Low-complexity constrained affine-projection algorithms

This paper proposes low-complexity constrained affine-projection (CAP) algorithms. The algorithms are suitable for linearly constrained filtering problems often encountered in communications systems. The CAP algorithms derived in this paper trade convergence speed and computational complexity in the same way as the conventional affine-projection (AP) algorithm. In addition, data-selective versions of the CAP algorithm are derived based on the concept of set-membership filtering. The set-membership constrained affine-projection (SM-CAP) algorithms include several constraint sets in order to construct a space of feasible solutions for the coefficient updates. The SM-CAP algorithms include a data-dependent step size that provides fast convergence and low mean-squared error. The paper also discusses important aspects of convergence and stability of constrained normalized adaptation algorithms and shows that normalization may introduce bias in the final solution.     

Set-membership binormalized data-reusing LMS algorithms

This paper presents and analyzes novel data selective normalized adaptive filtering algorithms with two data reuses. The algorithms [the set-membership binormalized LMS (SM-BN-DRLMS) algorithms] are derived using the concept of set-membership filtering (SMF). These algorithms can be regarded as generalizations of the previously proposed set-membership NLMS (SM-NLMS) algorithm. They include two constraint sets in order to construct a space of feasible solutions for the coefficient updates. The algorithms include data-dependent step sizes that provide fast convergence and low-excess mean-squared error (MSE). Convergence analyzes in the mean squared sense are presented, and closed-form expressions are given for both white and colored input signals. Simulation results show good performance of the algorithms in terms of convergence speed, final misadjustment, and reduced computational complexity.     

Convergence Performance of the Simplified Set-Membership Affine Projection Algorithm

Set-membership (SM) adaptive filtering is appealing in many practical situations, particularly those with inherent power and computational constraints. The main feature of the SM algorithms is their data-selective coefficient update leading to lower computational complexity and power consumption. The set-membership affine projection (SM-AP) algorithm does not trade convergence speed with misadjustment and computation complexity as many existing adaptive filtering algorithms. In this work analytical results related to the SM-AP algorithm are presented for the first time, providing tools to setup its parameters as well as some interpretation to its desirable features. The analysis results in expressions for the excess mean square error (MSE) in stationary environments and the transient behavior of the learning curves. Simulation results confirm the accuracy of the analysis and the good features of the SM-AP algorithms.     

Performance analysis of adaptive DFE using set-membership binormalized data-reusing LMS algorithm for frequency selective MIMO channels

This paper addresses the concern of complexity involved with adaptive equalization in wireless systems operating over time-varying and frequency selective multiple-input multiple-output (MIMO) channels. Here, we propose a decision feedback equalizer using binormalized data-reusing least mean square (BNLMS) algorithm with set-membership filtering for MIMO channels. The performance of the equalizer is investigated for a MIMO receiver in a multi-path fading environment as experienced in the indoor and pedestrian environment. The equalizer performance is also studied for channels having higher delay and Doppler spread. The convergence issues, BER performance and tracking capabilities are examined through computer simulations. Moreover, the computational complexity issue for this MIMO equalizer is compared with other existing data-selective algorithm based techniques.     

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。     

Steady-State MSE Performance of the Set-Membership Affine Projection Algorithm

The set-membership affine projection (SM-AP) algorithm has many desirable characteristics such as fast convergence speed, low power consumption due to data-selective updates, and low misadjustment. The main reason hindering the widespread use of the SM-AP algorithm is the lack of analytical results related to its steady-state performance. In order to bridge this gap, this paper presents an analysis of the steady-state mean square error (MSE) of a general form of the SM-AP algorithm. The proposed analysis results in closed-form expressions for the excess MSE and misadjustment of the SM-AP algorithm, which are also applicable to many other algorithms. This work also provides guidelines for the analysis of the whole family of SM-AP algorithms. The analysis relies on the energy conservation method and has the attractive feature of not assuming a specific model for the input signal. In addition, the choice of the upper bound for the error of the SM-AP algorithm is addressed for the first time. Simulation results corroborate the accuracy of the proposed analysis.     

Line search algorithms for adaptive filtering

Line search algorithms for adaptive filtering that choose the convergence parameter so that the updated filter vector minimizes the sum of squared errors on a linear manifold are described. A shift invariant property of the sample covariance matrix is exploited to produce an adaptive filter stochastic line search algorithm for exponentially weighted adaptive equalization requiring 3N+5 multiplications and divisions per iteration. This algorithm is found to have better numerical stability than fast transversal filter algorithms for an application requiring steady-state tracking capability similar to that of least-mean square (LMS) algorithms. The algorithm is shown to have faster initial convergence than the LMS algorithm and a well-known variable step size algorithm having similar computational complexity in an adaptive equalization experiment     

A general class of nonlinear normalized adaptive filteringalgorithms

The normalized least mean square (NLMS) algorithm is an important variant of the classical LMS algorithm for adaptive linear filtering. It possesses many advantages over the LMS algorithm, including having a faster convergence and providing for an automatic time-varying choice of the LMS stepsize parameter that affects the stability, steady-state mean square error (MSE), and convergence speed of the algorithm. An auxiliary fixed step-size that is often introduced in the NLMS algorithm has the advantage that its stability region (step-size range for algorithm stability) is independent of the signal statistics. In this paper, we generalize the NLMS algorithm by deriving a class of nonlinear normalized LMS-type (NLMS-type) algorithms that are applicable to a wide variety of nonlinear filter structures. We obtain a general nonlinear NLMS-type algorithm by choosing an optimal time-varying step-size that minimizes the next-step MSE at each iteration of the general nonlinear LMS-type algorithm. As in the linear case, we introduce a dimensionless auxiliary step-size whose stability range is independent of the signal statistics. The stability region could therefore be determined empirically for any given nonlinear filter type. We present computer simulations of these algorithms for two specific nonlinear filter structures: Volterra filters and the previously proposed class of Myriad filters. These simulations indicate that the NLMS-type algorithms, in general, converge faster than their LMS-type counterparts     

一种改进的数字同频直放站自适应反馈干扰抑制算法

基于数字地面电视广播(Digital Terrestrial Television Broadcasting,DTTB)同频直放站的回波干扰抑制,提出了一种变步长块LMS(Variable Step- size Block Normalized Least Mean Square,VSSBNLMS)自适应算法.此算法的目的是为了提高传统回波干扰抑制的自适应算法的收敛速度和降低计算复杂度.其将输入信号分为长度相等的块,在每一个数据块内,权值向量只更新一次,有效地降低了计算复杂度.另外,该算法通过输出误差控制更新步长的变化,与传统的归一化LMS(NLMS)和块LMS(BLMS)算法相比,提高了收敛速度.仿真结果表明,该算法具有良好的收敛速度和回波干扰抑制性能.     

Normalized LMS Adaptive Cancellation of Self-Image in Direct-Conversion Receivers

This paper presents an adaptive digital signal processing technique that cancels self-image interference due to frequency-independent, in-phase/quadrature-phase (I/Q) mismatch in zero-intermediate frequency (IF) direct-conversion receivers. The proposed technique, which is referred to as the normalized least-mean square adaptive self-image cancellation (NLMS-ASIC) algorithm, is an ASIC technique that controls the filter weight to minimize the power of the filter output signal using an NLMS type of weight-control mechanism. Some closed-form equations are derived for the mean-squared error (MSE), as well as the mean image-rejection ratio (IRR) of the proposed NLMS-ASIC algorithm. In particular, a step-size determination method is explained so that the requirements on the image-rejection performance and convergence time can be satisfied. The advantages of the proposed technique are demonstrated through computer simulations.      

A New Sequential Block Partial Update Normalized Least Mean M-Estimate Algorithm and its Convergence Performance Analysis

This paper proposes a new sequential block partial update normalized least mean square (SBP-NLMS) algorithm and its nonlinear extension, the SBP-normalized least mean M-estimate (SBP–NLMM) algorithm, for adaptive filtering. These algorithms both utilize the sequential partial update strategy as in the sequential least mean square (S–LMS) algorithm to reduce the computational complexity. Particularly, the SBP–NLMM algorithm minimizes the M-estimate function for improved robustness to impulsive outliers over the SBP–NLMS algorithm. The convergence behaviors of these two algorithms under Gaussian inputs and Gaussian and contaminated Gaussian (CG) noises are analyzed and new analytical expressions describing the mean and mean square convergence behaviors are derived. The robustness of the proposed SBP–NLMM algorithm to impulsive noise and the accuracy of the performance analysis are verified by computer simulations.     

Improved Soft Iterative Channel Estimation for Turbo Equalization of Time Varying Frequency Selective Channels

In this paper, we present computationally efficient iterative channel estimation algorithms for Turbo equalizer-based communication receiver. Least Mean Square (LMS) and Recursive least Square (RLS) algorithms have been widely used for updating of various filters used in communication systems. However, LMS algorithm, though very simple, suffers from a relatively slow and data dependent convergence behaviour; while RLS algorithm, with its fast convergence rate, finds little application in practical systems due to its computational complexity. Variants of LMS algorithm, Variable Step Size Normalized LMS (VSSNLMS) and Multiple Variable Step Size Normalized LMS algorithms, are employed through simulation for updating of channel estimates for turbo equalization in this paper. Results based on the combination of turbo equalizer with convolutional code as well as with turbo codes alongside with iterative channel estimation algorithms are presented. The simulation results for different normalized fade rates show how the proposed channel estimation based-algorithms outperformed the LMS algorithm and performed closely to the well known Recursive least square (RLS)-based channel estimation algorithm.     

BEACON: an adaptive set-membership filtering technique with sparseupdates

This paper deals with adaptive solutions to the so-called set-membership filtering (SMF) problem. The SMF methodology involves designing filters by imposing a deterministic constraint on the output error sequence. A set-membership decision feedback equalizer (SM-DFE) for equalization of a communications channel is derived, and connections with the minimum mean square error (MMSE) DFE are established. Further, an adaptive solution to the general SMF problem via a novel optimal bounding ellipsoid (OBE) algorithm called BEACON is presented. This algorithm features sparse updating, wherein it uses about 5-10% of the data to update the parameter estimates without any loss in mean-squared error performance, in comparison with the conventional recursive least-squares (RLS) algorithm. It is shown that the BEACON algorithm can also be derived as a solution to a certain constrained least-squares problem. Simulation results are presented for various adaptive signal processing examples, including estimation of a real communication channel. Further, it is shown that the algorithm can accurately track fast time variations in a nonstationary environment. This improvement is a result of incorporating an explicit test to check if an update is needed at every time instant as well as an optimal data-dependent assignment to the updating weights whenever an update is required     

用于稀疏系统辨识的低复杂度集员NLMS算法

针对现有的稀疏集员(SM,Set-Membership)自适应滤波算法,普遍存在稳态均方偏差(MSD,Mean Square Deviation)的稳定性较低及运算复杂度较高等问题,提出了一种新颖的稀疏集员NLMS(NLMS,Normalized Least Mean Square)算法.该方案提出一种运算复杂度更低的...     

线性系统集员估计问题研究

研究了线性系统下的Norton和基于OBE两种集员估计算法。Norton算法是通过最小体积或最小迹来优化时间更新阶段和测量更新阶段,但其计算量大、效率低。针对这一不足,OBE算法采用最小半径定界椭球来进行测量阶段的更新,从而简化了算法,减少了计算量。最后通过与传统Kalman滤波算法与Norton集员估计算法相比,验证了基于OBE集员估计算法的有效性。     

Partial-Update L∞ -Norm Based Algorithms

The computational complexity of an adaptive filtering algorithm increases with increasing the filter tap length and therefore, the use of such a filter can become prohibitive for certain applications, especially for real-time implementation. In this paper, we develop low-complexity adaptive filtering algorithms by incorporating the concept of partial updating of the filter coefficients into the technique of finding the gradient vector in the hyperplane based on the L_infin-norm criterion. Two specific partial update algorithms based on the sequential and M-Max coefficient updating are proposed. The statistical analyses of the two algorithms are carried out, and evolution equations for the mean and mean-square of the filter coefficient misalignment as well as the stability bounds on the step size are obtained. It is shown that the proposed partial update algorithm employing the M-Max coefficient updating can achieve a convergence rate that is closest to that of the full update algorithm. Finally, simulations are carried out to validate the theoretical results and study the convergence rate of the proposed algorithms     

基于集员滤波的宽带有源噪声控制算法

子带结构是提高宽带噪声控制的有效方法,归一化子带自适应滤波(NSAF)结构消除了传统子带结构在输出端产生混叠分量的问题,但由于在每个子带上采用相同的全带自适应滤波器,使得计算量高于传统子带结构,集员滤波(SMF)技术具有数据选择更新的特点,可有效降低计算量,且在收敛速度和稳态均方误差之间具有较好的折中性。在此引入集员滤波技术,建立基于NSAF结构的无延迟前馈有源噪声控制系统,降低计算量,最后仿真验证了该算法对宽带噪声具有更优的降噪效果。     

A Frequency Domain LMS Algorithm with Dynamic Selection of Frequency Bins

Frequency-domain (FD) adaptive filter algorithms are able to achieve a low computational complexity by using the overlap-and-save implementation means compared to time-domain (TD) ones. In this article, we propose a new FD least-mean-square (FD-LMS) algorithm which dynamically selects frequency bins in order to reduce the computational complexity and maintain the convergence performance of the conventional FD-LMS. The optimal selection of frequency bins is derived by the largest decrease between the successive FD mean square deviations (MSDs) at every data block. Simulation results show that the proposed algorithm provides a low steady-state normalized MSD (NMSD) and similar convergence rate compared to the conventional FD-LMS algorithm. In addition, it gains a low computational complexity.     

分布式子带自适应滤波算法

为了解决分布式最小均方算法在输入信号相关性较高时收敛速度较慢、分布式仿射投影算法计算复杂度较高等问题,本文提出了两种分布式子带自适应滤波算法,即递增式和扩散式子带自适应滤波算法.分布式子带自适应滤波算法将节点信号进行子带分割来降低信号的相关性,从而加快收敛速度.由于用于子带分割的滤波器组中包含了抽取单元,所以分布式子带自适应滤波算法和对应的分布式最小均方算法的计算复杂度相近.仿真结果表明,与分布式最小均方算法相比,分布式子带自适应滤波算法具有更好的收敛性能.     

Hybrid filtered error LMS algorithm: another alternative to filtered-x LMS

The filtered-error LMS (FELMS) algorithms are widely used in multi-input and multi-output control (MIMO) active noise control (ANC) systems as an alternative to the filtered-x LMS (FXLMS) algorithms to reduce the computational complexity and memory requirements. However, the available FELMS algorithms introduce significant delays in updating the adaptive filter coefficients that slow the convergence rate. In this paper, we introduce a novel algorithm called the hybrid filtered-error LMS algorithm (HFELMS) which, while still a form of the FELMS algorithm, allows users to have some freedom to construct the error filter that guarantees its convergence with a sufficiently small step size. Without increasing the computational complexity, the proposed algorithm can improve the control system performance in one of several ways: 1) increasing the convergence rate without extra computation cost; 2) reducing the remaining noise mean square error (MSE); or 3) shaping the excess noise power. Simulation results show the effectiveness of the proposed method.