A unifying framework for the analysis of proportionate NLMS algorithms

Despite being a de facto standard in sparse adaptive filtering, the two most important members of the class of proportionate normalised least mean square (PNLMS) algorithms are introduced empirically. Our aim is to provide a unifying framework for the derivation of PNLMS algorithms and their variants with an adaptive step‐size. These include algorithms with gradient adaptive learning rates and algorithms with adaptive regularisation parameters. Convergence analysis is provided for the proportionate least mean square (PLMS) algorithm in both the mean and mean square sense and bounds on its parameters are derived. An alternative, more insightful approach to the convergence analysis is also presented and is shown to provide an estimate of the optimal step‐size of the PLMS. Incorporating the so obtained step‐size into the PLMS gives the standard PNLMS together with a unified framework for introducing other adaptive learning rates. Simulations on benchmark sparse impulse responses support the approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Zero‐attracting variable‐step‐size least mean square algorithms for adaptive sparse channel estimation

Recently, sparsity‐aware least mean square (LMS) algorithms have been proposed to improve the performance of the standard LMS algorithm for various sparse signals, such as the well‐known zero‐attracting LMS (ZA‐LMS) algorithm and its reweighted ZA‐LMS (RZA‐LMS) algorithm. To utilize the sparsity of the channels in wireless communication and one of the inherent advantages of the RZA‐LMS algorithm, we propose an adaptive reweighted zero‐attracting sigmoid functioned variable‐step‐size LMS (ARZA‐SVSS‐LMS) algorithm by the use of variable‐step‐size techniques and parameter adjustment method. As a result, the proposed ARZA‐SVSS‐LMS algorithm can achieve faster convergence speed and better steady‐state performance, which are verified in a sparse channel and compared with those of other popular LMS algorithms. The simulation results show that the proposed ARZA‐SVSS‐LMS algorithm outperforms the standard LMS algorithm and the previously proposed sparsity‐aware algorithms for dealing with sparse signals. Copyright © 2015 John Wiley & Sons, Ltd.     

Algorithms of adaptive tracking of unknown multisinusoidal signals in linear systems with arbitrary input delay

The problem of adaptive tracking control is addressed for the class of linear time‐invariant plants with known parameters and arbitrary known input delay. The reference signal is a priori unknown and is represented by a sum of biased harmonics with unknown amplitudes, frequencies, and phases. Asymptotic tracking is provided by predictive adjustable control with parameters generated by one of three designed adaptation algorithms. The first algorithm is based on a gradient scheme and ensures zero steady‐state tracking error with all signals bounded. The other two algorithms additionally involve the scheme with fast parametric convergence improving the closed‐loop system performance. In all the algorithms, the problem of delay compensation is resolved by special augmentation of tracking error. The adjustable control law proposed do not require identification of the reference signal parameters.     

基于压缩感知的电力信号压缩与重构研究*

针对电力信号的采集和压缩问题,提出采用压缩感知理论对电力信号进行压缩采样和重构的方法,避免了传统的冗余采样。首先对采用压缩感知理论进行电能信号压缩采样的可行性进行了分析,并讨论了几种典型的压缩感知重构算法的具体实现方法和特性;然后采用这些算法,对一维稀疏信号和傅里叶变换基下稀疏的含有谐波和间谐波的电力信号进行重构实验。仿真结果表明,贪婪类压缩感知重构算法计算复杂度低、速度快,更适合一维电力信号的重构,其中SAMP算法可以在稀疏度未知的情况下,使用更少的采样值精确重构原始信号。     

Behavior of the least mean square algorithm with a periodically time‐varying input power

The paper analyzes the transient and steady‐state performances of a least mean square algorithm in the rarely‐studied situation of a time‐varying input power. A scenario of periodic pulsed variation of the input power is considered. The analysis is carried out in the context of tracking a Markov plant with a white Gaussian input. It is shown that the mean square deviation (MSD) converges to a periodic sequence having the same period as that of the variation of the input power. Expressions are derived for the convergence time and the steady‐state peak MSD. Surprisingly, it is found that neither the transient performance nor the steady‐state performance degrades with rapid variation of the input power. On the other hand, slow input power variation causes degradation in both the transient and steady‐state performances for given amplitude of variation of the input power. In the case of a time‐invariant plant, neither rapid nor slow variation of the input power causes degradation in the steady‐state performance. On the other hand, there is degradation in the transient performance for slow variation of the input power. Copyright © 2012 John Wiley & Sons, Ltd.     

Complex two‐dimensional TNIPM for l1 norm‐based sparse optimization to collocated MIMO radar

In collocated multiple‐input multiple‐output (MIMO) radar, because of the sparse nature of the received signal in the three dimensions of range, angle, and Doppler, accurate estimates of range/angle/Doppler parameters can be achieved using a sparse signal recovery. In this paper, we develop a complex two‐dimensional truncated Newton interior point method (2D TNIPM) for l₁‐norm‐based sparse optimization. Because of the 2D sparse representation of received signal in collocated MIMO radar systems, the performance of proposed algorithm is investigated in order to estimate the target position and velocity. Simulation results show that the 2D TNIPM requires much lower computations compared to the 1D one. Also, it outperforms some other 2D algorithms in the estimation of range, angle, and Doppler parameters under low signal‐to‐noise ratios. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Exponential wavelet iterative shrinkage thresholding algorithm with random shift for compressed sensing magnetic resonance imaging

We propose the use of exponent of wavelet transform (EWT) coefficients as a sparse representation which is combined with the iterative shrinkage/threshold algorithm (ISTA) for the reconstruction of compressed sensing magnetic resonance imaging. In addition, random shifting (RS) is employed to guarantee the translation invariance property of discrete wavelet transform. The proposed method is termed the exponential wavelet iterative shrinkage/threshold algorithm with random shifting (EWISTARS), which takes advantages of the sparse representation of EWT, the simplicity of ISTA, and the translation invariance of RS. Simulation results on brain, vertebrae, and knee MR images demonstrate that EWISTARS is superior to existing algorithms with regard to reconstruction quality and computation time. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Development and convergence analysis of new least‐mean‐square‐based algorithm equipped with exponential‐decay step size and disturbance compensation for active noise control

In real‐world active noise control (ANC) applications, disturbance can be picked up by error sensors and significantly degrade the steady‐state ANC performance. This study proposes two techniques in combination with a least‐mean‐square (LMS) based ANC algorithm, named normalized filtered‐x LMS/commutation error (NFxLMS/CE) algorithm, to deal with the disturbance that is independent of a reference signal. A new stochastic method to analyze convergence properties of the NFxLMS/CE algorithm under influence of the disturbance is first established. Given that the reference signal is persistently exciting of sufficient order, exponential convergence of the algorithm is derived with a step‐size condition. An exponential‐decay step size (EDSS) is then proposed to obtain a new ANC algorithm referred to as EDSS‐NFxLMS/CE algorithm. In addition, a disturbance‐compensation (DC) technique is developed for the EDSS‐NFxLMS/CE algorithm to obtain an EDSS‐NFxLMS/CE_DC algorithm such that the influence of the disturbance can be reduced. It is shown that the EDSS‐NFxLMS/CE_DC algorithm is exponentially convergent. Moreover, computer simulations show that the EDSS‐NFxLMS/CE_DC algorithm can achieve a better ANC performance in terms of convergence rate and level of noise reduction as compared with that using the EDSS‐NFxLMS/CE algorithm without DC and that using NFxLMS/CE_DC algorithm of constant step sizes. These results support the effectiveness of the proposed techniques and EDSS‐NFxLMS/CE_DC algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

A simple variable step size LMS adaptive algorithm

A new LMS based variable step size adaptive algorithm is presented. The step size is incremented or decremented by a small positive value, whenever the instantaneous error is positive or negative, respectively. The algorithm is simple, robust and efficient. It is characterized by fast convergence and low steady state mean squared error. The performance of the algorithm is analysed for a stationary zero‐mean white‐Gaussian input. MC simulations are provided to demonstrate its improved performance over the conventional LMS (Proc. IEEE 1976; 64 :1151–1162) and some other variable step size adaptive algorithms (IEEE Trans. Signal Process. 1992; 40 :1633–1642; IEEE Trans. Signal Process. 1997; 45 :631–639) within a range of statistical environments. For a non‐stationary input, the proposed algorithm behaves similar to these algorithms. A modified version of the algorithm is presented to perform in the presence of abrupt changes. Copyright © 2004 John Wiley & Sons, Ltd.     

动态网络下交替优化正交匹配追踪混合预编码

为解决毫米波大规模多输入多输出(multiple input multiple output, MIMO)系统中混合预编码频谱性能损失严重的问题,本文提出了一种动态网络下交替优化正交匹配追踪混合预编码算法。首先,通过恒模约束条件下的模拟预编码矩阵确定固定相位移相器与天线之间较好的初始连接状态,以提高迭代收敛速率;然后,根据连接状态构造最佳候选模拟预编码矩阵,从而求解全局最优的索引向量;最后,由最优索引向量组成的数字预编码矩阵反馈到动态网络,可动态实现移相器与天线阵列连接状态的交替优化更新。同时,所提出的算法只需要少量固定相位的移相器,在频谱性能和复杂度之间达到良好平衡。仿真结果表明,与其他现有算法相比,该算法具有更高频谱效率、更高迭代收敛速率和更低复杂度,特别是当射频链路数大于数据流数时,频谱效率的提升更加显著。     

Transient performance improvement in indirect model reference adaptive control using perturbation‐based extremum seeking identifier

One of the main drawbacks of model reference adaptive control (MRAC) is the weakness of its transient performance. The key reason of this imperfection is parameter's estimation error convergence. For many cases in the closed‐loop control, the plant input signal cannot satisfy the persistence of excitation (PE) condition which yields poor parameters estimation error convergence. In this paper, we use a fast perturbation‐based extremum seeking (PES) scheme without steady‐state oscillation as the parameter identifier in indirect MRAC. The estimated parameters through the PES identifier contain the additive sinusoidal signals with distinct frequencies in the transient, which satisfy the PE condition of the plant input. Therefore, convergence of the parameters estimation error to zero will be guaranteed that results in improvement of transient performance for indirect MRAC. Also, the contrary effects on the steady‐state behaviour is eliminated since the sinusoidal excitation signals amplitude exponentially converge to zero and reinitiate with every change in the unknown parameters. Simulation results for a second order example have been presented to illustrate the effectiveness of the proposed scheme.     

变步长自适应算法在有源滤波器谐波检测中的应用

对已有改进自适应算法性能进行分析,并尝试将其应用于有源滤波器谐波检测中。实验表明这些变步长算法的性能极易受到系统中噪声信号的干扰,改进效果不明显。该文提出了一种新的变步长自适应谐波检测算法。算法采用归一化的处理方法,以误差信号e(n)在待检测信号中所占比率K(n)作为自适应回馈量,并通过K(n)的相干平均估计来调节算法的步长。其优越性在于:即使在有较大噪声干扰的情况下,谐波检测过程也能保证既具有较快的动态响应速度,又保持较高的检测精度,而不像传统算法那样必需在两者性能上进行折中选择。仿真和实验结果证明了理论分析的有效性。文章还对该算法的收敛性和稳定性进行了分析,并就算法中参数的选取提供了参考标准。     

Mixed norm regularized recursive total least squares for group sparse system identification

A mixed l_p,0‐regularized recursive total least squares (RTLS) algorithm is considered for group sparse system identification. Regularized recursive least squares (RLS) has been successfully applied to group sparse system identification; however, the estimation performance in regularized RLS‐based algorithms deteriorates when both input and output are contaminated by noise (the error‐in‐variables problem). We propose an l_p,0‐RTLS algorithm to handle group sparse system identification with errors‐in‐variables. The proposed algorithm is an RLS‐like solution that utilizes l_p,0‐regularization. The proposed algorithm provides excellent performance as well as reduces the required complexity by effective inversion matrix handling. Simulations demonstrate the superiority of the proposed l_p,0‐regularized RTLS for a group sparse system identification setting. Copyright © 2015 John Wiley & Sons, Ltd.     

压缩感知理论在谐波检测中的运用

运用传统的奈奎斯特定理对电力系统中的谐波信号进行采样将会产生极其庞大的数据量,而全新的压缩感知理论突破了传统采样定理的限制,在信号满足稀疏性的前提下,只需要较少的数据就可以实现信号的重构。文中在对现有的贪婪匹配追踪和自适应算法分析总结的基础之上,结合谐波信号自身的特点,提出了一种新的稀疏度自适应压缩采样匹配追踪算法。此算法可在信号稀疏度未知的情况下,通过信号代理和回溯的思想自适应调节步长逐步逼近原始信号,从而实现以较少采样数据进行谐波检测的目标。MATLAB中的仿真实验表明,运用所提出的算法进行谐波检测的效果理想。     

Estimation algorithm for system with non‐Gaussian multiplicative/additive noises based on variational Bayesian inference

This paper considers estimation algorithms for linear and nonlinear systems contaminated by non‐Gaussian multiplicative and additive noises. Based on the variational idea, in order to derive optimal estimation algorithms, we combine the multiplicative noise with states as the joint parameters to estimate. The application of variational Bayesian inference to joint estimation of the state and the multiplicative noise is established. By treating the states as unknown quantities as well as the multiplicative noise, there are now correlations between the states and multiplicative noise in the posterior distribution. There are two main goals in Bayesian learning. The first is approximating the marginal likelihood (PDF of multiplicative noise) to perform model comparison. The second is approximating the posterior distribution over the states (also called a system model), which can then be used for prediction. The two goals constitute the iterative algorithm. The rules for determining the loop is the Kullback‐Leibler divergence between the true distribution of state and a chosen fixed tractable distribution, which is used to approximate the true one. The iterative algorithm is deduced, which is initialized based on the idea of sampling. Meanwhile, the convergence analysis of the proposed iterative algorithm is presented. The numerical simulation results in a comparison between the proposed method and these existing classic algorithms in the context of nonlinear hidden Markov models, state‐space models, and target‐tracking models with non‐Gaussian multiplicative noise demonstrate the superiorities, not only in speed, precision, and computation load but also in the ability to process non‐Gaussian complex noise.     

基于 LSA-MP 改进原子分解的 电能质量数据压缩方法

电能质量数据压缩是电能质量问题检测和识别中的重要步骤,其本质即为探寻电能质量稀疏特征的过程。针对稀疏分解中常用的匹配追踪算法在匹配最佳原子时计算复杂度高、耗时长,不能满足电力信号分析实时性要求的问题,应用收敛精度高、收敛速度快以及全局寻优能力强的闪电搜索算法搜索最佳原子,提出了闪电搜索匹配追踪算法。利用所提算法在构建的电能质量相关原子库中对电能质量信号进行原子分解,提取电能质量特征参数,将提取到的参数作为压缩后的电能质量数据,实现电能质量数据压缩。实验结果表明,所提算法匹配最佳原子的耗时约缩短为原算法的1/98,基于所提算法的电能质量数据压缩方法在匹配最佳原子满足电力信号分析的实时性要求,具有较高的压缩率和较低的重构误差,提高了数据压缩的性能。     

The innovation algorithms for multivariable state‐space models

This paper derives the input‐output representation of the dynamical system described by a linear multivariable state‐space model and the corresponding multivariate linear regressive model (ie, multivariate equation‐error model). A projection identification algorithm, a multivariate stochastic gradient identification algorithm, and a multi‐innovation stochastic gradient (MISG) identification algorithm are proposed for multivariate equation‐error systems by using the negative gradient search and the multi‐innovation identification theory. The convergence analysis of the MISG algorithm indicates that the parameter estimation errors converge to zero under the persistent excitation condition. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.     

An adaptive sliding‐mode observer for a class of uncertain nonlinear systems

In this paper, the problem of simultaneous state and parameter estimation is studied for a class of uncertain nonlinear systems. A nonlinear adaptive sliding‐mode observer is proposed based on a nonlinear parameter estimation algorithm. It is shown that such a nonlinear algorithm provides a rate of convergence faster than exponential, ie, faster than the classic linear algorithm. Then, the proposed parameter estimation algorithm is included in the structure of a sliding‐mode state observer, providing an ultimate bound for the full estimation error and attenuating the effects of the external disturbances. Moreover, the synthesis of the observer is given in terms of linear matrix inequalities. The corresponding proofs of convergence are developed based on the Lyapunov function approach and input‐to‐state stability theory. Some simulation results illustrate the efficiency of the proposed adaptive sliding‐mode observer.     

Fractionally spaced blind equalization with low‐complexity concurrent constant modulus algorithm and soft decision‐directed scheme

The paper proposes a low‐complexity concurrent constant modulus algorithm (CMA) and soft decision‐directed (SDD) scheme for fractionally spaced blind equalization of high‐order quadrature amplitude modulation channels. We compare our proposed blind equalizer with the recently introduced state‐of‐art concurrent CMA and decision‐directed (DD) scheme. The proposed CMA+SDD blind equalizer is shown to have simpler computational complexity per weight update, faster convergence speed, and slightly improved steady‐state equalization performance, compared with the existing CMA+DD blind equalizer. Copyright © 2004 John Wiley & Sons, Ltd.     

两种盲多用户检测算法的比较

多用户检测技术作为第三代移动通信系统的关键技术已经成为研究热点。文中对两种盲多用户检测算法在动态环境中的收敛性能进行比较,并通过计算机进行模拟仿真。其中一种是能够随输入信号矢量变化而变化的变步长最小输出能量盲算法;另外一种是既保持最小输出能量检测器的全局收敛性又具有最小均方误差检测器高输出信干比优点的判决反馈变步长盲算法。仿真结果表明,前者在动态强干扰下收敛快但波动较大。而后者收敛慢,但在稳态时输出较高的信干比。