一种基于格型正交化的二阶Volterra自适应滤波算法

针对 Volterra 自适应滤波器输入信号相关性或附加的非线性畸变的增强使自适应滤波器性能下降的问题,本文提出基于格型正交化的二阶 Volterra 自适应滤波算法.先对输入信号进行格型预处理,得到互相正交的后向预测误差信号;然后将其作为自适应滤波器的输入,从而大大降低了一次项、平方项和交叉乘积项信号各项之间的耦合,改善了自适应算法的收敛性能.有源噪声对消的仿真结果表明,在输入噪声强相关和附加较强非线性畸变时本算法仍具有较好的消噪性能.     

稀疏自适应Volterra滤波的QRD-RLS算法

求解非线性问题时,非线性Volterra滤波的性能明显优于线性滤波;稀疏结构Voherra滤波器有效降低了Volterra滤波的工程应用复杂度;本文针对稀疏Volterra滤波,改进了基于QR分解的RLS算法,在更换滤波器抽头的时候保留了先前的数据信息,从而加速当前抽头的收敛,加快了滤波器核矢量的更新和替换.仿真结果表明改进的QRD-RKS算法具有快速自适应能力;一同验证了稀疏Volterra滤波的有效性.     

Adaptive Volterra filtering using M-band wavelet transform andGram-Schmidt orthogonalisation

A new adaptive Volterra filter with fast convergence is proposed, where the M-band discrete wavelet transform and Gram-Schmidt orthogonalisation are utilised. In particular, the cascade combination of two such procedures reduces the eigenvalue spread of the Volterra input auto-correlation matrix, thus improving the convergence speed of the adaptive nonlinear filtering     

一种基于格型滤波的二阶Volterra自适应均衡算法

针对随着Volterra滤波器记忆元增多,计算复杂度成指数快速增加的问题,本文提出了一种基于格型滤波的二阶Volterra自适应算法.利用格型滤波器正交化处理输入信号,实现了二次项信号解耦,从而减少了自适应算法的输入信号自相关矩阵条件数,提高了自适应算法性能;同时也实现了二次项的权系数矩阵对角化,大大减少了二次项的权系数,使得滤波器权系数与输出成线性关系,权系数的LMS算法变得更加简便.计算机仿真结果表明,本文所提出的算法无论对线性信道还是非线性信道都有比文献[5]算法更快的收敛速度和更好的稳态性能.     

Adaptive lattice IIR filtering revisited: convergence issues andnew algorithms with improved stability properties

Several algorithms for adaptive IIR filters parameterized in lattice form can be found in the literature. The salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy. On the other hand, while computing the gradient signals that drive the direct form update algorithms is straightforward, it is not so for the lattice algorithms. This has led to simplified lattice algorithms using gradient approximations. Although, in general, these simplified schemes present the same stationary points as the original algorithms, whether this is also true for convergent points has remained an open problem. This also applies to nongradient-based lattice algorithms such as hyperstability based and the Steiglitz-McBride algorithms. Here, we answer this question in the negative, by showing that for several adaptive lattice algorithms, there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent. In addition, new lattice algorithms with properties are derived. They are based on the cascade lattice structure, which allows the derivation of sufficient conditions for local stability     

A lattice orthogonalization technique for integrated square error minimization

A recursive integrated square error minimization technique is developed to solve integral equations occurring in electromagnetic scattering problems. The underlying idea is a generalization of the concept of the second minimization step recently proposed by van den Berg. This is implemented by a structured lattice algorithm similar to the lattice algorithms which emerged in the last decade in signal processing theory.     

Multisource discrimination using IIR Volterra filtering

This paper exhibits an algorithm based on Volterra-type processing in order to detect several independent sources on the same carrier frequency and to determine the number of them. The use of infinite impulse response (IIR) Volterra filtering to build a suitable discrimination test is dictated by the need of higher-order moments in this type of nonlinear problem, as well as the need of IIR for convergence     

Volterra filtering and higher order whiteness

Some properties of Volterra filtering are established. Finite-order, finite-horizon Volterra filtering is investigated as well as its asymptotic properties. Next, the concepts of Volterra unpredictability and uninterpolability lead to generalizations of the notion of white noise to higher orders. These generalizations are introduced and relations are established between them     

数值稳健的自适应二阶Volterra滤波器

本文采用广义多信道模型，利用ＱＲ分解方法，实现了自适应二阶Ｖｏｌｔｅｒｒａ滤波器，计算机模拟结果表明该帝现收敛速度快，数值性能好。     

Adaptive parallel-cascade truncated Volterra filters

This paper studies adaptive truncated Volterra filters employing parallel-cascade structures. Parallel-cascade realizations implement higher order Volterra systems as a parallel connection of multiplicative combinations of lower order truncated Volterra systems. A normalized LMS adaptive filter is developed, and its performance capabilities are evaluated using a series of simulation experiments. The experimental results indicate that the normalized LMS adaptive parallel-cascade Volterra filter has superior convergence properties over several competing structures. This paper also includes an experiment that demonstrates the capability of the parallel-cascade adaptive system to reduce its implementation complexity by using fewer than the maximum number of branches required for the most general realization of the system     

Adaptive second-order Volterra delay filter

A new adaptive second-order Volterra delay filter is developed to include the linear and quadratic filter coefficients for system modelling and identification. The filter structure is very effective in modelling second-order Volterra systems with sparse system coefficients     

A fast algorithm for general Volterra filtering

Volterra filters are a classical instrument for nonlinear channels and systems modeling, noise and echo cancellation, signal estimation and detection, and various other applications. As is well known, the computational weight of Volterra filters exponentially grows with the nonlinearity degree. This work presents a contribution to the efficient computation of Volterra filters with generic order nonlinearity found in many telecommunication applications. Our technique rests on the interpretation of the Mth-order one-dimensional Volterra filters in terms of M-dimensional linear convolution, and it adopts a multidimensional fast convolution scheme. This makes the method applicable to any M. Interestingly enough, fast convolution based on the standard multidimensional fast Fourier transform (MD FFT) in the case of Volterra filters is outperformed by direct computation. Our method is efficient due to the use of a special MD FFT which can exploit the symmetries of the signals entering the computation of Volterra filters and which makes it superior to direct computation. The points of interests of the results presented are both the generality and the fact that they show that the well-known nonlinearity/multidimensionality tradeoff of Volterra filters can have computational implications.     

一种分阶自适应Volterra滤波算法

稳定分布可以更好地描述实际应用中所遇到的具有显著脉冲特性的随机噪声.这种噪声的二阶及二阶以上统计量均不存在,需要用分数低阶统计量描述.针对Volterra级数非线性项将稳定分布的尖峰脉冲特性更加放大,导致输入信号自相关矩阵的特征值扩展更大的问题,本文提出了一种对于二阶Volterra级数的线性项部分和非线性部分分别采用两个不同收敛因子的分阶Volterra滤波器最小平均p范数(DOVLMP)算法,并分析证明了该算法的收敛性能.仿真结果验证了本文方法较传统算法的优越性.     

Adaptive LMS filter with lattice prefilter

A filter structure consisting of a lattice predictor to function as a prefilter and a bank of subfilters using backward predictor errors is presented. It can realise a general transversal transfer function, has a good convergence rate, and is insensitive to the eigenvalue spread, even when a low order lattice predictor is used     

一种全解耦的Volterra自适应滤波器

本文研究了Volterra自适应滤波的解耦问题.通过对Volterra滤波器的伪线性组合结构的提出和分析,得到了一个新的关于均方误差MSE的表达式,并将Volterra自适应滤波问题描述为一个约束优化问题,从而导出了满足最小均方误差(MMSE)指标的具有分块对角型输入相关矩阵的全解耦Volterra标准方程,据此设计了一种全解耦的Volterra自适应滤波器,给出了滤波器权向量的自适应修正公式.仿真结果验证了本文方法的有效性.     

Semisystolic implementation of second-order Volterra digital filters based on recurrence algorithm of Volterra filtering

The letter presents a quasitriangular semisystolic array for the implementation of nonlinear second-order volterra digital filters. The performance of the proposed systolic array is based on the recurrence algorithm of Volterra filtering, which is also derived here.<>     

Adaptive minimum bit-error-rate filtering

Adaptive filtering has traditionally been developed based on the minimum mean square error (MMSE) principle and has found ever-increasing applications in communications. The paper develops adaptive filtering based on an alternative minimum bit error rate (MBER) criterion for communication applications. It is shown that the MBER filtering exploits the non-Gaussian distribution of filter output effectively and, consequently, can provide significant performance gain in terms of smaller bit error rate (BER) over the MMSE approach. Adopting the classical Parzen window or kernel density estimation for a probability density function (pdf), a block-data gradient adaptive MBER algorithm is derived. A stochastic gradient adaptive MBER algorithm is further developed for sample-by-sample adaptive implementation of the MBER filtering. Extension of the MBER approach to adaptive nonlinear filtering is also discussed.     

Adaptive lattice bilinear filters

Two fast least-squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models are presented. The lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem, thus using multichannel lattice filtering algorithms to solve the nonlinear filtering problem. The computational complexity of the algorithms is an order of magnitude smaller than that of previously available methods. The first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to compute the adaptive filter outputs. This method is conceptually very simple, but results in biased system models in the presence of measurement noise. The second is an approximate least-squares output error solution; the past samples of the output of the adaptive system itself are used to produce the filter output at the current time. Results indicate that the output error algorithm is less sensitive to output measurement noise than the equation error method     

Adaptive filtering with decorrelation for coloured AR environments

The aim of this paper is to improve the convergence speed and steady state error of LMS-type adaptive algorithms for coloured and nonstationary signals such as in acoustic echo cancellation. The performance of these algorithms is limited by the eigenvalue spread of the correlation matrix of the input signal and also by the power of the additive noise. In this paper, the decorrelating adaptive algorithms are classified into four types: input-decorrelating, error-decorrelating, joint-prefiltering and a combination of joint-prefiltering and input-decorrelating. The last two types of algorithms are studied and guidelines are given to choose the proper algorithms based on the power spectral densities of the input signal and noise. For a prefiltering structure, it is proven that if the adaptive filter operates on any prefiltered pair of input and desired signal the optimal solution will remain unchanged. It is suggested that a new adaptive decorrelation prefilter be included that is designed to achieve two objectives simultaneously: to increase the speed of convergence by reducing the correlation between the prefiltered samples of the input; and to improve the tracking and the steady state performance by reducing the noise power in the prefiltered domain. Simulations and theoretical results confirm that the introduced auxiliary whitening processes improve the performance of the adaptive algorithms by jointly whitening the input and the error signal.