输入信号进行更有效的去相关。另外，我们还根据矩阵求逆引理提出了一种计算量较小的两路仿射投影算法，并利用人耳的掩蔽效应进一步改善其收敛性能。
在系统辨识应用中，要求直接求解自适应滤波器的权系数向量。我们提出了一种简化的逆QR分解递推最小二乘算法。该算法直接求解权系数向量，避免
Adaptive filtering has been widely used in many applications, such as speech signal processing, echo cancellation, channel equalization, system identification, line enhancement, adaptive beamformer and biomedical signal processing, etc. Echo cancellation is of major importance in MODEM, long distance telephone, hands-free telephone and teleconference. However, a major difficulty encountered in applications like acoustic echo cancellation is the requirement for very long adaptive filters (N>1000). The implementation of such long adaptive filters requires heavy computational resources. The dissertation is focused on the research of reducing the computational complexity of large adaptive filters and their applications in echo cancellation.
Fast affme projection algorithm may possess NLMS like complexity while having a better convergence rate for colored input signals. In order to reduce the computational complexity of fast affine projection algorithm, two simplified algorithms are presented. The convergence performance of the simplified algorithms is comparable to that of affine projection algorithm even with less computational complexity. The prefilter in the simplified algorithms can be implemented by Leaky LMS or noisy LMS. In acoustic echo cancellation, the computational complexity is still too large even for algorithms with O(N) complexity. Block processing is an effective approach to further reduce the computational complexity. A block exact fast affine projection algorithm and a block exact simplified affine projection algorithm are proposed in the dissertation. The block exact affine projection algorithm is an exact equivalent of the original affine projection algorithm. Thus, it performs identically with affine projection algorithm and at the same time, offers a considerable saving in complexity. The block exact algorithm allows the use of small block length, thus making the effect of processing delay negligible. In order to improve the subject quality of echo cancellation, a perceptually weighted echo canceller is also
当输入信号为有色信号时，快速仿射投影算法的收敛速度比NLMS算法快，但计算量接近NLMS算法。为了减小快速仿射投影算法的计算量，我们提出了两种简化的仿射投影算法。这两种简化算法均节省了一定的计算量，并具有与快速仿射投影算法十分相近的收敛性能。简化算法中的前置滤波器可以采用Leaky LMS算法和噪声LMS算法两种方法实现。在声学回波消除应用中，即使采用计算复杂度为O(N)量级的自适应滤波算法，其计算量仍然显得过大。在自适应滤波器中采用分组处理技术，可以大大减小算法的运算量。因此，我们提出了一种分组准确快速仿射投影算法和分组准确简化仿射投影算法。分组准确仿射投影算法在数学上与原始的仿射投影算法完全等价，因此收敛性能也一样。但是，分组准确仿射投影算法大大降低了计算复杂度。分组准确仿射投影算法可以采用较小的分组以获得较短的处理延迟。此外，我们还尝试对回波消除器中的残差进行听觉加权，从而改善回波消除的主观质量。
立体声回声消除可以看作是单路回声消除的直接推广。但是，在多路回声消除中，由于多路输入信号之间存在强相关性，消除多路回波出现了与单路回波消除不同的新问题。本文对各种立体声回声消除自适应算法进行了初步的研究，并提出了一种改进的非线性预处理方法，可以对多路输入信号进行更有效的去相关。另外，我们还根据矩阵求逆引理提出了一种计算量较小的两路仿射投影算法，并利用人耳的掩蔽效应进一步改善其收敛性能。
在系统辨识应用中，要求直接求解自适应滤波器的权系数向量。我们提出了一种简化的逆QR分解递推最小二乘算法。该算法直接求解权系数向量，避免
Adaptive filtering has been widely used in many applications, such as speech signal processing, echo cancellation, channel equalization, system identification, line enhancement, adaptive beamformer and biomedical signal processing, etc. Echo cancellation is of major importance in MODEM, long distance telephone, hands-free telephone and teleconference. However, a major difficulty encountered in applications like acoustic echo cancellation is the requirement for very long adaptive filters (N>1000). The implementation of such long adaptive filters requires heavy computational resources. The dissertation is focused on the research of reducing the computational complexity of large adaptive filters and their applications in echo cancellation.
Fast affme projection algorithm may possess NLMS like complexity while having a better convergence rate for colored input signals. In order to reduce the computational complexity of fast affine projection algorithm, two simplified algorithms are presented. The convergence performance of the simplified algorithms is comparable to that of affine projection algorithm even with less computational complexity. The prefilter in the simplified algorithms can be implemented by Leaky LMS or noisy LMS. In acoustic echo cancellation, the computational complexity is still too large even for algorithms with O(N) complexity. Block processing is an effective approach to further reduce the computational complexity. A block exact fast affine projection algorithm and a block exact simplified affine projection algorithm are proposed in the dissertation. The block exact affine projection algorithm is an exact equivalent of the original affine projection algorithm. Thus, it performs identically with affine projection algorithm and at the same time, offers a considerable saving in complexity. The block exact algorithm allows the use of small block length, thus making the effect of processing delay negligible. In order to improve the subject quality of echo cancellation, a perceptually weighted echo canceller is also
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