Signal separation by symmetric adaptive decorrelation: stability,convergence, and uniqueness

The performance of signal enhancement systems based on adaptive filtering is highly dependent on the quality of the noise reference. In the LMS algorithm, signal leakage into the noise reference leads to signal distortion and poor noise cancellation. The origin of the problem lies in the fact that LMS decorrelates the signal estimate with the noise reference, which, in the case of signal leakage, makes little sense. An algorithm is proposed that decorrelates the signal estimate with a “signal-free” noise estimate, obtained by adding a symmetric filter to the classical structure. The symmetric adaptive decorrelation (SAD) algorithm no longer makes a distinction between signal and noise and is therefore a signal separator rather than a noise canceler. Stability and convergence are of the utmost importance in adaptive algorithms and hence are carefully studied. Apart from limitations on the adaptation constants, stability around the desired solution can only be guaranteed for a subclass of signal mixtures. Furthermore, the decorrelation criterion does not yield a unique solution, and expressions for the “phantom” solutions are derived. Simulations with short FIR filters confirm the predicted behavior     

基于无噪后验错误矢量信号能量的变正则因子仿射投影算法

变正则因子技术是提高仿射投影自适应算法性能的重要方法之一.由于环境噪声的影响,现有的变正则因子自适应算法收敛速度较慢且稳态误差较大,各种测量、评估误差的存在进一步恶化了算法性能.为提高自适应算法的跟踪性能,本文在分析无噪先验错误矢量、无噪后验错误矢量和额外均方错误间关系的基础上,提出通过最小化无噪后验错误矢量信号能量来推导自适应变正则因子表达式的方法.在实践应用中,该方法利用了测量噪声的统计方差特性,并提出一种更加光滑且更加容易控制的指数缩放因子评估方法.系统辨识的仿真结果表明本文方法与传统的变正则因子方法以及变步长方法相比有更快的收敛速度与更低的稳态误差.     

QR-based TLS and mixed LS-TLS algorithms with applications to adaptive IIR filtering

The least squares (LS), total least squares (TLS), and mixed LS-TLS approaches are compared as to their properties and performance on several classical filtering problems. Mixed LS-TLS is introduced as a QR-decomposition-based algorithm for unbiased, equation error adaptive infinite impulse response (IIR) filtering. The algorithm is based on casting adaptive IIR filtering into a mixed LS-TLS framework. This formulation is shown to be equivalent to the minimization of the mean-square equation error subject to a unit norm constraint on the denominator parameter vector. An efficient implementation of the mixed LS-TLS solution is achieved through the use of back substitution and inverse iteration. Unbiasedness of the system parameter estimates is established for the mixed LS-TLS solution in the case of uncorrelated output noise, and the algorithm is shown to converge to this solution. LS, TLS, and mixed LS-TLS performance is then compared for the problems of echo cancellation, noise reduction, and frequency equalization.     

Interference cancellation in respiratory sounds via amultiresolution joint time-delay and signal-estimation scheme

This paper is concerned with the problem of cancellation of heart sounds from the acquired respiratory sounds using a new joint time-delay and signal-estimation (JTDSE) procedure. Multiresolution discrete wavelet transform (DWT) is first applied to decompose the signals into several subbands. To accurately separate the heart sounds from the acquired respiratory sounds, time-delay estimation (TDE) is performed iteratively in each subband using two adaptation mechanisms that minimize the sum of squared errors between these signals. The time delay is updated using a nonlinear adaptation, namely the Levenberg-Marquardt (LM) algorithm, while the function of the other adaptive system-which uses the block fast transversal filter (BFTF)-is to minimize the mean squared error between the outputs of the delay estimator and the adaptive filter. The proposed methodology possesses a number of key benefits such as the incorporation of multiple complementary information at different subbands, robustness in presence of noise, and accuracy in TDE. The scheme is applied to several cases of simulated and actual respiratory sounds under different conditions and the results are compared with those of the standard adaptive filtering. The results showed the promise of the scheme for the TDE and subsequent interference cancellation     

一种残差模糊匹配的非线性目标跟踪改进算法

为解决目标跟踪中因系统滤波初值不准确和噪声统计特性未知引起标准非线性卡尔曼算法估计误差变大问题,该文提出一种基于残差的模糊自适应(RTSFA)非线性目标跟踪算法。在确定采样型滤波基本框架的基础上,给出了在线性化误差约束条件下高斯权值的积分一般形式,并利用李雅普诺夫第二方法证明了该算法估计误差有界收敛的充分条件。进一步构建自适应噪声协方差矩阵在线估计噪声特性,并引入Takagi-Sugeno模型和量测椭球界限规则选择噪声估计器调节因子,有效提高了算法的收敛速度和滤波精度。通过滤波初值信息不明和量测噪声时变的纯方位目标跟踪模型,验证了非线性目标跟踪算法具有更好的跟踪精度和更强的鲁棒性。     

Robust M-estimate adaptive filtering

An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed. Instead of using the conventional least-square cost function, a new cost function based on an M-estimator is used to suppress the effect of impulse noise on the filter weights. The resulting optimal weight vector is governed by an M-estimate normal equation. A recursive least M-estimate (RLM) adaptive algorithm and a robust threshold estimation method are derived for solving this equation. The mean convergence performance of the proposed algorithm is also analysed using the modified Huber (1981) function (a simple but good approximation to the Hampel's three-parts-redescending M-estimate function) and the contaminated Gaussian noise model. Simulation results show that the proposed RLM algorithm has better performance than other recursive least squares (RLS) like algorithms under either a contaminated Gaussian or alpha-stable noise environment. The initial convergence, steady-state error, robustness to system change and computational complexity are also found to be comparable to the conventional RLS algorithm under Gaussian noise alone     

Fast subsampled-updating stabilized fast transversal filter (FSUSFTF) RLS algorithm for adaptive filtering

We present a new, doubly fast algorithm for recursive least-squares (RLS) adaptive filtering that uses displacement structure and subsampled-updating. The fast subsampled-updating stabilized fast transversal filter (FSU SFTF) algorithm is mathematically equivalent to the classical fast transversal filter (FTF) algorithm. The FTF algorithm exploits the shift invariance that is present in the RLS adaptation of an FIR filter. The FTF algorithm is in essence the application of a rotation matrix to a set of filters and in that respect resembles the Levinson (1947) algorithm. In the subsampled-updating approach, we accumulate the rotation matrices over some time interval before applying them to the filters. It turns out that the successive rotation matrices themselves can be obtained from a Schur-type algorithm that, once properly initialized, does not require inner products. The various convolutions that appear In the algorithm are done using the fast Fourier transform (FFT). The resulting algorithm is doubly fast since it exploits FTF and FFTs. The roundoff error propagation in the FSU SFTF algorithm is identical to that in the SFTF algorithm: a numerically stabilized version of the classical FTF algorithm. The roundoff error generation, on the other hand, seems somewhat smaller. For relatively long filters, the computational complexity of the new algorithm is smaller than that of the well-known LMS algorithm, rendering it especially suitable for applications such as acoustic echo cancellation     

An adaptive filtering approach to spectral estimation and SARimaging

We present an adaptive FIR filtering approach, which is referred to as the amplitude and phase estimation of a sinusoid (APES), for complex spectral estimation. We compare the APES algorithm with other FIR filtering approaches including the Welch (1967) and Capon (1969) methods. We also describe how to apply the FIR filtering approaches to target range signature estimation and synthetic aperture radar (SAR) imaging. We show via both numerical and experimental examples that the adaptive FIR filtering approaches such as Capon and APES can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the FFT method, which is also a special case of the FIR filtering approach. We show that although the APES algorithm yields somewhat wider spectral peaks than the Capon method, the former gives more accurate overall spectral estimates and SAR images than the latter and the FFT method     

New unbiased adaptive IIR filter: it’s robust and variable step-size versions and application to active noise control

This paper proposes a robust variable step-size adaptive IIR filter realized by a new bias-free structure (BFS). Unlike equation error (EQE) method that uses a desired signal contaminated with observation noise, the BFS employs a filter driven by the output of the plant estimate and this achieves a bias-free estimate of the denominator of the system function. In addition, the adaptation is made robust to the observation noise by the Griffiths’ LMS adaptation, which uses the cross-correlation estimate between the input and the desired signal for its adaptation gradient computation. A robust variable step-size adaptation is also realized by the Griffiths’ gradient. The proposed structure is referred to as BFSGV and has good modeling capability with improved convergence rate and reduced misadjustment. For system identification, the proposed BFSGV algorithm gives a 3 dB improvement in the performance index over EQE method. The proposed BFSGV has been applied to active noise control (ANC). The BSFGV structure is used for secondary path (SP) estimation, and for the main path (MP), BFS structure with step-size varied according to Okello’s method (BSFV) is used. The new ANC system for narrowband noise field is found to be having 4 times faster convergence rate and an additional noise reduction of 15dB over that FIR for MP and the EQE for SP. Further, the use of the proposed ANC IIR algorithm achieves computational savings compared to that of FIR. For the broadband noise field, the proposed method that uses BSFV for MP and BSFGV for SP provides 18 times faster convergence rate and 2.5 dB reduction in ANC error compare to that of the ANC using FIR for MP and the EQE for SP estimation.     

Modified leaky LMS algorithm for channel estimation in DS-CDMAsystems

A simple adaptive least mean square (LMS) type algorithm for channel estimation is developed based on certain modifications to finite-impulse response (FIR) Wiener filtering. The proposed algorithm is nearly blind since it does not require any training sequence or channel statistics, and it can be implemented using only noise variance knowledge. A condition guaranteeing the convergence of the algorithm and theoretical mean square error (MSE) values are also derived. Computer simulation results demonstrate that the proposed algorithm can yield a smaller MSE than existing techniques, and that its performance is close to that of optimal Wiener filtering     

Stochastic analysis of the LMS algorithm with a saturationnonlinearity following the adaptive filter output

This paper presents a statistical analysis of the least mean square (LMS) algorithm with a zero-memory scaled error function nonlinearity following the adaptive filter output. This structure models saturation effects in active noise and active vibration control systems when the acoustic transducers are driven by large amplitude signals. The problem is first defined as a nonlinear signal estimation problem and the mean-square error (MSE) performance surface is studied. Analytical expressions are obtained for the optimum weight vector and the minimum achievable MSE as functions of the saturation. These results are useful for adaptive algorithm design and evaluation. The LMS algorithm behavior with saturation is analyzed for Gaussian inputs and slow adaptation. Deterministic nonlinear recursions are obtained for the time-varying mean weight and MSE behavior. Simplified results are derived for white inputs and small step sizes. Monte Carlo simulations display excellent agreement with the theoretical predictions, even for relatively large step sizes. The new analytical results accurately predict the effect of saturation on the LMS adaptive filter behavior     

Adaptive blind calibration of timing offset and gain mismatch for two-channel time-interleaved ADCs

In this paper, we describe a blind calibration method for gain and timing mismatches in a two-channel time-interleaved low-pass analog-to-digital converters (ADC). The method requires that the input signal should be slightly oversampled. This ensures that there exists a frequency band around the zero frequency where the Fourier transforms of the ADC subchannels are alias free. Low-pass filtering the ADC subchannels to this alias-free band reduces the blind calibration problem to a conventional gain and time delay estimation problem for an unknown signal in noise. An adaptive filtering structure with three fixed FIR filters and two adaptive gain and delay parameters is employed to achieve the calibration. A convergence analysis is presented for the blind calibration technique. Numerical simulations for a bandlimited white noise input and for inputs containing several sinusoidal components demonstrate the effectiveness of the proposed method.     

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.     

Comparison of RLS, LMS, and sign algorithms for tracking randomlytime-varying channels

The performance of adaptive FIR filters governed by the recursive least-squares (RLS) algorithm, the least mean square (LMS) algorithm, and the sign algorithm (SA), are compared when the optimal filtering vector is randomly time-varying. The comparison is done in terms of the steady-state excess mean-square estimation error ξ and the steady-state mean-square weight deviation, η. It is shown that ξ does not depend on the spread of eigenvalues of the input covariance matrix, R, in the cases of the LMS algorithm and the SA, while it does in the case of the RLS algorithm. In the three algorithms, η is found to be increasing with the eigenvalue spread. The value of the adaptation parameter that minimizes ξ is different from the one that minimizes η. It is shown that the minimum values of ξ and η attained by the RLS algorithm are equal to the ones attained by the LMS algorithm in any one of the three following cases: (1) if R has equal eigenvalues, (2) if the fluctuations of the individual elements of the optimal vector are mutually uncorrelated and have the same mean-square value, or (3) if R is diagonal and the fluctuations of the individual elements of the optimal vector have the same mean-square value. Conditions that make the values of ξ and η of the LMS algorithm smaller (or greater) than the ones of the RLS algorithm are derived. For Gaussian input data, the minimum values of ξ and η attained by the SA are found to exceed the ones attained by the LMS algorithm by 1 dB independently of R and the mutual correlation between the elements of the optimal vector     

Motion artifact cancellation in NIR spectroscopy using Wiener filtering

We present a Wiener filtering based algorithm for the elimination of motion artifacts present in Near Infrared (NIR) spectroscopy measurements. Until now, adaptive filtering was the only technique used in the noise cancellation in NIR studies. The results in this preliminary study revealed that the proposed method gives better estimates than the classical adaptive filtering approach without the need for additional sensor measurements. Moreover, this novel technique has the potential to filter out motion artifacts in functional near infrared (fNIR) signals, too.     

基于sigmoid函数的Volterra自适应有源噪声对消器

该文介绍了一种新颖的非线性自适应有源噪声对消器基于sigmoid函数的Volterra自适应有源噪声对消器,并采用输入信号和瞬时误差归一化的LMS自适应算法调整其系数。这种基于sigmoid函数的Volterra自适应有源噪声对消器具有参数少和便于实现的模快化结构等优点。仿真结果表明:这种基于sigmoid函数的Volterra自适应有源噪声对消系统具有良好的抗噪声性能。     

基于DSP的耳机噪声抵消系统的设计与实现

设计和实现了基于DSP的自适应有源降噪耳机系统。分析了有源降噪耳机系统的原理,基于SEED-DEC6416开发板实现了有源降噪耳机系统的硬件和软件设计,为保证系统的实时性对程序进行优化,降噪耳机系统实现了对实际环境中噪声信号的提取、自适应滤波和噪声抵消。实验结果表明系统,在实际噪声环境中可以对噪声进行抵消,并良好地恢复语音信号,验证了系统设计的可行性和算法的正确性。     

A Modular Analog NLMS Structure for Adaptive Filtering

This paper proposes a modular Analog Adaptive filter (AAF) algorithm, in which the coefficient adaptation is carried out by using a time varying step size analog normalized LMS (NLMS) algorithm, which is implemented as an external analog structure. The proposed time varying step size is estimated by using the first element of the crosscorrelation vector between the output error and reference signal, and the first element of the crosscorrelation vector between the output error and the adaptive filter output signal, respectively. Proposed algorithm reduces distortion when additive noise power increases or DC offsets are present, without significatively decreasing the convergence rate nor increasing the complexity of the conventional NLMS algorithms. Simulation results show that proposed algorithm improves the performance of AAF when DC offsets are present. The proposed VLSI structure for the time varying step size normalized NLMS algorithm has, potentially, a very small size and faster convergence rates than its digital counterparts. It is suitable for general purpose applications or oriented filtering solution such as echo cancellation and equalization in cellular telephony in which high performance, low power consumption, fast convergence rates and small size adaptive digital filters (ADF) are required. The convergence performance of analog adaptive filters using integrators like first order low pass filter is analyzed.     

Blind adaptive joint multiuser detection and equalization in dispersive differentially encoded CDMA channels

The problem of blind adaptive joint multiuser detection and equalization in direct-sequence code division multiple access (DS/CDMA) systems operating over fading dispersive channels is considered. A blind and code-aided detection algorithm is proposed, i.e., the procedure requires knowledge of neither the interfering users' parameters (spreading codes, timing offsets, and propagation channels), nor the timing and channel impulse response of the user of interest but only of its spreading code. The proposed structure is a two-stage one: the first stage is aimed at suppressing the multiuser interference, whereas the second-stage performs channel estimation and data detection. Special attention is paid to theoretical issues concerning the design of the interference blocking stage and, in particular, to the development of general conditions to prevent signal cancellation under vanishingly small noise. A statistical analysis of the proposed system is also presented, showing that it incurs a very limited loss with respect to the nonblind minimum mean square error detector, outperforms other previously known blind systems, and is near-far resistant. A major advantage of the new structure is that it admits an adaptive implementation with quadratic (in the processing gain) computational complexity. This adaptive algorithm, which couples a recursive-least-squares estimation of the blocking matrix and subspace tracking techniques, achieves effective steady-state performance.     

噪声有源自校正预测控制

有源噪声控制（ANC）的经典方法是采用有限脉冲响应（FIR）滤波器的Filter-X算法，该算法的一个主要缺点是次级声路径响应对控制滤波器参数自适应的收敛速度有较大影响。将预测控制方法应用到有源噪声控制领域，给出了一种参数在线自适应算法，该算法的收敛速度不受次级声路径响应的影响。仿真结果表明，给出的控制方法比传的Filter-X控制有更小的稳态误差，而且收敛速度更快。