C.F.N. Cowan

Genetic algorithms applied to the adaptation of IIR filters

Abstract A genetic algorithm (GA) approach to adaptive IIR filtering is presented in this paper. Conventional adaptive IIR filter algorithms suffer from potential instability and complexity problems, and as such there is an interest in adaptive IIR filters based on alternate algorithms. Genetic algorithms for IIR filter problems provide guaranteed filter stability. Three adaptive IIR filter structures - cascade, parallel and lattice - are studied. Experimental results show that the genetic algorithm has advantage in the case where poles are close to the unit circle and for high-order filter problems.

Adaptive echo cancellation using statistical shaping

This article presents a novel structure for bulk delay estimation in long echo cancellers which reduces the amount of excess error considerably. The miscalculation of the delay between the near end and the far end sections is one of the main causes of the excess error. Two analyses, based on the least mean square algorithm, are presented where a certain shape for the transitions (at the end of the near end and at the beginning of the far end sections) is considered. Transient and steady-state behavior and convergence conditions are studied, as well as a comparison between the algorithms developed for each transition. Simulation results agree well with theoretical derivations.

Stochastic convergence analysis of a partially adaptive two-layer perceptron using a system identification model

Abstract This paper studies the stationary points of the output layer of a two-layer perceptron which attempts to identify the parameters of a specific nonlinear system. The training sequence is modeled as the binary output of the nonlinear system when the input is comprised of an independent sequence of zero-mean Gaussian vectors with independent components. The training rule for the output layer weights is a modified version of Rosenblatts algorithm. Equations are derived which define the stationary points of the algorithm for an arbitrary output nonlinearity g (x). For the subsequent analysis, the output nonlinearity is specialized to g ( x ) = sgn( x ). The solutions to these equations show that the only stationary points occur when the hidden weights of the perceptron are constrained to lie on the plane spanned by the nonlinear system model. In this plane, the angles of the perceptron weights and of the nonlinear system model weights satisfy a pair of homogeneous linear equations with an infinity of solutions. However, there is a unique solution for algorithm convergence (i.e., zero error) such that the parameters of the two-layer perceptron must exactly match that of the nonlinear system.

Adaptive non-linear equalisation of digital communications channels

Abstract Non-linear distortion introduced by communications channels increases the probability of error. In this paper, an adaptive non-linear canceller is presented which attempts to remove non-linear interference from the output of a feedforward or decision feedback equaliser, improving the error rate. It may be implemented using a memory look-up table architecture, making it suitable for high speed real time operation.

Stochastic convergence analysis of a two-layer perceptron for a system identification model

The authors analyze the stationary points of a two-layer perceptron which attempts to identify the parameters of a specific nonlinear system. The training sequence is modeled as the binary output of the nonlinear system when the input is composed of an independent sequence of zero mean Gaussian vectors with independent components. The training rule is a modified version of Rosenblatts algorithm. It is shown that the two-layer perceptron correctly identifies all parameters of the unknown nonlinear system.<<ETX>>

Communications equalization using non-linear adaptive networks

The author describes how the equalization process may be viewed as a classification problem and describes how an optimum nonlinear classification strategy is formed. One solution to this classification problem is provided which allows classification on a symbol by symbol basis with an improved bit error rate performance relative to the linear system. A nonlinear structure can provide a near optimum decision boundary but one which still does not approach the performance of maximum-likelihood sequence estimation (MLSE). The various performance and complexity issues raised in the deployment of such nonlinear adaptive systems are examined. The development of a multichannel adaptive solution in this single channel temporal case provides a possible parallel to the MLSE solution.<<ETX>>

A compound near-far end least square-fourth error minimization for adaptive echo cancellation

This article presents a novel algorithm for echo cancellers with near-end and far-end sections. The algorithm consists of simultaneously applying the least mean square (LMS) algorithm to the near-end section of the echo canceller and the least mean fourth (LMF) algorithm to the far-end section. This combination results in a substantial improvement of the performance of the proposed scheme over the LMS algorithm in Gaussian and non-Gaussian environments (additive noise). However, the application of the LMF and the LMS algorithms to the near-end and the far-end sections, respectively, results in a poor performance. Simulation results, confirm the superior performance of the new algorithm.

Nonlinear adaptive filters for time variant equalization

Adaptive equalization is a well established procedure used in data communications systems to compensate for channel distortions and thus allow higher signalling rates. Such systems are made adaptive because the channel characteristics are both a-priori unknown and, usually, time variant. In many systems this time variation is slow and, therefore, does not cause a problem for the adaptive processes employed. However, in the case of certain application areas, such as mobile terminals, the rate of time variation can be significant in relation to the signalling rate. Under these circumstances the performance of normal adaptive equalizers degrades rapidly. This paper presents a new adaptive equalizer structure of a non-linear form which makes use of both time and instantaneous amplitude information to provide a structure which is matched to this particular problem. Simulation results are presented which demonstrate the superiority of this structure relative to normal linear equalizers.

Equalisers for digital communications using generalized distance measurement

It is shown that a previously published algorithm by C.F.N. Cowan (see Proc. 25th Asimolar Conf. on Signals, Systems and Computers, Pacific Grove, CA, USA, IEEE, 1991), for nonlinear equalization involving the measurement of the Mahalanobis distance makes the assumption that the clusters in the underlying observation space have a Gaussian distribution. If this assumption is violated, poor performance may be obtained. However, it is shown that the equalizer structure is capable of generating good approximations to the theoretical optimum decision boundary. It is the use of the Mahalanobis distance which is inappropriate in the non-Gaussian case. By using a more general concept of distance, it is demonstrated that it is possible to obtain significantly better results than those obtained using the Mahalanobis distance measure. The new method and previous algorithms are also extended to cover the case of multilevel transmitted signals.<<ETX>>