Adaptive Filters: Algorithms and Performance

Balanced-Realization Based Adaptive IIR Filtering

Authors:

Sundar G Sankaran,
A. A. (Louis) Beex,

Page (NA) Paper number 1583

Abstract:

Balanced realizations are attractive for adaptive filtering, due to their minimum parameter sensitivity and due to their usefulness in model-reduction problems. A balanced-realization based adaptive IIR filtering algorithm is presented. The proposed algorithm uses a stochastic-gradient based search technique to minimize the output error. The algorithm inherently guarantees that the adaptive filter will always remain stable, which obviates the need for the usual stability check after adaptation. Since the algorithm minimizes the output error, the resulting estimates are unbiased. We try to avoid possible convergence to local minima of the output-error surface by using "good" initial estimates, as obtained from equation-error based adaptive filters. Simulation results show that the proposed algorithm converges to the global minimum of the output-error surface.

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Hyperstable Polyphase Adaptive IIR Filters

Authors:

Carlos Mosquera, Dept. Tecnoloxias das Comunicacions, Universidade de Vigo, Vigo, Spain. (Spain)
Fernando Pérez-González, Dept. Tecnoloxias das Comunicacions, Universidade de Vigo, Vigo, Spain. (Spain)
Roberto López-Valcarce, Dept. Electrical and Computer Engineering, University of Iowa, Iowa City, USA. (USA)

Page (NA) Paper number 1491

Abstract:

This work considers the implementation of recursive identification algorithms based on hyperstability concepts with polyphase structures. It is shown that the SPR condition required for convergence of these schemes can always be met by using a sufficiently high polyphase expansion factor M. For a given M, the degree of persistent excitation required for parameter convergence is obtained. When a priori knowledge about the unknown system is available, a compensating filter can be designed to avoid the need for a high M.

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A Novel Adaptive Step Size Control Algorithm for Adaptive Filters

Authors:

Shin'ichi Koike,

Page (NA) Paper number 1054

Abstract:

A novel adaptive step size control algorithm is proposed, in which the step size is approximated to the theoretically optimum value via leaky accumulators, realizing quasi-optimal control. The algorithm is applicable to most of the known tap weight adaptation algorithms. Analysis yields a set of difference equations for theoretically calculating expected filter convergence, and derives residual mean squared error(MSE) after convergence in a formula explicitly solved. Experiment with some examples proves that the proposed algorithm is highly effective in improving the convergence rate. The theoretically calculated convergence is shown to be in good agreement with that obtained through simulations.

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A Novel Multirate Adaptive FIR Filtering Algorithm and Structure

Authors:

Cheng-Shing Wu,
An-Yeu Wu,

Page (NA) Paper number 5054

Abstract:

A new class of FIR filtering algorithms and VLSI architectures based on the multirate approach were recently proposed. They not only reduce the computational complexity in FIR filtering, but also retain attractive implementation-related properties such as regularity and multiply-and-accumulate (MAC) structure. In addition, the multirate feature can be applied to low-power/high-speed VLSI implementation. These properties make the multirate FIR filtering very attractive in many DSP and communication applications. In this paper, we propose a novel adaptive filter inherits the advantages of the multirate structures such as low computational complexity and low-power/high-speed applications. Moreover, the multirate feature helps to improve the convergence property of the adaptive filters.

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Analytical Development of the MMAXNLMS Algorithm

Authors:

Monther I Haddad,
Khaled A Mayyas,
Mohammed A Khasawneh,

Page (NA) Paper number 2452

Abstract:

In this paper a recently presented adaptive algorithm with reduced complexity is analysed for the white Gaussian input case. The new analysis is extented for the proposed case where updating includes more than one component of the weight vector. The new algorithm, which updates the weights correponding to the element sizes of the data vector with the largest magnitude, is compared with the case where the updated weights are chosen randomly according to a uniform density function. Analysis is performed for both cases and the results are verified via computer simulations.

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Householder-Transform Constrained LMS Algorithm with Reduced-Rank Updating

Authors:

Marcello L. R. de Campos, COPPE/Universidade Federal do Rio de Janeiro, Brazil (Brazil)
Stefan Werner, Helsinki University of Technology, Finland (Finland)
José A. Apolinário Jr., Instituto Militar de Engenharia, Brazil and Escuela Politécnica del Ejército, Ecuador (Brazil)

Page (NA) Paper number 2378

Abstract:

This paper proposes a new approach to linearly-constrained adaptive filtering, where successive Householder transformations are incorporated in the algorithm update equation in order to reduce computational complexity and coefficient-error norm. We show the derivation of two new algorithms, namely the unnormalized and the normalized Householder-transform constrained LMS algorithms (HCLMS and NHCLMS, respectively). Although the derivation is carried out based on the constrained LMS (CLMS) algorithm, the technique can be applied to other constrained algorithms as well. Simulation results of a linearly-constrained minimum-variance problem show that in finite-precision implementation the coefficient-error norms obtained with the new algorithms are significantly smaller than those obtained with the CLMS and the normalized CLMS algorithms.

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A New Adaptive Subband Structure with Critical Sampling

Authors:

Mariane R Petraglia,
Rogerio G Alves,

Page (NA) Paper number 2046

Abstract:

In this paper, a new adaptive subband structure with critical sampling of the subband signals, which yields exact modeling of FIR systems, is derived. An adaptation algorithm, which minimizes the sum of the subband squared-errors, is obtained for the updating of the coefficients of the new subband structure, resulting in significant rate improvement for colored input signals when compared to the full-band LMS algorithm. A simplified version of the adaptation algorithm, with reduced computational complexity, is also presented. An efficient implementation of the proposed subband structure is described, with computational savings of the order of the number of subbands when compared to the full-band LMS. Computer simulations illustrate the convergence behavior of the proposed algorithms.

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On The Convergence Properties Of Multidelay Frequency Domain Adaptive Filter

Authors:

Junghsi Lee, Dept. of Electrical Engineering, Yuan-Ze University, TAIWAN (Taiwan)
Sheng-Chieh Chang, Dept. of Electrical Engineering, Yuan-Ze University, TAIWAN (Taiwan)

Page (NA) Paper number 1772

Abstract:

Frequency domain adaptive filters have gained much attention recently. Although some work on performance analysis has been reported, there is still much to be done. This paper presents a convergence analysis of the multidelay frequency domain adaptive filter. We show, for the first time, the relationship between the convergence step-size and the convergence rate. The effect of step-size on adaptation accuracy is presented also. Extensive simulation results are provided to support the analysis. Surprisingly, all block processing algorithms ran well even though the step-sizes utilized are much bigger than the convergence bounds currently available in the literature.

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Analysis of Low Rank Transform Domain Adaptive Filtering Algorithm

Authors:

Balaji B Raghothaman, University of Texas at Dallas, Richardson, Texas, USA. (USA)
Darel Linebarger, University of Texas at Dallas, Richardson, Texas, USA. (USA)
Dinko Begusić, University of Split, Split, Croatia. (Croatia)

Page (NA) Paper number 1746

Abstract:

This paper analyzes an SVD based low rank transform domain adaptive filtering algorithm and proves that it performs better than Normalized LMS. The method extracts an underdetermined solution from an overdetermined least squares problem, using a part of the unitary transformation formed by the right singular vectors of the data matrix. The aim is to get as close to the solution of an overdetermined system as possible, using an underdetermined system. Previous work based on the same framework, but with the DFT as the transformation, has shown considerable improvement in performance over conventional time domain methods like NLMS and Affine Projection. The analysis of the SVD-based variant helps us to understand the convergence behavior of the DFT-based low complexity method. We prove that the SVD-based method gives a lower residual than NLMS. Simulations confirm the theoretical results.

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Second Moment Analysis of the Filtered-X LMS Algorithm

Authors:

Orlando J Tobias,
José C.M. Bermudez,
Neil J Bershad,
Rui Seara,

Page (NA) Paper number 1584

Abstract:

This paper presents a new analytical model for the second moment behavior of the Filtered-X LMS algorithm. The new model is not based on the independence theory, and is derived for gaussian inputs and slow adaptation. Monte Carlo simulations show excellent agreement with the behavior predicted by the theoretical model.

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