Analysis of LMS-Newton adaptive filtering algorithms with variableconvergence factor

An analysis of two LMS-Newton adaptive filtering algorithms with variable convergence factor is presented. The relations of these algorithms with the conventional recursive least-squares algorithm are first addressed. Their performance in stationary and nonstationary environments is then studied and closed-form formulas for the excess mean-square error (MSE) are derived. The paper deals, in addition, with the effects of roundoff errors for the case of fixed-point arithmetic. Specifically, closed-form formulas for the excess MSE caused by quantization are obtained. The paper concludes with experimental results that demonstrate the validity of the analysis presented     

Constrained adaptive filtering algorithms: asymptotic convergenceproperties for dependent data

The convergence properties of constrained adaptive filtering algorithms are established. The constraint is in the form of a bounded set in which the filter's coefficients must lie. A recursive procedure that converges to the deterministic solution of the constrained linear mean-square estimation problem is obtained, using an appropriate contraction mapping. The recursion is used to derive the adaptive algorithm for the filter coefficients. Bounds on the mean-square error of the coefficients. Bounds on the mean-square error of the estimates of the filter coefficients and on the excess error of the input signal estimate are derived for processes that are either strong mixing or asymptotically uncorrelated. The algorithms use a moving window of size n on the data from one adaptation step to the next. However, tighter bounds can be obtained when a skipped sampling mechanism is used     

Convergence analysis of the sign algorithm for adaptive filtering

We consider the convergence analysis of the sign algorithm for adaptive filtering when the input processes are uncorrelated and Gaussian and a fixed step size μ>0 is used. Exact recursive equations for the covariance matrix of the deviation error are established for any step size μ>0. Asymptotic time-averaged convergence for the mean-absolute deviation error, mean-square deviation error, and for the signal mean-square estimation error are established. These results are shown to hold for arbitrary step size μ>0     

A class of adaptive step-size control algorithms for adaptivefilters

A class of new adaptive step-size control algorithms, which is applicable to most of the LMS-derived tap weight adaptation algorithms, is proposed. Analysis yields a set of difference equations for theoretically calculating the transient behavior of the filter convergence and derives an explicit formula for the steady-state excess mean-square error (EMSE). Experiments for some examples prove that the proposed algorithm is highly effective in improving the convergence rate in both transient and tracking phases. The theoretically calculated convergence is shown to be in good agreement with that obtained through simulations. Alternative formulae of the step-size adaptation for specific tap weight adaptation algorithms are also proposed     

A statistical analysis of the affine projection algorithm for unity step size and autoregressive inputs

This paper presents a new statistical analysis of the affine projection (AP) algorithm. An analytical model is derived for autoregressive (AR) inputs for unity step size (fastest convergence). Deterministic recursive equations are derived for the mean AP weight and mean-square error for large values of N (the number of adaptive taps). The value of N is also assumed large compared to the algorithm order (number of input vectors used to determine the weight update direction). The model predictions display better agreement with Monte Carlo simulations in both transient and steady-state than models previously presented in the literature. The model's accuracy is sufficient for most practical design purposes.     

New algorithm for stochastic approximation (Corresp.)

A general stochastic approximation algorithm is given along with assumptions and conditions necessary to show that it converges. Convergence is proven in the mean-square sense. The rate of convergence is shown to be better than two algorithms proposed previously.     

Exact expectation analysis of the LMS adaptive filter

In almost all analyses of the least mean square (LMS) adaptive filter, it is assumed that the filter coefficients are statistically independent of the input data currently in filter memory, an assumption that is incorrect for shift-input data. We present a method for deriving a set of linear update equations that can be used to predict the exact statistical behavior of a finite-impulse-response (FIR) LMS adaptive filter operating upon finite-time correlated input data. Using our method, we can derive exact bounds upon the LMS step size to guarantee mean and mean-square convergence. Our equation-deriving procedure is recursive and algorithmic, and we describe a program written in the MAPLE symbolic-manipulation software package that automates the derivation for arbitrarily-long adaptive filters operating on input data with stationary statistics. Using our analysis, we present a search algorithm that determines the exact step size mean-square stability bound for a given filter length and input correlation statistics. Extensive computer simulations indicate that the exact analysis is more accurate than previous analyses in predicting adaptation behavior. Our results also indicate that the exact step size bound is much more stringent than the bound predicted by the independence assumption analysis for correlated input data     

Zero-insertion adaptive minimum mean-square error (MMSE) receiverfor asynchronous CDMA multiuser detection

This paper proposes an asynchronous code-division multiple-access multiuser detector, zero-insertion adaptive minimum mean-square error (ZA-MMSE) multiuser detector, in which a data stream is partitioned into blocks by inserted zero bits and detection proceeds block by block to ensure a balance between processing delay and detection efficiency. The bit error rate performance of the ZA-MMSE detector is evaluated under different multipath scenarios with varying severity characterized by average relative strength of the paths. The results are compared with decorrelator, revealing that the ZA-MMSE detector offers promising detection efficiency at a relatively low complexity, which is linear to the product of the number of users and block length. As an effort to implement it adaptively, the transient behavior of the ZA-MMSE detector with different recursive algorithms is studied. It is concluded that the least mean square algorithm is not suitable due to its power-dependent convergence; whereas the recursive least square algorithm offers a consistently fast convergence regardless of the received power, making it ideal for application in a time-varying channel with near-far effect     

Analysis of Convergence of a Frequency-Domain LMS Adaptive Filter Implemented as a Multi-Stage Adaptive Filter

We present an analysis of the convergence of the frequency-domain LMS adaptive filter when the DFT is computed using the LMS steepest descent algorithm. In this case, the frequency-domain adaptive filter is implemented with a cascade of two sections, each updated using the LMS algorithm. The structure requires less computations compared to using the FFT and is modular suitable for VLSI implementations. Since the structure contains two adaptive algorithms updating in parallel, an analysis of the overall system convergence needs to consider the effect of the two adaptive algorithms on each other, in addition to their individual convergence. Analysis was based on the expected mean-square coefficient error for each of the two LMS adaptive algorithms, with some simplifying approximations for the second algorithm, to describe the convergence behavior of the overall system. Simulations were used to verify the results.     

New Variable Step-Sizes Minimizing Mean-Square Deviation for the LMS-Type Algorithms

The least-mean-square-type (LMS-type) algorithms are known as simple and effective adaptation algorithms. However, the LMS-type algorithms have a trade-off between the convergence rate and steady-state performance. In this paper, we investigate a new variable step-size approach to achieve fast convergence rate and low steady-state misadjustment. By approximating the optimal step-size that minimizes the mean-square deviation, we derive variable step-sizes for both the time-domain normalized LMS (NLMS) algorithm and the transform-domain LMS (TDLMS) algorithm. The proposed variable step-sizes are simple quotient forms of the filtered versions of the quadratic error and very effective for the NLMS and TDLMS algorithms. The computer simulations are demonstrated in the framework of adaptive system modeling. Superior performance is obtained compared to the existing popular variable step-size approaches of the NLMS and TDLMS algorithms.     

A set of algorithms linking NLMS and block RLS algorithms

This paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares (NLMS) and the block recursive least squares (BRLS) algorithms. All these algorithms use small block lengths, thus allowing easy implementation and small input-output delay. It is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares (LMS) algorithm, while converging much faster. A precise evaluation of the arithmetic complexity is provided, and the adaptive behavior of the algorithm is analyzed. Simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the NLMS algorithm. The conclusions of the theoretical analysis are checked by simulations, illustrating that, even in the case where noise is added to the reference signal, the proposed algorithm allows altogether a faster convergence and a lower residual error than the NLMS algorithm. Finally, a sample-by-sample version of this algorithm is outlined, which is the link between the NLMS and recursive least squares (RLS) algorithms     

一种快速递归全局最小二乘算法

针对FIR系统输入和输出信号均被噪声干扰的情况,提出一种快速递归全局最小二乘(XS-RTLS)算法用于迭代计算全局最小二乘解,算法沿着输入数据的符号方向并采用著名的快速增益矢量,搜索约束瑞利商(c-RQ)的最小值得到系统参数估计。算法关于方向更新矢量的内积运算可通过加减运算实现,有效降低了计算复杂度;另外XS-RTLS算法没有进行相关矩阵求逆递归运算,因而具有长期稳定性,算法的全局收敛性通过Laslle不变性原理得到证明。最后通过仿真比较了XS-RTLS算法和递归最小二乘(RLS)算法在非时变系统和时变系统中的性能,验证了XS-RTLS算法的长期稳定性。     

Partial update LMS algorithms

Partial updating of LMS filter coefficients is an effective method for reducing computational load and power consumption in adaptive filter implementations. This paper presents an analysis of convergence of the class of Sequential Partial Update LMS algorithms (S-LMS) under various assumptions and shows that divergence can be prevented by scheduling coefficient updates at random, which we call the Stochastic Partial Update LMS algorithm (SPU-LMS). Specifically, under the standard independence assumptions, for wide sense stationary signals, the S-LMS algorithm converges in the mean if the step-size parameter /spl mu/ is in the convergent range of ordinary LMS. Relaxing the independence assumption, it is shown that S-LMS and LMS algorithms have the same sufficient conditions for exponential stability. However, there exist nonstationary signals for which the existing algorithms, S-LMS included, are unstable and do not converge for any value of /spl mu/. On the other hand, under broad conditions, the SPU-LMS algorithm remains stable for nonstationary signals. Expressions for convergence rate and steady-state mean-square error of SPU-LMS are derived. The theoretical results of this paper are validated and compared by simulation through numerical examples.     

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.     

Bias-remedy least mean square equation error algorithm for IIRparameter recursive estimation

In the area of infinite impulse response (IIR) system identification and adaptive filtering the equation error algorithms used for recursive estimation of the plant parameters are well known for their good convergence properties. However, these algorithms give biased parameter estimates in the presence of measurement noise. A new algorithm is proposed on the basis of the least mean square equation error (LMSEE) algorithm, which manages to remedy the bias while retaining the parameter stability. The so-called bias-remedy least mean square equation error (BRLE) algorithm has a simple form. The compatibility of the concept of bias remedy with the stability requirement for the convergence procedure is supported by a practically meaningful theorem. The behavior of the BRLE has been examined extensively in a series of computer simulations     

高阶调制通用恒模盲均衡算法

在无线通信高速数据传输中,限带效应及多径信道带来的码间干扰(ISI)严重影响接收信号的质量。目前广泛采用恒模盲均衡算法(CMA)消除ISI,但是对于高阶非恒定幅度调制信号,CMA算法收敛后的稳态误差很大,收敛效果较差。该文在改进原CMA算法误差更新函数的基础上,提出了一种新的均衡算法。新算法有效地降低了高阶调制下均衡器的稳态偏差并能适应各种调制体制。理论分析和数值仿真给出,新算法在MQAM以及MAPSK调制下都较原CMA算法性能有较大的提升,适合应用在高阶调制体制的通信系统中。     

l0-范数约束的稀疏多径信道RLS常模盲均衡算法

针对稀疏多径信道下MPSK信号的快速盲均衡问题,提出了一种l0-范数约束的递归最小二乘常模盲均衡算法.该算法借鉴传统的递归最小二乘常模盲均衡算法思想,结合稀疏自适应滤波理论,首先利用l0-范数对均衡器抽头系数进行稀疏性约束,构造出一种l0-范数约束的加权最小二乘误差代价函数,然后依据递归最小二乘算法推导出均衡器抽头系数更新公式.该算法发挥递归最小二乘常模算法收敛速度快的优势,并对幅度极小系数附加零点吸引调整,从而实现不同幅度抽头系数的快速收敛.理论分析与仿真结果表明,与现有算法相比,该算法在保证较低剩余符号间干扰的前提下,能有效提高均衡器的收敛速度.     

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.     

平方根变步长lp范数LMS算法的稀疏系统辨识

针对稀疏未知系统的辨识问题,提出了一种基于lp(0相似文献   

QR factorization based blind channel identification withsecond-order statistics

Most eigenstructure-based blind channel identification and equalization algorithms with second-order statistics need SVD or EVD of the correlation matrix of the received signal. In this paper, we address new algorithms based on QR factorization of the received signal directly without calculating the correlation matrix. This renders the QR factorization-based algorithms more robust against ill-conditioned channels, i.e., those channels with almost common zeros among the subchannels. First, we present a block algorithm that performs the QR factorization of the received data matrix as a whole. Then, a recursive algorithm is developed based on the QR factorization by updating a rank-revealing ULV decomposition. Compared with existing algorithms in the same category, our algorithms are computationally more efficient. The computation in each recursion of the recursive algorithm is on the order of O(m²) if only equalization is required, where m is the dimension of the received signal vector. Our recursive algorithm preserves the fast convergence property of the subspace algorithms, thus converging faster than other adaptive algorithms such as the super-exponential algorithm with comparable computational complexities. Moreover, our proposed algorithms do not require noise variance estimation. Numerical simulations demonstrate the good performance of the proposed algorithms