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Abstract The affine projection (AP) algorithm is one of the most celebrated adaptive filtering algorithms, and it achieves a good tradeoff between the convergence rate and computational complexity. However, the complexity of the AP algorithm increases with the projection order. A wealth of fast AP algorithms have been proposed to reduce the complexity in the last two decades. However, those low-complexity methods have not been well analyzed and compared. To fill this gap, this paper reviews the fast AP algorithms, including both fast filtering approaches and efficient solutions of the linear system of equations. The advantages and disadvantages of each fast implementation version are clarified based on an extensive performance evaluation, which could be useful to engineers when selecting a suitable algorithm for their specific applications and could also be a starting point for experts in this field to develop better solutions. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers connections between the cost functions of some parameter identification methods for system modelling, including the well known projection algorithm, stochastic gradient (SG) algorithm and recursive least squares (RLS) algorithm, and presents a modified SG algorithm by introducing the convergence index and a multi-innovation projection algorithm, a multi-innovation SG algorithm and a multi-innovation RLS algorithm by introducing the innovation length, aiming at improving the convergence rate of the SG and RLS algorithms. Furthermore, this paper derives an interval-varying multi-innovation SG and an interval-varying multi-innovation RLS algorithm in order to deal with missing data cases. [Copyright &y& Elsevier]

Abstract: The least mean p-norm (LMP) algorithm is an effective algorithm for processing the signal of α-stable distribution. This paper proposes data block adaptive filtering algorithms for the α-stable random processes based on the fractional lower order statistics (FLOS). The data block algorithms change the direction of coefficient increment vector by introducing a matrix which includes the information of more past input signal vectors than which are used in the LMP algorithm during the iteration process, taking full advantage of the past values of the gradient vector during the adaptation. Simulations studies indicate that the proposed algorithms increase convergence rate in non-Gaussian stable distribution noise environments compared to the existing algorithms based on FLOS summarized in this paper. [Copyright &y& Elsevier]

This paper proposes a novel diffusion subband adaptive filtering algorithm for distributed networks. To achieve a fast convergence rate and small steady-state errors, a variable step size and a new combination method is developed. For the adaptation step, the upper bound of the mean-square deviation (MSD) of the algorithm is derived and the step size is adaptive by minimizing it in order to attain the fastest convergence rate on every iteration. Furthermore, for a combination step realized by a convex combination of the neighbor-node estimates, the proposed algorithm uses the MSD, which contains information on the reliability of the estimates, to determine combination coefficients. Simulation results show that the proposed algorithm outperforms the existing algorithms in terms of the convergence rate and the steady-state errors. [ABSTRACT FROM AUTHOR]

The Normalized Least Mean Square (NLMS) algorithm with a filtered-x structure (FxNLMS) is a widely used adaptive algorithm for Active Noise Control (ANC) due to its simplicity and ease of implementation. One of the major drawbacks is its slow convergence. A modified filtered-x structure (MFxNLMS) can be used to moderately improve the speed of convergence, but it does not offer a huge improvement. A greater increase in the speed of convergence can be obtained by using the MFxNLMS algorithm with orthogonal correction factors (M-OCF), but the usage of orthogonal correction factors also increases the computational complexity and limits the usage of the M-OCF in massive real-time applications. However, Graphics Processing Units (GPUs) are well known for their potential for highly parallel data processing. Therefore, GPUs seem to be a suitable platform to ameliorate this computational drawback. In this paper, we propose to derive the M-OCF algorithm to a partitioned block-based version in the frequency domain (FPM-OCF) for multichannel ANC systems in order to better exploit the parallel capabilities of the GPUs. The results show improvements in the convergence rate of the FPM-OCF algorithm in comparison to other NLMS-type algorithms and the usefulness of GPU devices for developing versatile, scalable, and low-cost multichannel ANC systems. [ABSTRACT FROM AUTHOR]

Several techniques have been proposed in the literature to accelerate the convergence of adaptive algorithms for the identification of sparse impulse responses (i.e., with energy concentrated in a few coefficients). Among these techniques, the improved µ-law proportionate normalized least mean squares (IMPNLMS) algorithm is one of the most effective. This paper presents an accurate transient analysis of this algorithm and derives an estimate of its steady-state MSE, without requiring the assumption of white Gaussian input signals. [ABSTRACT FROM AUTHOR]

Abstract: A kind of weighted orthogonal constrained independent component analysis (ICA) algorithms with weighted orthogonalization for achieving this constraint is proposed recently. It has been proved in the literature that weighted orthogonal constrained ICA algorithms keep the equivariance property and have much better convergence speed, separation ability and steady state misadjustment, but the convergence is not yet analyzed in the published literature. The goal of this paper is to fill this gap. Firstly, a characterization of the stationary points corresponding to these algorithms using symmetric Minimum Distance Weighted Unitary Mapping (MDWUM) for achieving the weighted orthogonalization is obtained. Secondly, the monotonic convergence of the weighted orthogonal constrained fixed point ICA algorithms using symmetric MDWUM for convex contrast function is proved, which is further extended to nonconvex contrast functions case by adding a weighted orthogonal constraint term onto the contrast function. Together with the boundedness of contrast function, the convergence of fixed point ICA algorithms with weighted orthogonal constraint using symmetric MDWUM is implied. Simulation experiments results show that the adaptive ICA algorithms using symmetric MDWUM are better in terms of accuracy than the ones with pre-whitening, and the fixed-point ICA algorithms using symmetric MDWUM converge monotonically. [Copyright &y& Elsevier]

Abstract: This paper presents a new technique for designing IIR filters that have minimum deviation from equiripple response. The algorithm is also able to find transfer functions with unequal numerator and denominator orders, which are suitable for both digital and analog IIR sampled-data realizations. Elliptic filters are produced as a particular case, when equal numerator and denominator orders are specified. Pole-zero mapping is used for scalar update of optimization parameters, thereby reducing the algorithm complexity. Zeros are structurally allocated on the unit circumference for efficient stopband shaping. Moreover, filter stability is easily enforced by restricting the radii of the poles to be lower than 1. A Taylor series expansion is employed to determine the step size of the parameter updates. The proposed approach is based on evaluations of partial cost functions to avoid local minima, and hence increase the robustness and the convergence rate of the optimization process. Design examples are shown to illustrate the efficacy of the proposed design technique, compared to alternative design techniques. [Copyright &y& Elsevier]

Abstract: This paper addresses the problem of joint block diagonalization (JBD) of a set of given matrices. As is known that the nonunitary JBD algorithm has some advantages over the existing orthogonal one for convolutive blind source separation (CBSS). However, the nonunitary JBD algorithm is prone to converge to some unexpected degenerate solutions (singular or ill-conditioned solutions). Especially for the matrices of large dimension or the case that the number of the diagonal blocks is relatively large, the performances of the nonunitary JBD algorithm degrade more severely. To eliminate the degenerate solutions, we optimize a penalty term based weighted least-squares criterion and thus develop a fast efficient algorithm. The performance of the proposed algorithm is evaluated by computer simulations and compared with the existing state-of-the-art nonunitary JBD algorithm. The simulation results demonstrate the robustness and performance improvement of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: The dithered signed-error constant modulus algorithm (DSE-CMA) is an approach less computationally than CMA but exhibits ill-convergence. On the contrary, the concurrent CMA with soft decision-directed scheme () improves the convergence rate of CMA by adding SDD but brings lots of computational complexity. As a tradeoff, in this paper we combine the virtues of DSE-CMA and SDD, then propose a new algorithm, which compensates the phase shift and provides convergence faster than DSE-CMA with lower complexity than . More importantly, an approximation of its steady-state mean square error performance is derived. Simulation results show the superiority of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: Normalized forms of adaptive algorithms are usually sought in order to obtain convergence properties independent of the input signal power. Such is the case of the well-known Normalized LMS (NLMS) algorithm. The Least-Mean Fourth (LMF) adaptive algorithm has been shown to outperform LMS in different situations. However, the LMF stability is dependent on both the signal power and on the adaptive weights initialization. This paper studies the behavior of two normalized forms of the LMF algorithm for Gaussian inputs. Contrary to what could be expected, the mean-square stability of both normalized algorithms is shown to be dependent upon the input signal power. Thus, the usefulness of the NLMF algorithm is open to question. [Copyright &y& Elsevier]

Abstract: In this paper, we propose new adaptive algorithms for the extraction and tracking of the least (minor) or eventually, principal eigenvectors of a positive Hermitian covariance matrix. The main advantage of our proposed algorithms is their low computational complexity and numerical stability even in the minor component analysis case. The proposed algorithms are considered fast in the sense that their computational cost is flops per iteration where n is the size of the observation vector and is the number of eigenvectors to estimate. We consider OJA-type minor component algorithms based on the constraint and non-constraint stochastic gradient technique. Using appropriate fast orthogonalization procedures, we introduce new fast algorithms that extract the minor (or principal) eigenvectors and guarantee good numerical stability as well as the orthogonality of their weight matrix at each iteration. In order to have a faster convergence rate, we propose a normalized version of these algorithms by seeking the optimal step-size. Our algorithms behave similarly or even better than other existing algorithms of higher complexity as illustrated by our simulation results. [Copyright &y& Elsevier]

Abstract: In this paper, a new FIR adaptive filtering algorithm is proposed. The approach uses a variable step-size and the instantaneous value of the autocorrelation matrix in the coefficient update equation that leads to an improved performance. Convergence analysis of the algorithm has been presented. Simulation results show that the algorithm performs better than the Transform Domain LMS with Variable Step-Size (TDVSS) in stationary Additive White Gaussian Noise (AWGN) and Additive Correlated Gaussian Noise (ACGN) environments in a system identification setting. It is shown that the algorithm has a performance better than RLS and very similar to RRLS algorithm with a considerable reduction in computational complexity. Additionally, the performance of the proposed algorithm is shown to be superior to that of the Stabilized Fast Transversal Recursive Least Squares (SFTRLS) algorithm under the same conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a novel identification algorithm for a class of dual-rate sampled-data systems whose input–output data are measured by two different sampling rates. A polynomial transformation technique is employed to derive a mathematical model for such dual-rate systems. The proposed modified stochastic gradient algorithm has faster convergence rate than stochastic gradient algorithms for parameter identification using the dual-rate input–output data. Convergence properties of the algorithm are analyzed. Finally, illustrative and comparison examples are provided to verify the effectiveness and performance improvement of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, a new method, named interacting MCMC particle filter, is proposed to track maneuvering target. The particles are sampled from the target posterior distribution via direct interacting MCMC sampling method, which avoids sample impoverishment and increases the robustness of the algorithm. Moreover, the interacting MCMC particle filter algorithm accelerates the MCMC convergence rate via propagating each particle based on both its history information and the information from other particles. [Copyright &y& Elsevier]

Abstract: In this paper, we elaborate an extension of classical power iteration method to nonlinear power iteration for blind separation of multiple independent sources from observed array output signals. The present algorithm, referred to as NPI, considers the estimating of the separating matrix as a nonlinear power iteration problem. By naturally choosing the positive definite normalizer for nonlinear power term, the resulting algorithm not only yields robust convergence behavior but also guarantees the orthonormality of the separating matrix at each iteration. To circumvent the difficulty of solving the inverse square root for the normalizer, an efficient adaptive singular value decomposition (SVD) technique is also adopted to obtain a fast implementation of NPI. The estimation accuracy and convergence speed of the present algorithm are illustrated through simulation results and compared with the existing adaptive algorithms. [Copyright &y& Elsevier]

Abstract: Interference can be a significant problem in loosely organized networks such as ad-hoc radio networks. One technique for dealing with interference is to attempt joint detection of all signals arriving at a node. Iterative algorithms based on the turbo-principle yield significant performance improvements when applied to this problem. This paper concentrates on performance analysis of iterative interference cancellation for forward-error correction coded signals in the presence of Rayleigh fading. The variance transfer analysis of Alexander et al. [European Trans. Telecommun. 9 (5) (1998) 419–426] is generalized for unequal user powers and codes. A surprising result is that the received power variation due to fading can assist convergence. [Copyright &y& Elsevier]

The paper investigates blind finite-impulse-response (FIR) equalization schemes for quadrature amplitude modulation signalling. We compare a bootstrap maximum a posteriori probability (MAP) equalizer with a recently introduced concurrent constant modulus algorithm (CMA) and decision directed (DD) equalizer (CMA+DD). Both equalizers are known to outperform the CMA considerably in the situations where carrier recovery is performed and the signal constellation is known. The concurrent CMA+DD equalizer has a complexity that is slightly more than twice of the CMA, and the bootstrap MAP equalizer has computational requirements that are only slightly more complex than the CMA. Simulation results indicate that the bootstrap MAP blind FIR equalizer has a faster convergence rate and better steady-state performance than the concurrent CMA+DD blind FIR equalizer, but tuning of the former is more complicated than the latter. [Copyright &y& Elsevier]