Chair: V. John Mathews, University of Utah, (USA)
P. L. Combettes, City University of New York (USA)
P. Bondon, CNRS/ESE (FRANCE)
We address the problem of linear mean-square estimation with arbitrary convex constraints for dependent processes. Two algorithms are proposed and their convergence is established. The first algorithm, which is deterministic, covers the case of known correlation structures; the second, which is stochastic and adaptive, covers the case of unknown correlation structures. Since existing algorithms can handle at most one simple constraint this contribution is relevant to signal processing problems in which arbitrary convex inequality constraints are present.
Jose Carlos M. Bermudez, Federal University of Santa Catarina (BRAZIL)
Neil J. Bershad, University of California - Irvine (USA)
This paper presents a study of the quantization effects in the finite precision LMS algorithm with power-of-two step sizes. Nonlinear recursions are derived for the mean and second moment matrix of the weight vector about the Wiener weight for white gaussian data models and small algorithm step size. The solutions of these recursions are shown to agree very closely with the Monte Carlo simulations during all phases of the adaptation process. A design curve is presented to demonstrate the use of the theory to select the number of quantizer bits and the adaptation step size to yield desired transient and steady-state behaviors.
Byung-Eul Jun, KAIST (KOREA)
Dong-Jo Park, KAIST (KOREA)
Yong-Woon Kim, KAIST (KOREA)
This paper presents a statistical behavior analysis of a sign-sign least mean square algorithm, which is obtained by clipping both the reference input signal and the estimation error, for adaptive filters with correlated Gaussian data. The study focuses on derivation of expressions for the first and second moment behaviors of the filter coefficient vector and analysis for the mean square error of the filter. The previous analysis of this type for the sign-sign algorithm is based on the assumption that the input sequence to the adaptive filter is independent, identically distributed Gaussian, but this restriction is removed in our analysis. Theoretical expressions derived are verified numerically through computer simulations for an example of system identification.
Andrew W. Hull, University of Illinois at Urbana - Champaign (USA)
W. Kenneth Jenkins, University of Illinois at Urbana - Champaign (USA)
The method of Preconditioned Conjugate Gradients (PCG) is introduced as an accelerator for simple IIR algorithms to significantly increase the convergence rate without dramatically adding to their complexity. This paper presents the IIR extension of the previously reported FIR PCG algorithm. In this novel formulation, the identification problem of the IIR coefficients separates into two sub-problems, each of which may be solved by application of fast adaptive FIR techniques. Present IIR algorithms require greater computational cost, or converge more slowly. It is the adoption of the PCG concept that permits a development of an O{log N} adaptive algorithm. It is shown that the use of the preconditioned conjugate gradients in the Gauss-Newton update leads naturally to the application of the planar least squares inverse to bound the poles of the adaptive system by projecting an unstable denominator onto a stable polynomial.
Markus Rupp, University of California (USA)
Ali H. Sayed, University of California (USA)
Gradient-descent adaptive algorithms are among the most widely used in current practice, with many different variants that generally fit into two major groups: one group includes algorithms that are especially suited for FIR (or finite-impulse-response) modeling, while the other group includes algorithms that are tailored for IIR (or infinite-impulse-response) modeling. In the first group, the regression (or data) vectors do not depend on the unknown parameters, which leads to convenient linear models that often facilitate the analysis of the algorithms. In the second category, on the other hand, the regression vectors are dependent on the unknown parameters, thus giving rise to nonlinear functionals and to a richer structure that requires a more thorough analysis. This paper focuses on a widely used adaptive IIR algorithm, the so-called Feintuch's algorithm, and provides a study of its robustness, stability, and convergence properties in a deterministic framework.
Akihiro Hirano, NEC Corporation (JAPAN)
Akihiko Sugiyama, NEC Corporation (JAPAN)
This paper proposes a new noise-robust adaptive FIR filtering algorithm with an adaptive step-size which takes non-stationarity of speech signals into account. The proposed algorithm controls the step-size based on the reference input signal power and the estimated noise power. Implementation of an acoustic echo canceller based on this algorithm using digital signal processors is also described. Computer simulation results using a real speech signal show that the proposed algorithm improves the ERLE (echo return loss enhancement) by more than 10 dB compared with conventional noise-robust adaptive-step algorithms. The implemented echo canceller achievess 25 dB of the ERLE, which agrees with the computer simulation results.
S.C. Douglas, University of Utah (USA)
In this paper, we derive new adaptive step size algorithms for two general classes of modified stochastic gradient adaptive filters that include the sign-error, sign-data, sign-sign, and normalized gradient adaptive filters as specific cases. These computationally-simple parameter adjustment algorithms are based on stochastic gradient approximations of steepest descent procedures for the unknown parameters. Analyses of the algorithms show that the stationary points of the steepest descent procedures yield the optimum step size values at each time instant as obtained from statistical analyses of the adaptive filter updates. Simulations verify the theoretical results and indicate that near- optimal tracking performance can be obtained from each of the adaptive step size algorithms without any knowledge of the rate of change of the unknown system.
Orhan Arikan, Bilkent University
Murat Belge, Bilkent University
A. Enis Cetin, KoC University
Engin Erzin, Bilkent University (TURKEY)
A large class of physical phenomenon observed in practice exhibit non-Gaussian behavior. In this paper, alpha-stable distributions, which have heavier tails than Gaussian distribution, are considered to model non-Gaussian signals. Adaptive signal processing in the presence of such kind of noise is a requirement of many practical problems. Since, direct application of commonly used adaptation techniques fail in these applications, new approaches for adaptive filtering for alpha-stable random processes are introduced.
H.J. Butterweck, Eindhoven University of Technology (THE NETHERLANDS)
Current analysis of the LMS algorithm makes use of an independence assumption stating statistical independence of successive input vectors. This assumption conflicts with the inherent deterministic coherence of the vector input signal and, as such, is the source of conceptual and didactic difficulties. Nevertheless, due to its analytic convenience and its moderate agreement with experimental results, it is in widespread use. In this paper, a theory of the steady-state behaviour of the LMS algorithm is presented that avoids the independence assumption with its inherent problems and yields a number of new results. Simulations support the analytic conclusions.
K. Mayyas, University of Ottawa (CANADA)
T. Aboulnasr, University of Ottawa (CANADA)
This paper presents a robust variable step size LMS-type algorithm with the attractive property of achieving a small final misadjustment while providing fast convergence at early stages of adaptation. The performance of the algorithmis not affected by presence of noise. Approximate analysis of convergence and steady state performance for a zero-mean stationary Gaussian inputs and a nonstationary optimal weight vector is provided. Simulations results clearly indicate its superior performance for stationary cases. For nonstationary environment, our algorithm provides performance equivalent to that of the regular LMS algorithm.