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Type: Journal article
Title: Markov approach to percolation theory based propagation in random media
Author: Rainsford, T.
Bender, A.
Citation: IEEE Transactions on Antennas and Propagation, 2008; 56(5):1402-1412
Publisher: IEEE-Inst Electrical Electronics Engineers Inc
Issue Date: 2008
ISSN: 0018-926X
Statement of
Tamath Rainsford and Axel Bender
Abstract: For line-of-sight links in random media or urban areas, propagation may be approximated through sequential reflections of an optical ray in a two-dimensional medium of disordered lossless scatterers. Franceschetti et al. approximated such percolation-based optical-ray propagation by a Markov process with two absorbing barriers, provided numerical solutions for the probability of a ray passing through the percolation lattice and solved—both approximately and exactly—a corresponding problem based on the theory of martingales. In this paper we solve exactly the Markov-theoretical formulation of the problem and prove that both the Markov and martingale approaches are equivalent. Our proof is an application of the Perron-Frobenius theory which provides an elegant framework for the study of the asymptotic behavior of stochastic processes. We demonstrate that for a wide range of vacancies and incident angles the exact solution of the Markov-theoretical formulation performs significantly better than the commonly used Wald approximation in the martingale approach. This has a number of implications on the accuracy of the model, especially for low density propagation media.
Keywords: electromagnetic propagation in random media
Markov processes
mobile communication
urban areas
Description: Copyright © 2008 IEEE
DOI: 10.1109/TAP.2008.922626
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Appears in Collections:Aurora harvest 6
Electrical and Electronic Engineering publications

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