Felix Albu

Coordinate descent iterations in fast affine projection algorithm

We propose a new approach for real-time implementation of the fast affine projection (FAP) algorithm. This is based on exploiting the recently introduced dichotomous coordinate descent (DCD) algorithm, which is especially efficient for solving systems of linear equations on real-time hardware and software platforms since it is free of multiplication and division. The numerical stability of the DCD algorithm allows the new combined DCD-FAP algorithm also to be stable. The convergence and complexity of the DCD-FAP algorithm is compared with that of the FAP, Gauss-Seidel FAP (GS-FAP), and modified GS-FAP algorithms in the application to acoustic echo cancellation. The DCD-FAP algorithm demonstrates a performance close to that of the FAP algorithm with ideal matrix inversion and the complexity smaller than that of the Gauss-Seidel FAP algorithms.

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

A variable step size evolutionary affine projection algorithm

It is well known that the affine projection algorithm (APA) offers a good tradeoff between convergence rate/tracking and computational complexity. Recently, the evolutionary APA (E-APA) with a variable projection order has been proposed. In this paper, we propose a variable step size (VSS) version of the E-APA, called VSS-E-APA. It is shown that the VSS-E-APA is robust to near-end signal variations. Also, it has both a fast convergence speed and a small steady-state error and a much reduced numerical complexity than the VSS-APA.

The multichannel Gauss-Seidel fast affine projection algorithm for active noise control

It is well known that fast affine projection algorithms can produce a good trade-off between convergence speed and computational complexity. Recently, a multichannel fast affine projection algorithm was introduced for active noise control, using a sliding window recursive least- squares algorithm inside the affine projection algorithm. It was reported that not only can this algorithm provide the expected tradeoff between convergence performance and computational complexity, it can also provide the best convergence performance (even over more complex recursive least-squares algorithms) when non-ideal noisy acoustic plant models are used in the adaptive noise control system. In this paper, we propose a multichannel fast affine projection algorithm for active noise control systems, with a lower complexity and the potential for a better numerical stability than the previously published algorithm. The new algorithm is based on the Gauss-Seidel fast affine projection algorithm. The computational complexity of the new algorithm is evaluated, and it is shown through simulations that the new algorithm provides the same good performance as the previously published algorithm.

A proportionate affine projection algorithm using dichotomous coordinate descent iterations

This paper proposes a low-complexity proportionate affine projection algorithm (PAPA) suitable for echo cancellation. It is known that proportionate-type algorithms exploit the sparseness character of the echo path in order to achieve faster convergence and tracking as compared to the conventional algorithms. The proposed algorithm results as a combination between a recently proposed “memory”-PAPA (MPAPA) and an iterative technique for solving the matrix inversion problem, i.e., the dichotomous coordinate descent (DCD) with a leading element. Simulations performed in the context of network echo cancellation indicate the good performance of the proposed algorithm.

An efficient variable step-size proportionate affine projection algorithm

Proportionate-type affine projection algorithms (PAPAs) are very attractive choices for echo cancellation. These algorithms combine the good features (convergence and tracking) of the affine projection algorithm (APA) and the proportionate idea, which exploits the sparseness character of the echo path in order to further increase their convergence rate. In this paper, we develop a variable step-size (VSS) version of a recently proposed PAPA. The new algorithm achieves a good compromise between fast convergence rate and low misadjustment, but also has a low computational complexity as compared to its classical counterparts.

Variable step size dichotomous coordinate descent affine projection algorithm

A new affine projection (AP) algorithm based on dichotomous coordinate descent (DCD) iterations has been recently proposed for acoustic echo cancellation (AEC). It uses a constant step size parameter and, therefore, has to compromise between fast convergence and tracking on the one hand, and low misadjustment and robustness to the presence and variations of a near-end signal on the other hand. In this paper we propose a variable step-size (VSS) version of the DCD-AP algorithm (VSS-DCD-AP) that does not require any a priori information about the acoustic environment. It is shown that the new algorithm is robust against near-end signal variations, including double-talk (DT).

Efficient implementation of a variable projection order affine projection algorithm

Many fast affine projection (FAP) algorithms have been proposed in the last two decades. These algorithms offer a good tradeoff between convergence rate and computational complexity. Most of the existing FAP algorithms use a constant projection order. Recently, the evolutionary APA (E-APA) with a variable projection order has been proposed. In this paper, an efficient implementation of the E-APA based on dichotomous coordinate descent (DCD) method is proposed and investigated. It is shown that the proposed algorithm obtains both fast convergence speed and small steady-state error.

Modified filtered-x dichotomous coordinate descent recursive affine projection algorithm

In this paper, we propose a new multichannel filtered-x affine projection algorithm based on dichotomous coordinate descent (DCD) iterations for active noise control (ANC) systems. It includes a fast recursive filtering procedure with the filter update incorporated in the DCD iterations. It is shown that the proposed algorithm has a lower complexity, and superior convergence properties than the multichannel filtered-x LMS algorithm. Also, it compares favorably to a previously published DCD based algorithm for ANC systems.