William A. Sethares

Nonlinear parameter estimation via the genetic algorithm

A modified genetic algorithm is used to solve the parameter identification problem for linear and nonlinear IIR digital filters. Under suitable hypotheses, the estimation error is shown to converge in probability to zero. The scheme is also applied to feedforward and recurrent neural networks. >

A blind adaptive TEQ for multicarrier systems

This letter exploits the cyclic prefix to create a blind adaptive globally convergent channel-shortening algorithm, with a complexity like least mean squares. The cost function is related to that of the shortening signal-to-noise solution of Melsa et al. (see IEEE Trans. Commun., vol.44, p.1662-72, Dec. 1996), and simulations are provided to demonstrate the performance of the algorithm.

Exploiting sparsity in adaptive filters

This paper studies a class of algorithms called natural gradient (NG) algorithms. The least mean square (LMS) algorithm is derived within the NG framework, and a family of LMS variants that exploit sparsity is derived. This procedure is repeated for other algorithm families, such as the constant modulus algorithm (CMA) and decision-directed (DD) LMS. Mean squared error analysis, stability analysis, and convergence analysis of the family of sparse LMS algorithms are provided, and it is shown that if the system is sparse, then the new algorithms will converge faster for a given total asymptotic MSE. Simulations are provided to confirm the analysis. In addition, Bayesian priors matching the statistics of a database of real channels are given, and algorithms are derived that exploit these priors. Simulations using measured channels are used to show a realistic application of these algorithms.

Local consonance and the relationship between timbre and scale

The principle of local consonance is based on an explicit parametrization of Plomp and Levelt’s [J. Acoust. Soc. Am. 38, 548–560 (1965)] consonance curves. It explains the relationship between the spectrum of a sound (its timbre) and a tuning (or scale) in which the timbre will appear most consonant. This relationship is defined in terms of the local minima of a family of dissonance curves. For certain timbres with simple spectral configurations, dissonance curves can be completely characterized, and bounds are provided on the number and location of points of local consonance. Computational techniques are presented which answer two complementary questions: Given a timbre, what scale should it be played in? Given a desired scale, how can appropriate timbres be chosen? Several concrete examples are given, including finding scales for nonharmonic timbres (the natural resonances of a uniform beam, ‘‘stretched’’ and ‘‘compressed’’ timbres, FM timbres with noninteger carrier‐to‐modulation ratios), and finding t...

Weak convergence and local stability properties of fixed step size recursive algorithms

A recursive equation that subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation (ODE). The ODEs describing the motion of several common adaptive filters are examined in some simple settings, including the least mean square (LMS) algorithm and all three of its signed variants (the signed regressor, the signed error, and the sign-sign algorithms). Stability and instability results are presented in terms of the eigenvalues of a correlation-like matrix. This generalizes known results for LMS, signed regressor LMS, and signed error LMS, and gives new stability criteria for the sign-sign algorithm. The ability of the algorithms to track moving parameterizations can be analyzed in a similar manner, by relating the time varying system to a forced ODE. The asymptotic distribution about the forced ODE is an Ornstein-Uhlenbeck process, the properties of which can be described in a straightforward manner. >

Automatic decentralized clustering for wireless sensor networks

We propose a decentralized algorithm for organizing an ad hoc sensor network into clusters. Each sensor uses a random waiting timer and local criteria to determine whether to form a new cluster or to join a current cluster. The algorithm operates without a centralized controller, it operates asynchronously, and does not require that the location of the sensors be known a priori. Simplified models are used to estimate the number of clusters formed, and the energy requirements of the algorithm are investigated. The performance of the algorithm is described analytically and via simulation.

Convex cost functions in blind equalization

Existing blind adaptive equalizers that use nonconvex cost functions and stochastic gradient descent suffer from lack of global convergence to an equalizer setup that removes sufficient ISI when an FIR equalizer is used. The authors impose convexity on the cost function and anchoring of the equalizer away from the all-zero setup. They establish that there exists a globally convergent blind equalization strategy for 1D pulse amplitude modulation (PAM) systems with bounded input data (discrete or continuous) even when the equalizer is truncated. The resulting cost function is a constrained l/sub 1/ norm of the joint impulse response of the channel and the equalizer. The results apply to arbitrary linear channels (provided there are no unit circle zeros) and apply regardless of the initial ISI (that is whether the eye is initially open or closed). They also show a globally convergent stochastic gradient scheme based on an implementable approximation of the l/sub 1/ cost function. >

Excitation conditions for signed regressor least mean squares adaptation

The stability of the signed regressor variant of least-mean-square (LMS) adaptation is found to be heavily dependent on the characteristics of the input sequence. Averaging theory is used to derive a persistence of excitation condition that guarantees exponential stability of the signed regressor algorithm. Failure to meet this condition (which is not equivalent to persistent excitation for LMS) can result in exponential instability, even with the use of leakage. This persistence of excitation condition is interpreted in both deterministic and stochastic settings. >

Power oscillation damping control strategies for FACTS devices using locally measurable quantities

This paper presents a way to derive power oscillation damping control strategies for flexible AC transmission system (FACTS) devices, and derives these laws for the four major types of FACTS devices using an energy function (Lyapunov) method. All controls rely only on locally measurable information, and are independent of system topology, implying structural uncertainty need not affect power oscillation damping control strategies. >

Approaches to blind equalization of signals with multiple modulus

The constant modulus algorithm (CMA) and decision-directed (DD) equalizer are two ways to approach blind equalization of signals that are known to lie on a circle of fixed radius, but where specific values at any given time are unknown. In m-ary quadrature amplitude modulation, the signals lie on n circles of known radius. The authors present two possible approaches to the n-modulus problem, both in the spirit of feature reconstruction algorithms. The multiple-modulus algorithm uses a straightforward generalization of the CMA cost function to derive its update, whereas the decision-adjusted-modulus algorithm is a hybrid of the CMA and DD approaches.<<ETX>>