Step-size Affine Projection Algorithm Research Articles

A variable diagonal-matrix-step-size APA robust to impulsive noises

This study introduces a variable diagonal-matrix-step-size affine projection algorithm (APA), which shows robustness against to impulsive noises. Unlike the normal scalar step-size method, the independent step size for each input vector is used as the entry of the diagonal matrix, and the optimal step size at each time step is ascertained by conducting mean-square-deviation (MSD) analysis. In addition, a recursive equation of weight update has been derived without approximating posteriori error as priori error. Using the Lagrange multiplier method, we formulate a scalar step size affine projection algorithm that shows resilience to impulsive noises. This algorithm emerges as a solution to a constrained optimization problem. To further enhance convergence performance, a diagonal-matrix-step size is introduced and its MSD is analyzed. The step size at each time step is optimized by interpreting the MSD mathematically, resulting in the variable diagonal-matrix-step size APA (VDMSS-APA). Various simulations exhibit low steady-state error and fast convergence rate of the proposed algorithm.

Discrete-time rate-dependent hysteresis modeling and parameter identification of piezoelectric actuators

A discrete-time-modified Bouc–Wen model is proposed to describe the non-symmetrical and rate-dependent hysteresis of piezoelectric actuators for micro-vibration control applications. The modified model combines a non-symmetrical Bouc–Wen model and a frequency-dependent dynamic module. A series of experiments are conducted to characterize the rate-dependent hysteresis of piezoelectric stack actuators under sinusoidal excitations at a range of 1 to 20 Hz. The experimental results verify the validity of the modified model. The modified Bouc–Wen model increases the complexity of Bouc–Wen hysteresis nonlinear differential equation, which brings difficulties to parameter identification. To identify the parameters of Bouc–Wen model, an improved hybrid differential evolution and Jaya (DE-Jaya) algorithm is introduced with a hybrid mutant operator and Jaya operator that tried to balance between convergence speed and solution accuracy. The improved algorithm is tested on benchmark functions and compared with other optimizations to prove its effectiveness. The comparison results show that hybrid DE-Jaya algorithm has better performance in convergence speed and solution accuracy. The identified discrete-time-modified Bouc–Wen model is used as the secondary path in a filtered-x variable step-size affine projection algorithm (FXVSSAPA), and experimental verifications are done on a micro-vibration control platform. The experimental results show that the FXVSSAPA algorithm can converge to the steady-state error faster and verify the effectiveness of the proposed discrete-time-modified Bouc–Wen model.

Self-adaptive stepsize affine projection based parameter estimation of IPMSM using square-wave current injection

Affine projection algorithm (APA) has been used to estimate the parameters of interior permanent magnet synchronous motor (IPMSM). However, there is not a strict guideline of choosing the stepsize of this algorithm to make sure that the results of parameter estimation are convergent. In order to solve such problem, self-adaptive stepsize affine projection algorithm for parameter estimation of IPMSM is proposed in this paper. Compared with traditional affine projection algorithm, this method can obtain the stepsize automatically based on the operation condition, which can ensure the convergence and celerity of the process of parameter estimation. Then, on the basis of self-adaptive stepsize affine projection algorithm, a novel parameter estimation method based on square-wave current injection is proposed. By this method, the error of estimated parameter caused by stator resistance, linkage magnetic flux and dead-time voltage can be reduced effectively. Finally, the proposed parameter estimation method is verified by experiments on a 2.2-kW IPMSM drive platform.

An optimal variable step-size affine projection algorithm for the modified filtered-x active noise control

This paper introduces an optimal variable step-size affine projection algorithm for the modified filtered-x active noise control systems. First, the recursion form of the error covariance from the tap weight update equation is constructed, not ignoring the dependency between the estimation error and the secondary noise signal. Such consideration has not been concerned previously for the analysis of the modified filtered-x affine projection algorithm. Second, a recursion form of the mean square deviation is derived from that of the error covariance. From the recursion form, an optimal step size is decided to get the fastest convergence rate. Both the recursion forms of the mean square deviation and the optimal step size require scalar additions and multiplications that do not contribute to the overall complexity seriously. The simulation results on the active noise control environments show both fast convergence rate and low steady-state error.

Adaptive feedback cancellation based on variable step-size affine projection for hearing aids

A new variable step-size (VSS) affine projection algorithm (APA) (VSS-APA) was proposed for adaptive feedback cancellation suitable for hearing aids. So, a nonlinear function between step-size and estimation error is established and automatically adjusted according to the change of the estimation error, which leads to low misalignment and fast convergence speed. Analysis of the proposed algorithm offers large capacities in converging to the objective system. Simulation shows that the proposed algorithm achieves lower misalignment and faster convergence speed compared to fixed step-size APA and conventional adaptive algorithms.

Nonparametric VSS-APA based on precise background noise power estimate

The adaptive algorithm used for echo cancellation (EC) system needs to provide 1) low misadjustment and 2) high convergence rate. The affine projection algorithm (APA) is a better alternative than normalized least mean square (NLMS) algorithm in EC applications where the input signal is highly correlated. Since the APA with a constant step-size has to make compromise between the performance criteria 1) and 2), a variable step-size APA (VSS-APA) provides a more reliable solution. A nonparametric VSS-APA (NPVSS-APA) is proposed by recovering the background noise within the error signal instead of cancelling the a posteriori errors. The most problematic term of its variable step-size formula is the value of background noise power (BNP). The power difference between the desired signal and output signal, which equals the power of error signal statistically, has been considered the BNP estimate in a rough manner. Considering that the error signal consists of background noise and misalignment noise, a precise BNP estimate is achieved by multiplying the rough estimate with a corrective factor. After the analysis on the power ratio of misalignment noise to background noise of APA, the corrective factor is formulated depending on the projection order and the latest value of variable step-size. The new algorithm which does not require any a priori knowledge of EC environment has the advantage of easier controllability in practical application. The simulation results in the EC context indicate the accuracy of the proposed BNP estimate and the more effective behavior of the proposed algorithm compared with other versions of APA class.

Teacher - Student Graphical User Interface For Testing And Comparing The Performance Of Adaptive Algorithms Used In Smart Antenna Networks

AbstractSmart antenna networks are receiving a lot of interest in these days, as new advanced and fast processors are being developed. Capable of pointing the main beam in a certain desired direction and create nulls in the radiation pattern in the direction of interference, smart antenna networks are a good solution in a bandwidth limited environment as the number of users continuously grow. This technique is called beamforming. For many years smart antennas were not practical as they involve the use of a processor that runs an adaptive algorithm. Slow processors meant low speed of convergence and a slow adaptation. There are a lot of adaptive algorithms that can fur fill the job that a smart antenna system has to accomplish. The main purpose of this paper is however to present the main advantages of creating a MATLAB GUI (Graphical User Interface) in order to study these algorithms. The GUI described studies 62 adaptive algorithms, some described in literature, some propose by the authors. We will make a short description of the LMS (Least Mean Squares Algorithm), the APA (Affine Projection Algorithm) and the GASSAPA (Gradient Adaptive Scalar Step Size Affine Projection Algorithm) and compare them with the use of the graphical interface.

Variable step-size affine projection algorithm based on global speech absence probability for adaptive feedback cancellation

A novel approach is proposed for improving adaptive feedback cancellation using a variable step-size affine projection algorithm (VSS-APA) based on global speech absence probability (GSAP). The variable step-size of the proposed VSS-APA is adjusted according to the GSAP of the current frame. The weight vector of the adaptive filter is updated by the probability of the speech absence. The performance measure of acoustic feedback cancellation is evaluated using normalized misalignment. Experimental results demonstrate that the proposed approach has better performance than the normalized least mean square (NLMS) and the constant step-size affine projection algorithms.

Variable matrix-type step-size affine projection algorithm with orthogonalized input vectors

In this paper, we propose a variable matrix-type step-size affine projection algorithm (APA) with orthogonalized input vectors. We generate orthogonalized input vectors using the Gram–Schmidt process to implement the weight update equation of the APA using the sum of normalized least mean squares (NLMS)-like updating equations. This method allows us to use individual step sizes corresponding to each NLMS-like equation, which is equivalent to adopting the step size in the form of a diagonal matrix in the APA. We adopt a variable step-size scheme, in which the individual step sizes are determined to minimize the mean square deviation of the APA in order to achieve the fastest convergence on every iteration. Furthermore, because of the weight vector updated successively only along each innovative one among the reused inputs and effect of the regularization absorbed into the derived step size, the algorithm works well even for badly excited input signals. Experimental results show that our proposed algorithm has almost optimal performance in terms of convergence rate and steady-state estimation error, and these results are remarkable especially for badly excited input signals.

A variable step-size affine projection algorithm with a step-size scaler against impulsive measurement noise

This letter proposes a variable step-size (VSS) affine projection algorithm (APA) associated with a step-size scaler to improve the APA's robustness against impulsive measurement noise. In the proposed VSS APA, the step-size scaler is applied to the equations for updating the step size, which are developed by interpreting the behavior of the mean square deviation (MSD) of the conventional APA. To reduce the computational complexity, we also propose a simplified version of the step-size scaler, which is suitable for application in the APA. Simulations show that the proposed algorithm leads to an excellent transient and steady-state behavior with colored inputs in impulsive-noise environments.

Enhancement of Convergence Properties of Adaptive CDMA Receiver over Rayleigh Flat Fading Channel

CDMA system is a promising multiple access technique which extremely increases the channel capacity and supports multiple-access and multimedia transmission. However, the performance of CDMA system degrades in presence of multipath and dense multiple-access environment .Usually an adaptive filter is utilized to compensate the effect of multipath and multiple- access interference and signal fading over the channel. This paper provides a variable step size algorithm to accelerate convergence of the adaptive filter. The optimum performance is achieved by governing the rate of convergence and the amount of steady state excess mean square error (MSE).The performance is optimized in thispaper by two main methods mainly: variable step size parameters and gradient adaptively regularization parameter. The first method is implemented through variable step size least mean square algorithm VSSLMS, modified variable step size MVSS algorithm and variable step size affine projection algorithm VS-APA. On the other hand, the second method isimplemented using generalized normalized gradient descent algorithm GNGD and generalized square-error-regularized LMS algorithm GSER-LMS. This paper concerns with comparative study of the five mentioned adaptive algorithms,(VSSLMS – MVSS – VS-APA – GNGD – GSER-LMS), to overcome the multipath and multiple-access problems of CDMA systems. The mentioned algorithms had the advantages of fast convergence and low steady state MSE, these advantages candidate the mention algorithms to improve the bit error rate (BER) performance of the CDMA system, in the presence of multipath and multiple-access environment. The results indicate that the proposed algorithm provides faster convergence compared with the fixed step size and fixed regularization parameters algorithms.

Robust Time Delay Estimation Using Variable Step-Size Affine Projection Algorithm with M-estimators

摘要: 该文提出了一种基于M估计变步长自适应仿射投影方法的稳健时延估计(TDE)算法。该算法将自适应仿射投影算法应用于时延估计,无须事先假定信号和噪声的统计特性,自适应调整自身参数;应用稳健M估计理论,抵消重尾噪声干扰。数值仿真表明,在高斯噪声、非高斯噪声甚至冲激噪声的干扰下,该文算法比高阶统计量法和最小均方自适应法有更强的稳健性和更高的估计精度。 关键词: 时延估计; M估计; 变步长自适应仿射投影算法; 高阶统计量

A robust variable step-size affine projection algorithm

We present a robust variable step-size affine projection algorithm (RVSS-APA) using a recently introduced new framework for designing robust adaptive filters. The algorithm is the result of minimizing the square norm of the a posteriori error vector subject to a time-dependent constraint on the norm of the filter update. The RVSS-APA is then successfully tested in different environments for system identification and acoustic echo cancellation applications.

Variable step-size affine projection algorithm with exponential smoothing factors

Presented is an improved variable step-size affine projection algorithm (VS-APA) with exponential smoothing factor, namely VS-APA-EXP, in which an exponential function of the projected error norm is used as smoothing factor. Simulation results illustrate that the proposed algorithm is superior in terms of mean-square deviation (MSD) compared with existing algorithms.

A Variable Step-Size Affine Projection Algorithm Designed for Acoustic Echo Cancellation

The adaptive algorithms used for acoustic echo cancellation (AEC) have to provide (1) high convergence rates and good tracking capabilities, since the acoustic environments imply very long and time-variant echo paths, and (2) low misadjustment and robustness against background noise variations and double-talk. In this context, the affine projection algorithm (APA) and different versions of it are very attractive choices for AEC. However, an APA with a constant step-size parameter has to compromise between the performance criteria (1) and (2). Therefore, a variable step-size APA (VSS-APA) represents a more reliable solution. In this paper, we propose a VSS-APA derived in the context of AEC. Most of the APAs aim to cancel p (i.e., projection order) previous a posteriori errors at every step of the algorithm. The proposed VSS-APA aims to recover the near-end signal within the error signal of the adaptive filter. Consequently, it is robust against near-end signal variations (including double-talk). This algorithm does not require any a priori information about the acoustic environment, so that it is easy to control in practice. The simulation results indicate the good performance of the proposed algorithm as compared to other members of the APA family.

Variable Step-Size Affine Projection Algorithm With a Weighted and Regularized Projection Matrix

This paper presents a regularized modification to the weighted variable step-size affine projection algorithm (APA). The regularization overcomes the ill-conditioning introduced by both the forgetting process and the increasing size of the input matrix. The algorithm was tested by trials with colorized input signals and different parameter combinations. Simulations illustrate that the proposed algorithm is superior in terms of convergence speed and misadjustment compared with existing algorithms.

Robust pseudo affine projection algorithm with variable step-size

Recently, a variable step-size affine projection (VSS-AP) algorithm has been introduced. The algorithm provides faster convergence rate and lower misadjustment but has heavy computational complexity. Proposed is a new variable step-size pseudo affine projection (VSS-PAP) algorithm, which not only has a much lower complexity than the VSS-AP algorithm but also provides performance comparable with the conventional algorithm. Simulation results confirm fast convergence rate and small misalignment of the proposed algorithm with less computational complexity.

Variable Step Size Affine Projection Algorithm for Adaptive Multiuser DS-CDMA MMSE Receiver

In this paper, we consider the use of affine projection algorithm (APA) for interference suppression in direct sequence code-division multiple-access (DS-CDMA) system. We first derive the multiuser fixed step-size APA (FSS-APA) algorithm. The computational complexity offered by the APA algorithm is linear in terms of the number of taps with additional terms of O (L 2) and a matrix inversion of dimension L, where L is known as the order of the filter. The value of L is chosen very small as compared to the number of filter-taps N T . We next propose a novel variable step-size APA (VSS-APA) algorithm, which further improves the performance of the FSS-APA algorithm with very small increase in computational complexity as compared to the FSS-APA. It is demonstrated that the performance of the APA based minimum mean-square error (MMSE) receivers is far superior to that of the normalized least-mean-square (NLMS) based receivers. Though, the recursive-least-square (RLS) algorithm based adaptive receivers offer better performance but at the cost of much higher computational complexity.

An order-tracking technique for the diagnosis of faults in rotating machineries using a variable step-size affine projection algorithm

This paper describes principles and applications of an adaptive order tracking diagnosis technique for fault diagnosis in rotating machinery. An adaptive high-resolution order tracking method with a variable step-size affine-projection algorithm (VSS APA) is used to diagnose faults in the gear-set and centrifugal fan blades. In comparison with conventional order-tracking methods such as recursive least-square filtering algorithm, the proposed VSS APA technique has fast convergence speed for adaptive filtering process. The VSS APA-based order-tracking technique can overcome problems encountered in FFT based methods. The smearing problem is treated as the tracking of frequency-varying band-pass signals. Ordered amplitudes can be calculated with high-resolution adaptive filter algorithm after experimental implementations carried out to evaluate the proposed algorithm in gear-set and centrifugal fan blades defect diagnosis. The experimental result indicates that the proposed algorithm is effective in rotating machinery fault diagnosis.