A robust variable step-size affine projection algorithm (original) (raw)
Delay coefficients based variable step size algorithm for subband affine projection adaptive filters
IEICE Electronics Express, 2009
Subband adaptive filters are preferred in acoustic echo cancellation systems with long echo tail lengths due to speed of convergence and complexity savings. Recently, a new and novel subband affine projection (SAP) algorithm was reported based on the polyphase decomposition of the adaptive filter and noble identities. For good system performance it is important to have a good variable step size (VSS) algorithm as part of an adaptive filter. In this paper, based on the method of delay coefficients (DC), we propose 1 a VSS algorithm for the SAP adaptive filter, which is called as delay coefficients based variable step size subband affine projection algorithm (DC-VSS-SAP). We examine in detail the similarities and differences between DC method for the subband and fullband scenarios. Further, we show how the method of DC can be used to detect changes in echo paths and speed up convergence of the adaptive filter.
A Family of Selective Partial Update Affine Projection Adaptive Filtering Algorithms
iranian journal of electrical and electronic engineering, 2009
In this paper we present a general formalism for the establishment of the family of selective partial update affine projection algorithms (SPU-APA). The SPU-APA, the SPU regularized APA (SPU-R-APA), the SPU partial rank algorithm (SPU-PRA), the SPU binormalized data reusing least mean squares (SPU-BNDR-LMS), and the SPU normalized LMS with orthogonal correction factors (SPU-NLMS-OCF) algorithms are established by this general formalism. In these algorithms, the filter coefficients are partially updated rather than the entire filter coefficients at every iteration which is computationally efficient. Following this, the transient and steady-state performance analysis of this family of adaptive filter algorithms are studied. This analysis is based on energy conservation arguments and does not need to assume a Gaussian or white distribution for the regressors. We demonstrate the performance of the presented algorithms through simulations in system identification and acoustic echo cancel...
New optimal variable step size-adaptive regularized-affine projection algorithm
International Journal of Speech Technology, 2019
In this paper, a new optimal variable step size-adaptive regularized-affine projection algorithm (OVSS-AR-APA) is proposed and compared with existing variable step size APA family of algorithms. Instead of having a constant regularization parameter, the modified sigmoid function variation is used to choose the optimum regularization parameter in the proposed algorithm. Here, the algorithm dynamically adjusts the regularization parameter according to input noise variations. Also, the exponentially weighted value of the error with variable regularization parameter is used for making the step size parameter variable. The existing and proposed algorithms are implemented for noise cancellation from audio signals at various input SNR levels for different filter orders. It is observed from simulations that the proposed algorithm outperforms the existing algorithms in terms of SNR improvements, MSE and convergence rate at all input SNR levels for different filter orders with moderate computational complexity. The OVSS-AR-APA algorithm shows a maximum of 21.54 dB of improvement in SNR at-20dB input SNR level at filter order 5.
Application of Affine Projection Algorithm in Adaptive Noise Cancellation
2014
This paper presents the application of two classes of Affine Projection Algorithm (APA) for Adaptive Noise Cancellation. The output results are compared on the basis of signal to noise ratio (SNR) and frequency spectrum of the filtered signal. The two classes of Affine Projection Algorithm used to adapt the noise, involve Conventional APA and Adaptive Step Size APA. Computer Simulations for various classes of APA are carried out using Matlab. For colored input and correlated data, APA family is suitable to accelerate the convergence of Least Mean Squares (LMS) Algorithm at a computational cost. In adaptive step size APA, step size is adapted on the basis of absolute mean value of error vector.
An Efficient Proportionate Affine Projection Algorithm for Echo Cancellation
IEEE Signal Processing Letters, 2000
Proportionate-type normalized least-mean-square algorithms were developed in the context of echo cancellation. In order to further increase the convergence rate and tracking, the "proportionate" idea was applied to the affine projection algorithm (APA) in a straightforward manner. The objective of this letter is twofold. First, a general framework for the derivation of proportionate-type APAs is proposed. Second, based on this approach, a new proportionate-type APA is developed, taking into account the "history" of the proportionate factors. The benefit is also twofold. Simulation results indicate that the proposed algorithm outperforms the classical one (achieving faster tracking and lower misadjustment). Besides, it also has a lower computational complexity due to a recursive implementation of the "proportionate history." Index Terms-Adaptive filtering, echo cancellation, proportionate affine projection algorithm.
IEEE Transactions on Speech and Audio Processing, 2003
In the field of adaptive signal processing, it is well known that affine projection algorithms or their low-computational implementations fast affine projection algorithms can produce a good tradeoff between convergence speed and computational complexity. Although these algorithms typically do not provide the same convergence speed as recursive-least-squares algorithms, they can provide a much improved convergence speed compared to stochastic gradient descent algorithms, without the high increase of the computational load or the instability often found in recursive-least-squares algorithms. In this paper, multichannel affine and fast affine projection algorithms are introduced for active noise control or acoustic equalization. Multichannel fast affine projection algorithms have been previously published for acoustic echo cancellation, but the problem of active noise control or acoustic equalization is a very different one, leading to different structures, as explained in the paper. The computational complexity of the new algorithms is evaluated, and it is shown through simulations that not only can the new algorithms provide the expected tradeoff between convergence performance and computational complexity, they can also provide the best convergence performance (even over recursive-least-squares algorithms) when nonideal noisy acoustic plant models are used in the adaptive systems.
Optimal Regularization Parameter of the Multichannel Filtered-x Affine Projection Algorithm
IEEE Transactions on Signal Processing, 2007
We discuss the optimal regularization parameter of the Filtered-Affine Projection (FX-AP) algorithm suitable for feedforward active noise control. While the original FX-AP algorithm always provides a biased estimate of the minimum-meansquare solution, we show that the optimal regularized FX-AP algorithm is capable to eliminate the bias of the asymptotic solution and thus that the regularization parameter can optimize both the convergence speed and the residual MSE of the algorithm. We derive some expressions for the optimal regularization parameter, and we discuss some heuristic estimations of the optimal regularization parameter in practical conditions. Index Terms-Active noise control, affine projection algorithm, multichannel adaptive filtering, optimal regularization parameter.
2004
The Affine Projection Algorithm (APA) has been shown to improve the performance of Over-Sampled Subband Adaptive Filters (OS-SAFs) compared to classical Normalized Least Mean Square (NLMS) algorithms. Because of the complexity of APA, however, only low-order APAs are practical for real-time implementation. Thus, in this paper, we propose a reduced-complexity version of the Gauss-Seidel Fast APA (GSFAPA) for adapting the subband filters in OS-SAF systems. We propose modifying the GSFAPA with a complexity reduction method based on partial filter update, and also with a low-cost method for combined regularization and step size control. We show the advantage of the new algorithmtermed Low-Cost Gauss-Seidel Fast Affine Projection -compared to the APA in a subband echo canceller application.
Pseudo Affine Projection Algorithms Revisited: Robustness and Stability Analysis
IEEE Transactions on Signal Processing, 2000
The so-called Affine Projection (AP) algorithm is of large interest in many adaptive filters applications due to its considerable speed-up in convergence compared to its simpler version, the LMS algorithm. While the original AP algorithm is well understood, gradient type variants of less complexity with relaxed step-size conditions called pseudo affine projection offer still unresolved problems. This contribution shows i) local robustness properties of such algorithms, ii) global properties of these, concluding 2 -stability conditions that are independent of the input signal statistics, as well as iii) steady-state values of moderate to high accuracy by relatively simple terms when applied to long filters. Of particular interest is the existence of lower step-size bounds for one of the variants, a bound that has not been observed before.
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2007
We propose a gradient-limited affine projection algorithm (GL-APA), which can achieve fast and double-talk-robust convergence in acoustic echo cancellation. GL-APA is derived from the M-estimationbased nonlinear cost function extended for evaluating multiple error signals dealt with in the affine projection algorithm (APA). By considering the nonlinearity of the gradient, we carefully formulate an update equation consistent with multiple input-output relationships, which the conventional APA inherently satisfies to achieve fast convergence. We also newly introduce a scaling rule for the nonlinearity, so we can easily implement GL-APA by using a predetermined primary function as a basis of scaling with any projection order. This guarantees a linkage between GL-APA and the gradientlimited normalized least-mean-squares algorithm (GL-NLMS), which is a conventional algorithm that corresponds to the GL-APA of the first order. The performance of GL-APA is demonstrated with simulation results.