Pseudo Affine Projection Algorithm Research Articles

A decision feedforward channel equalization system based pseudo affine projection (DFE-PAP) algorithm

This paper addresses the problem of channel equalization in the context of digital communication systems. The important problem in these systems is the inter-symbol interference (ISI) that distorts the signal quality. In this work, we propose a new adaptive equalizer based on a pseudo affine projection technique to equalize the channel. The proposed equalizer uses multi-pseudo affine projections of the channel output to update the filter equalizer. Our proposed solution uses the Decision Feedforward Equalization (DFE) structure to eliminate the ISI and accelerate the convergence speed by the multi-projection technique. Our proposed equalizer is noted DFE-PAP (Decision Feedforward Equalizer based Pseudo Affine Projection). We have done intensive experiments to evaluate the performance of the proposed DFE-PAP equalizer even in the case of dispersive channels. We have used objective and subjective criteria to compare the proposed DFE-PAP with the classical DFE Normalized Least Mean Square (DFE-NLMS) equalizer. All the obtained results show the good performance of the proposed equalizer.

A new two‐microphone Gauss‐Seidel pseudo affine projection algorithm for speech quality enhancement

SummaryThis study addresses the problem of speech quality enhancement by adaptive and nonadaptive filtering algorithms. The well‐known two‐microphone forward blind source separation (TM‐FBSS) structure has been largely studied in the literature. Several two‐microphone algorithms combined with TM‐FBSS have been recently proposed. In this study, we propose 2 contributions: In the first, a new two‐microphone Gauss‐Seidel pseudo affine projection (TM‐GSPAP) algorithm is combined with TM‐FBSS. In the second, we propose to use the new TM‐GSPAP algorithm in speech enhancement. Furthermore, we show the efficiency of the proposed TM‐GSPAP algorithm in speech enhancement when highly noisy observations are available. To validate the good performances of our algorithm, we have evaluated the adaptive filtering properties in computational complexity and convergence speed performance by system mismatch criteria. A fair comparison with adaptive and nonadaptive noise reduction algorithms are also presented. The adaptive algorithms are the well‐known two‐microphone normalized least mean square algorithm, and the recently published two‐microphone pseudo affine projection algorithm. The nonadaptive algorithms are the one‐microphone spectral subtraction and the two‐microphone Wiener filter algorithm. We evalute the quality of the output speech signal in each algorithm by several objective and subjective criteria as the segmental signal‐to‐noise ratio, cepstral distance, perceptual evaluation of speech quality, and the mean opinion score. Finally, we validate the superior performances of the proposed algorithm with physically measured signals.

Robust Variable Step-Size Decorrelation Normalized Least-Mean-Square Algorithm and its Application to Acoustic Echo Cancellation

In this paper, we present a robust variable step-size decorrelation normalized least-mean-square (RVSSDNLMS) algorithm. A new constrained minimization problem is developed by minimizing the l 2 norm of the a decorrelated posteriori error signal with a constraint on the filter coefficients in the l 2 norm sense. Solving this minimization problem gives birth to the efficient RVSSDNLMS algorithm. The convergence performance and computational complexity of RVSSDNLMS algorithm are analyzed. Finally, simulations show that the proposed RVSSDNLMS considerably outperforms the normalized least-mean-square (NLMS), robust variable step-size NLMS, and pseudoaffine projection algorithms in terms of convergence rate and steady-state error in Gaussian noise and impulsive noise environments.

A New Theoretical Model for the Pseudo Affine Projection Algorithm for Unity Step Size and Autoregressive Inputs

The behavior of the Pseudo Affine Projection (PAP) adaptive algorithm is based on the projection of the present input vector onto a subspace defined by a collection of previous input vectors. Existing analytic models for PAP behavior have considered such a projection using expressions that are in fact valid only after a short initialization period. As a consequence, such models are capable of accurately predict the algorithm convergence behavior whenever the parameters of the problem render the effects of this initialization period unimportant. When this is not the case, the PAP behavior predicted by these models can deviate significantly from reality. This work studies the effect of the initialization on the convergence behavior of the PAP algorithm. The analysis is performed for real-valued signals and for unity step-size (fastest convergence). A new analytical model is derived that incorporates a deterministic initial transient phase at the very beginning of the adaptation process. This phase is due both to the arbitrary initialization of the coefficient vector and to the projection subspace, and is responsible for the modified algorithm behavior. Recursive deterministic equations are derived for the mean weight and mean-square error behaviors for a large number of adaptive filter taps, when compared to the algorithm order. Steady-state theoretical equations are also derived. Monte Carlo simulations show significant modeling improvements for specific parameter sets, both during transient and in steady-state, when compared to the most accurate existing PAP model.

Optimal step-size of pseudo affine projection algorithm

A new statistical analysis model is used to analyze the pseudo affine projection (PAP) algorithm with the optimal step-size in this paper. By setting the weight error to be zero in the direction of the adaptive weight update, the optimal step-size is obtained. Two assumptions for the direction vector are proposed, which simplify the analysis of the convergence behavior for the optimal step-size PAP algorithm. Under this condition, deterministic recursive equations for the weight error and for the mean-square error are derived in the direction of the adaptive weight update. Simulation results are provided to corroborate the analytical results.

Modified Pseudo Affine Projection Algorithm for Feedback Cancellation in Hearing Aids

Modified Pseudo Affine Projection Algorithm for Feedback Cancellation in Hearing Aids

가변 스텝 사이즈를 이용한 개선된 의사 인접 투사 알고리즘

NLMS 알고리즘의 수렴 특성을 개선하기 위해 제안된 인접 투사 알고리즘의 성능을 향상시킨 알고리즘을 제안하였다. 기존의 인접 투사 또는 의사 인접 투사 알고리즘은 지연된 입력 신호 벡터 및 오차 신호 벡터를 기반으로 하기 때문에 복잡할 뿐만 아니라, 기존의 스칼라 오차를 기반으로 하는 LMS 형 알고리즘에서 개발된 기법을 적용하는데 어려움이 있다. 본 논문에서는 의사 인접 투사 알고리즘의 경우, 스칼라 오차 신호를 이용한다는 사실과 수렴 후 입력 신호가 오차 신호에 직교한다는 직교 원리에 근거하여 적은 연산량으로도 우수한 수렴 성능을 보이는 가변 스텝 사이즈 알고리즘을 제안하였다. 시스템 확인 모델 하에서 컴퓨터 모의 실험을 통하여 제안된 알고리즘이 기존의 알고리즘들에 비하여 적은 연산량에도 불구하고 정상 및 비정상 환경에서 수렴 특성이 우수함을 보였다. In this paper, we propose an enhanced algorithm for affine projection algorithms which have been proposed to speed up the convergence of the conventional NLMS algorithm. Since affine projection (AP) or pseudo AP algorithms are based on the delayed input vector and error vector, they are complicated and not suitable for applying methods developed for the LMS-type algorithms which are based on the scalar error signal. We devised a variable step size algorithm for pseudo AP using the fact that pseudo AP algorithms are updated using the scalar error and that the error signal is getting orthogonal to the input signal. We carried out a performance comparison of the proposed algorithm with other pseudo AP algorithms using a system identification model. It is shown that the proposed algorithm presents good convergence characteristics under both stationary and non-stationary environments despites its low complexity.

Pseudo Affine Projection Algorithms Revisited: Robustness and Stability Analysis

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 ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -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.

Adaptive Regularization Parameter for Pseudo Affine Projection Algorithm

An adaptive regularized affine projection (AR-AP) algorithm has recently been proposed in order to achieve good misalignment performance. However, the algorithm requires high computational complexity. To overcome this problem, we propose an adaptive regularized pseudo affine projection (AR-PAP) algorithm. Additionally, we derive the lower bound of the regularization parameter in order to guarantee the stability of the AR-PAP algorithm. Simulation results show that the performance of the proposed algorithm is better than that of the AR-AP algorithm despite its significantly lower complexity.

A Stochastic Model for a Pseudo Affine Projection Algorithm

This paper presents a statistical analysis of a Pseudo Affine Projection (PAP) algorithm, obtained from the Affine Projection algorithm (AP) for a step size alpha < 1 and a scalar error signal in the weight update. Deterministic recursive equations are derived for the mean weight and for the mean square error (MSE) for a large number of adaptive taps N compared to the order P of the algorithm. Simulations are presented which show good to excellent agreement with the theory in the transient and steady states. The PAP learning behavior is of special interest in applications where tradeoffs are necessary between convergence speed and steady-state misadjustment.

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.

Pseudo-Affine Projection Algorithms for Multichannel Active Noise Control

For feedforward multichannel active noise control (ANC) systems, the use of adaptive finite-impulse response (FIR) filters is a popular solution, and the multichannel filtered-x least-mean-square (FX-LMS) algorithm is the most commonly used algorithm. The drawback of the FX-LMS is the slow convergence speed, especially for broadband multichannel systems. Recently, some fast affine projection algorithms have been introduced for multichannel ANC, as an interesting alternative to the FX-LMS algorithm. They can provide a significantly improved convergence speed at a reasonable additional computational cost. Yet, the additional computational cost or the potential numerical instability in some of the recently proposed algorithms can prevent the use of those algorithms for some applications. In this paper, we propose two pseudo-affine projection algorithms for multichannel ANC: one based on the Gauss-Seidel method and one based on dichotomous coordinate descent (DCD) iterations. It is shown that the proposed algorithms typically have a lower complexity than the previously published fast affine projection algorithms for ANC, with very similar good convergence properties and good numerical stability. Thus, the proposed algorithms are an interesting alternative to the standard FX-LMS algorithm for ANC, providing an improved performance for a computational load of the same order

Fast block exact Gauss-Seidel pseudo affine projection algorithm

A block affine projection algorithm that is less complex but mathematically equivalent to a recently proposed Gauss-Seidel pseudo affine projection (GS-PAP) algorithm is proposed. This reduced complexity is achieved by applying a partitioning method to the original sample-by-sample algorithm. It is shown that the derived algorithm has better convergence and tracking abilities than those of the NLMS algorithm. Its application in an acoustic echo cancellation is investigated.