An efficient robust adaptive filtering algorithm based on parallelsubgradient projection techniques

This paper presents a novel robust adaptive filtering scheme based on the interactive use of statistical noise information and the ideas developed originally for efficient algorithmic solutions to the convex feasibility problems. The statistical noise information is quantitatively formulated as stochastic property closed convex sets by the simple design formulae developed in this paper. A simple set-theoretic inspection also leads to an important statistical reason for the sensitivity to noise of the affine projection algorithm (APA). The proposed adaptive algorithm is computationally efficient and robust to noise because it requires only an iterative parallel projection onto a series of closed half spaces that are highly expected to contain the unknown system to be identified and is free from the computational load of solving a system of linear equations. The numerical examples show that the proposed adaptive filtering scheme realizes dramatically fast and stable convergence for highly colored excited speech like input signals in severe noise situations     

一种基于并行次梯度投影技术的加速声回波抵消算法

该文在并行次梯度投影技术(Parallel Subgradient Projection,PSP)的基础上,提出一种加速回波抵消算法。加速算法通过一种角度寻优策略,对由分属不同状态下的输入信号组成的空间进行寻优,从而找到一对最优投影空间。然后向这一对最优半空间的交集投影,实现对自适应算法的加速。实验仿真表明,加速算法相比传统方法收敛速率更快,无论是用均方误差还是自适应滤波器失准(Echo Path Misalignment)指标衡量加速算法在性能上都有一定程度的提升。     

Fast principal component extraction by a weighted informationcriterion

Principal component analysis (PCA) is an essential technique in data compression and feature extraction, and there has been much interest in developing fast PICA algorithms. On the basis of the concepts of both weighted subspace and information maximization, this paper proposes a weighted information criterion (WINC) for searching the optimal solution of a linear neural network. We analytically show that the optimum weights globally asymptotically converge to the principal eigenvectors of a stationary vector stochastic process. We establish a dependent relation of choosing the weighting matrix on statistics of the input process through the analysis of stability of the equilibrium of the proposed criterion. Therefore, we are able to reveal the constraint on the choice of a weighting matrix. We develop two adaptive algorithms based on the WINC for extracting in parallel multiple principal components. Both algorithms are able to provide adaptive step size, which leads to a significant improvement in the learning performance. Furthermore, the recursive least squares (RLS) version of WINC algorithms has a low computational complexity O(Np), where N is the input vector dimension, and p is the number of desired principal components. In fact, the WINC algorithm corresponds to a three-layer linear neural network model capable of performing, in parallel, the extraction of multiple principal components. The WINC algorithm also generalizes some well-known PCA/PSA algorithms just by adjusting the corresponding parameters. Since the weighting matrix does not require an accurate value, it facilitates the system design of the WINC algorithm for practical applications. The accuracy and speed advantages of the WINC algorithm are verified through simulations     

基于自适应次梯度投影算法的压缩感知信号重构

本文提出一种利用自适应次梯度投影算法（Adaptive Subgridient Projection Method,ASPM）进行压缩感知（Compressed Sensing,CS）信号重构的方案。APSM算法首先根据CS重构模型建立包含稀疏重构信号并具有随机属性的凸集,然后运用并行次梯度投影的思想将对该凸集的投影转化为对多个闭合半平面的投影,最后将更新后的干扰抑制滤波器系数矢量投影到限定集合上。同时为了获得快速收敛性,本文设计了在迭代的不同阶段自适应地调节该膨胀系数的机制。理论分析和仿真结果表明,本算法具有快速收敛性和较低的重构误差,在不同的噪声强度下具有较高的鲁棒性。      

一种新自适应滤波快速算法及其 在多路回波消除中的应用

本文提出了一种新的自适应滤波算法,该算法结构简单、计算量适中且收敛速度快,弥补了一般变步长LMS自适应算法计算量小但收敛速度欠佳,以及仿射投影算法(APA)收敛速度快但计算量非常大的缺陷.该算法计算量与一般LMS算法相当,而收敛速度却与APA算法相当,其结构比APA及相应的改进算法要简单得多.我们不仅对所提算法的收敛性及性能进行了分析,而且将它用于多路回波消除中获得了成功,仿真结果表明,该算法与Sankaran(1997)所提NLMS-OCF算法及Benesty(1996)所提APA-MC算法比较,在收敛速度和收敛精度相当的情况下,其计算复杂度大大减少.从而新算法具备更好的实时性.     

Reduced-complexity transform-domain adaptive algorithm with selective coefficient update

This paper proposes a new low-complexity transform-domain (TD) adaptive algorithm for acoustic echo cancellation. The algorithm is based on decomposing the long adaptive filter into smaller subfilters and employing the selective coefficient update (SCU) approach in each subfilter to reduce computational complexity. The resulting algorithm combines the fast converging characteristic of the TD decomposition technique and the benefits of the SCU of low complexity with minimal performance losses. The improvement in convergence speed comes at the expense of a corresponding increase in misadjustment. To overcome this problem, a hybrid of the proposed algorithm and the standard TD LMS algorithm (TDLMS) is presented. The hybrid algorithm retains the fast convergence speed capabilities of the original algorithm while allowing for low final MSE. Simulations show that the hybrid algorithm offers a superior performance when compared to the standard TDLMS algorithm with less computational overhead.     

基于RLS_DGD的查找表更新算法

在间接学习结构的数字预失真技术中,需要使用自适应算法来更新查找表（LUT,LookUp Table）。在各种自适应算法中,RLS算法收敛快但是复杂度高。为降低其计算复杂度,这里提出采用二维坐标下降的RLS（RLS_DCD, RLS using Dichotomous Coordinate Descent）算法更新查找表,达到在数字预失真器系数的预测过程中以较低的运算量实现快速收敛的目的。仿真结果和分析表明,与采用RLS的自适应查找表更新算法比较,在邻信道功率比（ACPR, Adjacent Channel Power Ratio）改善指标相当的情况下,采用RLS—DCD的自适应查找表更新算法能大幅度降低其运算量。     

Adaptive array beamforming based on an efficient technique

This paper presents a new processing technique for adaptive array beamforming. We first properly decompose the optimal weight vector associated with the original array beamformer into several adaptive weight subvectors. An adaptive algorithm based on the conventional RLS algorithm is derived to update the weight subvectors. The required computational complexity is also evaluated for the proposed technique. The convergence rate of the proposed technique is mainly affected by the size of the largest weight subvector. Faster convergence speed and less array sensitivity to the pointing errors can be achieved by using the proposed technique. Several simulation results are included for illustration and comparison     

改进仿射投影算法及其在电子回声消除中的应用

在电子回声消除应用中,为提高自适应算法的收敛速度,提出一种改进的仿射投影算法及其快速实现形式.新算法利用回声路径的稀疏结构特征,通过收敛步长控制矩阵,按滤波器各系数幅值大小,等比例地为其指定相应收敛步长,以加快大系数收敛,最终达到加快滤波器整体收敛速度的目的.对新算法进行的统计学分析,为其快速收敛于目标系统的算法特性提供了理论依据.仿真实验表明与传统自适应算法相比,新算法能减小稳态失调并大幅提高收敛速度,其低计算复杂度亦保证了系统的实时性.     

A novel subspace tracking using correlation-based projection approximation

In this paper, we propose a novel subspace estimation technique, which is called correlation-based projection approximation subspace tracking (COPAST). The COPAST utilizes the projection approximation approach onto the correlation matrix to develop the subspace tracking algorithm. With the projection approximation, the RLS-based COPAST and the sequential-based COPAST algorithms are presented. The RLS-based COPAST algorithm has the better performance but the higher computational complexity than the recently developed PAST method. On the other hand, the sequential-based COPAST has reduced the computational complexity to nearly that of the PAST. Besides, the sequential-based COPAST has faster initial convergence speed than the PAST, while both nearly converge to the same value.     

Blind multiuser detection using linear prediction

We propose a blind multiuser detection technique for array processing and code division multiple access (CDMA) systems that does not require knowledge of the array geometry or transmitter signature sequences. The technique has two key elements: an adaptive algorithm for separating the signal subspace from the noise subspace and an adaptive whitener based on linear prediction. The proposed algorithm offers low complexity, fast convergence, compatibility with shaped signal constellations, near-Wiener steady-state performance, and optimal near-far resistance     

An Affine Projection Sign Algorithm Robust Against Impulsive Interferences

A new affine projection sign algorithm (APSA) is proposed, which is robust against non-Gaussian impulsive interferences and has fast convergence. The conventional affine projection algorithm (APA) converges fast at a high cost in terms of computational complexity and it also suffers performance degradation in the presence of impulsive interferences. The family of sign algorithms (SAs) stands out due to its low complexity and robustness against impulsive noise. The proposed APSA combines the benefits of the APA and SA by updating its weight vector according to the $L_{1}$-norm optimization criterion while using multiple projections. The features of the APA and the $L_{1}$-norm minimization guarantee the APSA an excellent candidate for combatting impulsive interference and speeding up the convergence rate for colored inputs at a low computational complexity. Simulations in a system identification context show that the proposed APSA outperforms the normalized least-mean-square (NLMS) algorithm, APA, and normalized sign algorithm (NSA) in terms of convergence rate and steady-state error. The robustness of the APSA against impulsive interference is also demonstrated.      

Simplified per-survivor Kalman processing in fastfrequency-selective fading channels

Per-survivor processing (PSP) is now seen as an attractive approach to performing maximum-likelihood sequence estimation (MLSE) over mobile radio channels that are rapidly time varying. An optimal PSP strategy incorporates statistical channel modeling and Kalman filtering. For severely time-dispersive channels, this approach becomes prohibitively complex. A novel filtering algorithm is presented to approximate Kalman PSP. MLSE with the new scheme offers a large reduction in computational complexity, and achieves performance close to the optimal Kalman approach and superior to existing PSP schemes in rapidly fading channels. The exact expressions presented for the pairwise error probability of MLSE with Kalman PSP may be used to predict the detector performance without resorting to lengthly simulations     

一种快速复值自适应滤波算法

本文提出了一种基于欧几里德方向集方法的复值快速自适应滤波算法，它的计算复杂度为 Ｏ（Ｎ），并在理论上证明了该算法的稳定性。它的性能通过将其应用于自适应ＦＩＲ滤波中来加以说明，计算机仿真结果表明了该算法具有较快的收敛速度，这为自适应复值滤波提供了一种新方法。     

基于FABA-SISO的时变频率选择性衰落信道CPM信号盲均衡

该文针对时变频率选择性衰落信道下高阶连续相位调制(CPM)信号盲均衡中存在的均衡性能较差、复杂度较高以及收敛速度慢等问题,从双向自适应信道均衡的角度出发,将线性调制信号均衡中使用的前后向自适应软输入软输出(FABA-SISO)算法推广,建立一种新的基于FABA-SISO的信道盲均衡方法,并结合逐幸存处理(PSP)思想和Kalman滤波,提出一种适用于高阶CPM信号的自适应盲均衡算法。该算法通过使用FABA-SISO算法,同时利用过去、现在和将来的观察数据进行Kalman滤波信道估计,有效改善了信道估计的精度,同时使用PSP算法来降低系统的复杂度,使得算法具有较好的工程应用性。仿真结果表明所提算法具有良好的盲均衡性能以及收敛性。     

A fast recursive total least squares algorithm for adaptive IIR filtering

This work develops a new fast recursive total least squares (N-RTLS) algorithm to recursively compute the total least squares (TLS) solution for adaptive infinite-impulse-response (IIR) filtering. The new algorithm is based on the minimization of the constraint Rayleigh quotient in which the first entry of the parameter vector is fixed to the negative one. The highly computational efficiency of the proposed algorithm depends on the efficient computation of the gain vector and the adaptation of the Rayleigh quotient. Using the shift structure of the input data vectors, a fast algorithm for computing the gain vector is established, which is referred to as the fast gain vector (FGV) algorithm. The computational load of the FGV algorithm is smaller than that of the fast Kalman algorithm. Moreover, the new algorithm is numerically stable since it does not use the well-known matrix inversion lemma. The computational complexity of the new algorithm per iteration is also O(L). The global convergence of the new algorithm is studied. The performances of the relevant algorithms are compared via simulations.     

Low-complexity data reusing methods in adaptive filtering

Most adaptive filtering algorithms couple performance with complexity. Over the last 15 years, a class of algorithms, termed "affine projection" algorithms, have given system designers the capability to tradeoff performance with complexity. By changing parameters and the size/scale of data used to update the coefficients of an adaptive filter but without fundamentally changing the algorithm structure, a system designer can radically change the performance of the adaptive algorithm. This paper discusses low-complexity data reusing algorithms that are closely related to affine projection algorithms. This paper presents various low-complexity and highly flexible schemes for improving convergence rates of adaptive algorithms that utilize data reusing strategies. All of these schemes are unified by a row projection framework in existence for more than 65 years. This framework leads to the classification of all data reusing and affine projection methods for adaptive filtering into two categories: the Kaczmarz and Cimmino methods. Simulation and convergence analysis results are presented for these methods under a number of conditions. They are compared in terms of convergence rate performance and computational complexity.     

RLS-based adaptive algorithms for generalized eigen-decomposition

The aim of this paper is to develop efficient online adaptive algorithms for the generalized eigen-decomposition problem which arises in a variety of modern signal processing applications. First, we reinterpret the generalized eigen-decomposition problem as an unconstrained minimization problem by constructing a novel cost function. Second, by applying projection approximation method and recursive least-square (RLS) technique to the cost function, a parallel adaptive algorithm for a basis for the r-dimensional (r>0) dominant generalized eigen-subspace and a sequential algorithm based on deflation technique for the first r-dominant generalized eigenvectors are derived. These algorithms can be viewed as counterparts of the extended projection approximation subspace tracking (PAST) and PASTd algorithms, respectively. Furthermore, we modify the parallel algorithm to explicitly estimate the first r-generalized eigenvectors in parallel, not the generalized eigen-subspace. More important, the modified parallel algorithm can be used to extract multiple generalized eigenvectors of two nonstationary sequences, while the proposed sequential algorithm lacks this ability because of slow convergence of minor generalized eigenvectors due to error propagation of the deflation technique. Third, following convergence analysis methods for PAST and PASTd, we prove the asymptotic convergence properties of the proposed algorithms. Finally, computer simulations are performed to investigate the accuracy and the speed advantages of the proposed algorithms.     

基于可变阶数的集员滤波仿射投影算法

为了解决传统集员滤波仿射投影(SM-AP)算法收敛速度与稳态失调和计量复杂度之间的矛盾,提出一种新的数据选择性仿射投影算法。此算法在传统SM-AP算法的基础上,引入可变阶数(也称数据重用因子),称为基于可变数据重用因子的集员滤波仿射投影(VDRF-SM-AP)算法。通过利用步长提供的信息,此算法可以自动地分配数据重用因子,实现了在初始阶段数据重用因子大,收敛后数据重用因子小的目标,从而既保证了收敛速度又降低了稳态失调。通过理论分析和仿真验证,新算法的整体复杂度比其他传统的SM-AP算法低很多,同时保留了传统的SM-AP算法的快速收敛特性,但是却能达到更小的稳态失调。     

Efficient zero-phase constrained frequency-domain block LMSadaptive algorithm

An efficient zero-phase constrained frequency-domain block LMS adaptive algorithm, that has reduced computational complexity and fast convergence speed for highly correlated input signals is proposed. The algorithm is applied to narrowband interference rejection in direct-sequence spread spectrum systems and a simulation results is presented