Mean Square Deviation Analysis Research Articles

Performance Analysis of the Standard Constrained Maximum Versoria Criterion Based Adaptive Algorithm

Recently, robust adaptive filtering approaches relied on the Maximum Versoria Criterion (MVC) have gained the attention of researchers and have been widely studied. In this brief, with the energy conservation approach, transient and steady-state mean-square deviation (MSD) analysis of the standard constrained MVC (CMVC) are derived under both Gaussian and non-Gaussian noise distributions. For a Gaussian noise condition, an accurate solution is obtained, while for non-Gaussian noise conditions, we used approximate Taylor's expansion to derive the transient and steady-state MSD. Finally, we evaluated the theoretical analysis with some numerical simulations of system identification in different Gaussian and non-Gaussian noise scenarios to validate the finding.

An improved mean-square performance analysis of the diffusion least stochastic entropy algorithm

The diffusion least stochastic entropy (DLSE) algorithm yields a better performance than the diffusion complex-valued least mean-square (DCLMS) algorithm for second-order noncircular noise. The existing theoretical steady-state mean-square deviation (MSD) shows a low accuracy due to the use of improper estimations and approximations. Besides, its transient MSD has not been thoroughly studied. This paper provides an improved performance analysis. We first improve the method of estimating the circularity coefficient (CC) of the error signal, which is required for the update equation of the DLSE. This improvement leads to a better match between the theoretical and simulated MSD and makes the transient MSD analysis mathematically tractable. The MSD analysis is performed by using the Gaussian moment factorizing theorem with some statistical assumptions. Besides, another key performance measure, i.e., the excess mean-square error (EMSE) of the DLSE is also analyzed. Simulation results validate the theoretical findings of the DLSE algorithm for second-order noncircular input signals and noise.

Combined-Sample Multiband-Structured Subband Filtering Algorithms

This paper introduces two combined-sample multiband-structured subband adaptive filters (MSAFs). In the design, an adaptive convex combination scheme of two self-reliant multi-sampled MSAF (MS-MSAF) with different sampled periods is firstly developed, which leads to the so-called CTMS-MSAF algorithm. Secondly, based on an adaptive filter, the combined-sample MS-MSAF (CMS-MSAF) algorithm is proposed via designing a time-varying sampled period, which possesses lower computational complexity than the former. Then, the convergence behaviors of the CTMS-MSAF and CMS-MSAF algorithms are investigated using standard mean-square deviation analysis. Finally, the simulation study in the system identification and acoustic echo cancellation applications shows that at the same steady-state error, the CMS-MSAF method provides a faster convergence rate than the improved convex combination of two MSAFs, combined-step-size MSAF and CTMS-MSAF algorithms.

Delayed Combination of Adaptive Filters in Colored Noise

In this work, we study the combination of adaptive filters in colored noise environments. First, a combination framework using delayed weights is introduced to tackle the colored noise. Based on this, delayed convex and affine combinations of two LMS filters are developed, resulting in the so-called Dcvx-LMS and Daff-LMS algorithms. Then, the convergence behaviors of the two algorithms are investigated using standard mean-square deviation analysis. In addition, to speed up the convergence and reduce the computational complexity, we propose delayed combination with periodic feedback, delayed combined-step-size and block implementation methods. Finally, simulation results demonstrate the superiority of our algorithms over previously reported techniques in the presence of colored noise.

Steady-state mean-square deviation analysis of improved ℓ0-norm-constraint LMS algorithm for sparse system identification

The ℓ0-norm-constraint LMS (ℓ0-LMS) algorithm is one of the widely used sparse LMS algorithms for the identification of sparse system, and its performance is quite attractive compared to other precursors. However, ℓ0-LMS is still confronted with some limitations on the optimal parameter selection and the estimated coefficient accuracy of sparse system identification. In this paper, we proposed an improved ℓ0-LMS (ℓ0-ILMS) algorithm to address these limitations. The convergence condition and the parameter selection rules for optimal steady-state mean-square deviation (MSD) of ℓ0-ILMS are discussed. Compared with ℓ0-LMS, the steady-state MSD of ℓ0-ILMS is lower and less sensitive to the tuning parameters and measurement noise power. Numerical simulations comparing the performance of standard LMS, ℓ0-LMS and ℓ0-ILMS demonstrate the effectiveness of ℓ0-ILMS.

Steady-State Mean-Square Deviation Analysis of the Zero-Attracting CLMS Algorithm With Circular Gaussian Input

When the complex least mean-square (CLMS) algorithm is used to estimate a complex sparse system, its convergence rate is relatively slow. To make full use of the sparsity of the unknown system to improve convergence rate, a zero-attracting CLMS (ZA-CLMS) algorithm has recently been proposed. In order to predict the statistical behavior of the complex adaptive filter after converging, this paper analyzes the steady-state mean-square deviation (MSD) performance of ZA-CLMS with circular Gaussian input. For mathematical tractability, in the analysis, the unknown system weights are divided into two sets according to their values and some statistical assumptions are used. The simulation results are provided to show the superior performance of ZA-CLMS for complex sparse system identification and to verify the validity of the theoretical expressions for predicting the steady-state MSD performance.

An Improved Variable Regularization Parameter for Sign Subband Adaptive Filter

This paper proposes an improved variable regularization parameter (VRP) for sign subband adaptive filter, which is derived on the basis of the mean-square deviation (MSD) analysis. Since it is difficult to get access to the exact values of some quantities in the MSD, the VRP is calculated by minimizing the upper bound of a certain term which is employed to update the MSD. Moreover, a re-initialization mechanism that can enhance the tracking capability is developed. We also discuss the computational complexity of our finding. The proposed scheme enjoys more merits than several prior algorithms, which is illustrated by sufficient simulations designed for both the system identification and acoustic echo cancelation applications in the presence of impulsive noise.

A Sequential Selection Normalized Subband Adaptive Filter with Variable Step-Size Algorithms

This letter proposes a sequential selection normalized subband adaptive filter (SS-NSAF) in order to reduce the computational complexity. In addition, a variable step-size algorithm is also proposed using the mean-square deviation analysis of the SS-NSAF. To enhance the performance in terms of the convergence speed, we propose an improved variable step-size SS-NSAF using a two-stage concept. The simulation results show the low computational complexity and low misalignment errors using the proposed algorithm.

A family of robust adaptive filtering algorithms based on sigmoid cost

In this paper, a new framework of cost function for designing robust adaptive filtering algorithms is developed. This new cost framework, called sigmoid cost function, results from imbedding the conventional cost function into the sigmoid framework. Utilizing this proposed sigmoid cost framework, several important members (e.g., the sigmoid least mean square, sigmoid least absolute difference, sigmoid least mean fourth, sigmoid least mean logarithmic square, sigmoid least logarithmic absolute difference algorithms) of this family of robust adaptive filtering algorithms are proposed. In the proposed sigmoid cost framework with a steepness parameter α, a greater (smaller) value of α results in a slower (faster) convergence. Thus, an adaptive α is proposed which is based on an exponential function with respect to the L1-norm of the system error. In addition, the mean-square deviation analysis of the proposed algorithms is also carried out and their accuracies are verified via system identification experiment. Simulations in system identification and acoustic echo-cancellation scenarios have demonstrated that the proposed algorithms outperform the corresponding order's generalized maximum correntropy criterion, normalized least mean square using step-size scaler, sign algorithm and least logarithmic absolute difference algorithms.

Steady‐state mean‐square deviation analysis of the sign subband adaptive filter

The steady-state mean-square deviation (MSD) analysis of the sign subband adaptive filter is proposed. The proposed analysis is derived by the update recursion of the MSD using Price's theorem and chi-distribution in stationary environments. Experimental results show that the proposed analysis is very close to simulated results not only for white input but also for coloured input signals.

Mean-square deviation analysis of the zero-attracting variable step-size LMS algorithm

The well-known variable step-size least-mean-square (VSSLMS) algorithm provides faster convergence rate while maintaining lower mean-square error than the conventional LMS algorithm. The performance of the VSSLMS algorithm can be improved further in a channel estimation problem if the impulse response of the channel is sparse. Recently, a zero-attracting (ZA)-VSSLMS algorithm was proposed to exploit the sparsity of a channel. This was done by imposing an \(\ell _1\)-norm penalty to the original cost function of the VSSLMS algorithm which utilizes the sparsity in the filter taps during the adaptation process. In this paper, we present the mean-square deviation (MSD) analysis of the ZA-VSSLMS algorithm. A steady-state MSD expression for the ZA-VSSLMS algorithm is derived. An upper bound of the zero-attractor controller (\(\rho \)) that provides the minimum MSD is also provided. Moreover, the effect of the noise distribution on the MSD performance is shown theoretically. It is shown that the theoretical and simulation results of the algorithm are in good agreement with a wide range of parameters, different channel, input signal, and noise types.

Mean-Square Deviation Analysis of Multiband-Structured Subband Adaptive Filter Algorithm

A multiband-structured subband adaptive filter (MSAF) algorithm was introduced to achieve a fast convergence rate for the correlated input signal. The convergence analysis of the adaptive filter algorithm is an important concept because it provides a guideline to design the adaptive filter. However, the convergence analysis of the MSAF algorithm has not been researched as extensively as that of the normalized least-mean-square algorithm. Therefore, it needs to be researched. In this paper, we present a new approach to the mean-square deviation (MSD) analysis of the MSAF algorithm by using the persistently exciting input and the practical assumption that the stopband attenuation of the prototype filter is high. Unlike the previous analysis, the proposed analysis is possible to be applied to the long-length adaptive filter such as the acoustic echo cancellation. The proposed analysis is also applied to a non-stationary model with a random walk of the optimal weight vector. The simulation results match with the theoretical results in both the transient-state and steady-state MSD.

Variable step‐size non‐negative normalised least‐mean‐square‐type algorithm

This paper proposes a fast and precise adaptive filtering algorithm for online estimation under a non-negativity constraint. A novel variable step-size (VSS) non-negative normalised least-mean-square (NLMS)-type algorithm based on the mean-square deviation (MSD) analysis with a non-negativity constraint is derived. The NLMS-type algorithm under the non-negativity constraint is derived by using the gradient descent of the given cost function and the fixed-point iteration method. Furthermore, the VSS derived by minimising the MSD yields improvement of the filter performance in the aspects of the convergence rate and the steady-state estimation error. Simulation results show that the proposed algorithm outperforms existing algorithms.

Efficient variable step‐size diffusion normalised least‐mean‐square algorithm

An efficient variable step-size diffusion normalised least-mean-square algorithm is proposed via a mean-square deviation (MSD) analysis for the distributed estimation. The proposed algorithm has two distinguishing features for computational efficiency. In the adaptation step, an intermittent adaptation rule that dynamically adjusts an update interval is proposed to reduce the redundant updates. In the diffusion step, instead of the existing combination rules, a selection rule is proposed to select the intermediate estimate of the most reliable node among its neighbour nodes for the estimate at each node. Moreover, to achieve both fast convergence rate and low steady-state error, a variable step size is obtained by minimising the MSD.

Steady-state mean-square deviation analysis of improved normalized subband adaptive filter

A new minimization criterion for the normalized subband adaptive filter (NSAF), which is called improved NSAF (INSAF), was introduced recently to improve the performance of the steady-state mean-square deviation (MSD). However, the steady-state MSD analysis of the INSAF was not studied. Therefore, this paper proposes a general solution of steady-sate MSD analysis of the INSAF algorithm, which is based on the substitution of the past weight error vector in the weight error vector. The simulation shows that our theoretical results correspond closely with the computer simulation results in various environments.

An Affine Projection Algorithm With Update-Interval Selection

This paper presents a mean-square deviation (MSD) analysis of the periodic affine projection algorithm (P-APA) and two update-interval selection methods to achieve improved performance in terms of the convergence and the steady-state error. The MSD analysis of the P-APA considers the correlation between the weight error vector and the measurement noise vector. Using this analysis, it is verified that the update interval governs the trade-off between the convergence rate and the steady-state errors in the P-APA. To overcome this drawback, the proposed APAs increase the update interval when the adaptive filter reaches the steady state. Consequently, these algorithms can reduce the overall computational complexity. The simulation results show that the proposed APAs perform better than the previous algorithms.

Optimal Step-Size Affine Projection Algorithm

This letter describes how to set up the step size of the affine projection algorithm (APA) based on mean-square deviation analysis. The analysis considers the cross-correlation between the current weight error vector and the prior measurement noises associated with the reused inputs vectors for better prediction of the learning behavior of the APA. With the predetermined step size based on the analysis, the proposed approach eliminates the parameter-tuning process and the derived algorithm achieves both the fast convergence rate and the low steady-state error. Simulation results show that the proposed algorithm performs better than previous algorithms.

Normalised subband adaptive filter with variable step size

Proposed is a normalised subband adaptive filter algorithm with a variable step size based on the mean-square deviation (MSD) analysis. Since the spectrum of each input signal in subbands is close to that of white noise, the MSD can be approximated. The step size in this study is chosen such that the MSD undergoes the largest decrease from one iteration to the next, which leads to a fast convergence rate and a small misalignment. Simulation results confirm that the proposed algorithm outperforms existing algorithms in the literature.

Mean-Square Deviation Analysis of Affine Projection Algorithm

This paper presents an improved mean-square deviation (MSD) analysis of the standard affine projection algorithm (APA) based on two distinctive features. First, the propagation model of the error covariance includes the cross-correlation between the current weight error vector and the prior measurement noises associated with the reused inputs; such a cross-correlation has merely been considered previously. Second, the analysis based on <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> most recent accumulated iterations, rather than a typical analysis based on a current single iteration, is suggested to reveal a previously unseen phenomenon, where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> denotes the tap-length of the filter. Simulation results are in better agreement with the proposed theoretical results, than the previous theoretical ones, over a wide range of parameters such as tap-length, projection order, and step-size.

Dynamic Switching Mechanisms in LOV1 and LOV2 Domains of Plant Phototropins

LOV domains are the light-sensitive portion of plant phototropins. They absorb light through a flavin cofactor, photochemically form a covalent bond between the chromophore and a cysteine residue in the protein, and proceed to mediate activation of an attached kinase domain. Although the photoreaction itself is now well-characterized experimentally and computationally, it is still unclear how the formation of the adduct leads to kinase activation. We have performed molecular dynamics simulations on the LOV1 domain of Chlamydomonas reinhardtii and the LOV2 domain of Avena sativa, both before and after the photoreaction, to answer this question. The extensive simulations, over 240 ns in duration, reveal significant differences in how the LOV1 and LOV2 domains respond to photoactivation. The simulations indicate that LOV1 activation is likely caused by a change in hydrogen bonding between protein and ligand that destabilizes a highly conserved salt bridge, whereas LOV2 activation seems to result from a change in the flexibility of a set of protein loops. Results of electrostatics calculations, principal component analysis, sequence alignments, and root mean-square deviation analysis corroborate the above findings.