Analysis of the LNS Implementation of the Fast Affine Projection algorithms (original) (raw)
IEEE Signal Processing Letters, 2000
A straightforward generalization of the so-called affine projection algorithm (APA) to the multichannel (MC) case is easily obtained. However, due to the strong correlation between the input signals of the various channels, the resulting algorithm converges very slowly. This letter describes the way to overcome this problem and derives an efficient algorithm that turns out to make use of additional orthogonal projections.
Robust variable step-size affine projection algorithm suitable for acoustic echo cancellation
The affine projection algorithm (APA) and different versions of it have proved to be very attractive choices for acoustic echo cancellation (AEC). In this context, a classical APA with a constant step-size has to compromise between two performance criteria, i.e., 1) high convergence rates and good tracking capabilities, and 2) low misadjustment and robustness against background noise variations and doubletalk. Consequently, a variable step-size APA (VSS-APA) is a more reliable solution. In this paper we propose a VSS-APA that is designed to recover the near-end signal from the error signal of the adaptive filter. Therefore, it is robust against near-end signal variations, including double-talk. Moreover, since it does not require a priori information about the acoustic environment, the proposed algorithm is easy to control in real-world AEC applications.
This paper presents a field-programmable gate array (FPGA) implementation of a recently proposed variable stepsize affine projection algorithm (VSS-APA), in the context of acoustic echo cancellation. The proposed hardware implementation scheme takes advantage of the algorithm's specific features. Area and speed results are provided for the Xilinx Virtex 5 XC5VFX70T chip from the Xilinx ML507 evaluation board, when considering the particular case of the projection order p = 2. The overall performance of this acoustic echo canceller (AEC) indicates that it could be a reliable solution for real-world acoustic echo cancellation scenarios.
A LOW COMPLEXITY PROPORTIONATE AFFINE PROJECTION ALGORITHM FOR ECHO CANCELLATION
Proportionate-type affine projection algorithms were developed in the context of echo cancellation, as a generalization of the proportionate-type normalized least-mean-square algorithms. A matrix inversion is required within the affine projection algorithm (APA). In the case of proportionatetype APAs, the update of the matrix to be inverted is very computationally expensive. In this paper, an efficient update of this matrix is proposed and the procedure is applied for a recently developed proportionate-type APA. It is shown that the proposed algorithm achieves similar performance but significantly lowers numerical complexity as compared to known proportionate-type APAs.
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.
FPGA implementation of an efficient proportionate affine projection algorithm for echo cancellation
2011
This paper presents a field-programmable gate array (FPGA) implementation of a low-complexity proportionate affine projection algorithm (PAPA), in the context of echo cancellation. The proposed algorithm results as a combination between the recently developed “memory”-improved PAPA (MIPAPA) and a dichotomous coordinate descent (DCD) method. The MIPAPA takes into account the “history” of the proportionate factors, which is not the case for the classical PAPAs. Moreover, it achieves a lower computational complexity due to a recursive implementation of the “proportionate history;” as a consequence, the matrix that has to be inverted within the MIPAPA has the time-shift property, which can also lower the complexity. Concerning this task, the DCD technique efficiently performs the matrix inversion, requiring only addition operations. The proposed hardware implementation scheme takes advantage of the algorithm's specific features. The overall performance of the proposed DCD-MIPAPA ind...
GAUSS-SEIDEL BASED VARIABLE STEP-SIZE AFFINE PROJECTION ALGORITHMS FOR ACOUSTIC ECHO CANCELLATION
Fast affine projection (FAP) algorithms have proved to be very attractive choice for acoustic echo cancellation (AEC). These algorithms offer a good trade-off between convergence rate and computational complexity. Most of the existing FAP algorithms use a constant step-size and need to compromise between several performance criteria (e.g., fast convergence and low misalignment). In this paper, two FAP algorithms based on the Gauss-Seidel method and using a variable step-size (VSS) are proposed for AEC. It is shown that the proposed algorithms are more robust against nearend signal variations (including double-talk) than their counterparts that use a fixed step-size.
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.
Set-membership affine projection algorithm for echo cancellation
This paper proposes a new data-selective affine projection algorithm for echo cancellation. The algorithm generalizes the concepts of the conventional set-membership affine-projection by incorporating a lower bound on the output error in order to prevent undesirable attenuation of the far-end signal. It is shown that the echo signal can more reliably be removed from the far-end user signals by employing the new algorithm in double talk situations. In addition, the proposed algorithm retains the fast convergence of the conventional SM-AP algorithm while keeping a reduced number of coefficient updates. Simulation results, using the ITU-T G.168 recommendation setup parameters, are presented in order to confirm the good features of the proposed algorithm.