Convergence acceleration of the doubly periodic Green's function for the analysis of thin wire arrays

A method is proposed to accelerate the evaluation of the Green's function of an infinite double periodic array of thin wire antennas. The method is based on the expansion of the Green's function into series corresponding to the propagating and evanescent waves and the use of Poisson and Kummer transformations enhanced with the analytic summation of the slowly convergent asymptotic terms. Unlike existing techniques the procedure reported here provides uniform convergence regardless of the geometrical parameters of the problem or plane wave excitation wavelength. In addition, it is numerically stable and does not require numerical integration or internal tuning parameters, since all necessary series are directly calculated in terms of analytical functions. This means that for nonlinear problem scenarios that the algorithm can be deployed without run time intervention or recursive adjustment within a harmonic balance engine. Numerical examples are provided to illustrate the efficiency and accuracy of the developed approach as compared with the Ewald method for which these classes of problems requires run time splitting parameter adaptation.

Cost function adaptation: a stochastic gradient algorithm for data echo cancellation

A family of stochastic gradient algorithms and their behaviour in the data echo cancellation work platform are presented. The cost function adaptation algorithms use an error exponent update strategy based on an absolute error mapping, which is updated at every iteration. The quadratic and nonquadratic cost functions are special cases of the new family. Several possible realisations are introduced using these approaches. The noisy error problem is discussed and the digital recursive filter estimator is proposed. The simulation outcomes confirm the effectiveness of the proposed family of algorithms.

Adaptive data echo cancellation using cost function adaptation

For a digital echo canceller it is desirable to reduce the adaptation time, during which the transmission of useful data is not possible. LMS is a non-optimal algorithm in this case as the signals involved are statistically non-Gaussian. Walach and Widrow (IEEE Trans. Inform. Theory 30 (2) (March 1984) 275-283) investigated the use of a power of 4, while other research established algorithms with arbitrary integer (Pei and Tseng, IEEE J. Selected Areas Commun. 12(9)(December 1994) 1540-1547) or non-quadratic power (Shah and Cowan, IEE.Proc.-Vis. Image Signal Process. 142 (3) (June 1995) 187-191). This paper suggests that continuous and automatic, adaptation of the error exponent gives a more satisfactory result. The family of cost function adaptation (CFA) stochastic gradient algorithm proposed allows an increase in convergence rate and, an improvement of residual error. As special case the staircase CFA algorithm is first presented, then the smooth CFA is developed. Details of implementations are also discussed. Results of simulation are provided to show the properties of the proposed family of algorithms. (C) 2000 Elsevier Science B.V. All rights reserved.