Recursive inverse algorithm: Mean-square-error analysis

Salman, Mohammad Shukri; Kükrer, Osman; Hocanin, Aykut

doi:10.1016/j.dsp.2017.04.001

Cited by 24 publications

(19 citation statements)

References 18 publications

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“…), C( ) represents the filter weight vector calculated at time , v( ) = Wx( ) represents the transformed input signal and W represents the wavelet transform matrix of size × . ( ) represents the variable step-size [16] which satisfies the convergence criterion [9], the autocorrelation matrix R( ) represents the estimate of the tap-input vector, and p( ) represents the estimate of the cross-correlation vector between the desired output signal ( ) and the tap-input vector estimated, recursively, as:…”

Section: Dwt Second-order Recursive Inverse Algorithmmentioning

confidence: 99%

“…It has been shown that the RI algorithm performs significantly better than LMS algorithm and its variants. Also, its performance is very comparable to that of the RLS algorithm, in terms of convergence rate and excess mean square error (MSE) [16], in various settings, with less computational complexity. Futher improvement of the performance of the recursive inverse algorithm was achived by considering second-order estimation of the correlations in the update equation of the RI algorithm [17].…”

Section: Introductionmentioning

confidence: 99%

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Discrete-wavelet-transform recursive inverse algorithm using second-order estimation of the autocorrelation matrix

2020

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The recursive least squares (RLS) algorithm was introduced as an alternative to least mean square (LMS) algorithm with enhanced performance. Computational complexity and instability in updating the autocolleltion matrix are some of the drawbacks of the RLS algorithm that were among the reasons for the introduction of the second-order recursive inverse (RI) adaptive algorithm. The 2 nd order RI adaptive algorithm suffered from low convergence rate in certain scenarios that required a relatively small initial step-size. In this paper, we propose a new second-order RI algorithm that projects the input signal to a new domain namely discrete wavelet transform (DWT) as pre step before performing the agorthim. This transformation overcomes the low convergence rate of the second-order RI algorithm by reducing the selfcorrelation of the input signal in the mentioned scenatios. Expeirments are conducted using the noise cancellation setting. The performance of the proposed algorithm is compared to those of the RI, original second-order RI and RLS algorithms in different Gaussian and impulsive noise environments. Simulations demonstrate the superiority of the proposed algorithm in terms of convergence rate compared to those algorithms.

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Section: Dwt Second-order Recursive Inverse Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discrete-wavelet-transform recursive inverse algorithm using second-order estimation of the autocorrelation matrix

2020

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“…A possible solution to overcome this problem is to use a variable forgetting factor (VFF-RLS) algorithm [18,19]. Recursive inverse (RI) algorithm [20,21] had been proposed to overcome the drawbacks and limitations of the above mentioned adaptive filters. It had been shown that the RI algorithm performs considerably better than the LMS algorithm and its variants.…”

Section: Introductionmentioning

confidence: 99%

Discrete wavelet transform-based RI adaptive algorithm for system identification

Salman

Eleyan

Al-Sheikh

2020

IJECE

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In this paper, we propose a new adaptive filtering algorithm for system identification. The algorithm is based on the recursive inverse (RI) adaptive algorithm which suffers from low convergence rates in some applications; i.e., the eigenvalue spread of the autocorrelation matrix is relatively high. The proposed algorithm applies discrete-wavelet transform (DWT) to the input signal which, in turn, helps to overcome the low convergence rate of the RI algorithm with relatively small step-size(s). Different scenarios has been investigated in different noise environments in system identification setting. Experiments demonstrate the advantages of the proposed DWT recursive inverse (DWT-RI) filter in terms of convergence rate and mean-square-error (MSE) compared to the RI, discrete cosine transform LMS (DCTLMS), discrete-wavelet transform LMS (DWT-LMS) and recursive-least-squares (RLS) algorithms under same conditions.

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“…The recursive inverse (RI) algorithm [22,23] and the iterative Wiener filter (IWF) algorithm [24] have recently been proposed. RI and IWF have the same structure besides a step size calculation.…”

Section: Introductionmentioning

confidence: 99%

“…They perform similarly to the conventional RLS algorithm in terms of convergence and mean squared error, without using the inverse of the auto-covariance matrix. Therefore, RI [22,23] and IWF [24] can be considered algorithms without the numerical instability of RLS.…”

Section: Introductionmentioning

confidence: 99%

Maximum Correntropy Criterion Based l1-Iterative Wiener Filter for Sparse Channel Estimation Robust to Impulsive Noise

Lim

2020

Applied Sciences

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In this paper, we propose a new sparse channel estimator robust to impulsive noise environments. For this kind of estimator, the convex regularized recursive maximum correntropy (CR-RMC) algorithm has been proposed. However, this method requires information about the true sparse channel to find the regularization coefficient for the convex regularization penalty term. In addition, the CR-RMC has a numerical instability in the finite-precision cases that is linked to the inversion of the auto-covariance matrix. We propose a new method for sparse channel estimation robust to impulsive noise environments using an iterative Wiener filter. The proposed algorithm does not need information about the true sparse channel to obtain the regularization coefficient for the convex regularization penalty term. It is also numerically more robust, because it does not require the inverse of the auto-covariance matrix.

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Recursive inverse algorithm: Mean-square-error analysis

Cited by 24 publications

References 18 publications

Discrete-wavelet-transform recursive inverse algorithm using second-order estimation of the autocorrelation matrix

Discrete-wavelet-transform recursive inverse algorithm using second-order estimation of the autocorrelation matrix

Discrete wavelet transform-based RI adaptive algorithm for system identification

Maximum Correntropy Criterion Based l1-Iterative Wiener Filter for Sparse Channel Estimation Robust to Impulsive Noise

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