面向信道均衡的仿射投影算法非维纳解研究

The affine projection (AP) algorithm is widely expected to operate near the corresponding Wiener filter solution. An exception to this popular perception occurs when the algorithm is used to adapt a transversal equalizer in the presence of additive narrowband interference. The steady-state AP equalizer behavior does not correspond to that of the fixed Wiener equalizer: the mean of its weights is different from the Wiener weights, and its mean squared error (MSE) performance may be significantly better than the Wiener performance. The contributions of this project serve to better understand this so-called non-Wiener phenomenon of the AP and AP adaptive transversal equalizers. Based on the result that the AP algorithm is a special case of the Normalized Least Mean Square algorithm with Orthogonal Correction Factors where the delay is set to unity,there will have three mainly contributions in this project. The first contribution will be the analysis of the mean of the AP weights in steady-state, assuming a large interference-to-signal ratio (ISR). The analysis is based on the Butterweck expansion of the weight update equation. The equalization problem is transformed to an equivalent interference estimation problem to make the analysis of the Butterweck expansion tractable. The analytical results will be valid for all step-sizes. The second contribution will be the MSE estimator based on the expression for the mean of the AP equalizer weight vector. For the development of the MSE estimator, the transfer function approximation of the AP algorithm will be generalized for the steady-state analysis of the AP algorithm. This generalization will also be used to analysis the cause of the breakdown of the MSE estimators when the interference is not strong, as the assumption that the variation of the weight vector around its mean is small relative to the mean of the weight vector itself. The third contribution will be the analysis of optimal step-size for the AP algorithm. We will develop the recursive equation for the optimal step-size and analysis the relations between the AP equalizer parameters and the narrowband interference. So we can design the adaptive transversal equalizer to reject the narrowband interference. The research of this project will further expand the concept of Wiener solution and narrowband anti-interference. It will achieve the development theory of the adaptive transversal equalization and speech signal processing.

当自适应横向均衡器用来抑制窄带干扰时，传统的自适应滤波理论不再适用，促使研究者探索自适应横向均衡器的"非维纳"特性，以提高通信装置抗窄带干扰的能力。同时仿射投影（Affine Projection, AP）算法提供了一种"权衡"自适应滤波算法复杂度、鲁棒性、收敛性和失调量的方法。本项目旨在利用AP算法作为一种带有正交因子的归一化最小均方算法的特例，在窄带干扰的环境中，基于Butterweck权值分解的方法，研究建立AP算法横向均衡器的"非维纳"解；利用传递函数分析的方法，研究建立AP算法均衡器的权值均方误差及其稳定状态的解；研究不同的迭代步长对AP算法均衡器权值波动的影响，建立优化的迭代步长及其递归迭代表达式，研究怎么样的操控自适应横向均衡器，以提高通信接收装置抗窄带干扰的能力。本项目的研究成果将进一步拓展抗窄带干扰装置的设计方法，对信道均衡、语音信号处理等方面理论的发展具有重要的意义。

当自适应横向均衡器用来抑制非平稳的窄带压制式干扰时，North指出传统的自适应滤波理论不再适用，其主要原因在于传统自适应滤波算法，包括LMS算法和AP算法前后迭代方向近似于平行，基本不收敛，表现为明显的“非维纳”特性。本项目利用AP算法作为一种带有正交因子的归一化最小均方算法的特例，在非平稳的窄带压制干扰环境中，基于Butterweck权值分解的方法，研究建立了AP算法横向均衡器的“非维纳”解，分析了权值误差收敛性的随机统计模型，并通过避免矩阵的求逆运算，减少了算法的运算复杂度；利用传递函数分析的方法，研究建立了AP算法均衡器的权值均方误差及其稳定状态的解；分析了AP算法在自适应滤波器迭代方向的误差，建立了AP-DE算法，其误差引起方向与自适应滤波器的迭代方向完全一致，在一定程度上促进了自适应滤波的收敛性和跟踪性；同时，分析了其收敛性和跟踪性的随机统计模型，研究了不同的迭代步长对AP算法均衡器权值波动的影响，建立了优化的迭代步长及其递归迭代表达式；研究了怎么样的操控自适应横向均衡器，以提高无线通信接收装置抗窄带干扰的能力；同时，利用实测的无线通信数据，对非平稳的窄带瞄准式干扰进行了分析，说明了所建立方法的有效性和可行性。本项目的研究成果将进一步拓展抗窄带干扰装置的设计方法，对无线通信、卫星导航、雷达等系统主瓣抗非平稳窄带干扰方面理论的发展具有重要的意义。