A Markovian Model for Coarse-Timescale Channel Variation in Wireless Networks

Abstract

A wide range of wireless channel models have been developed to model variations in received signal strength. In contrast to prior work, which has focused primarily on channel modeling on a short, per-packet timescale (millisecond), we develop and validate a finite-state Markovian model that captures variations due to shadowing, which occur at coarser time scales. The Markov chain is constructed by partitioning the entire range of shadowing into a finite number of intervals. We determine the Markov chain transition matrix in two ways: (i) via an abstract modeling approach in which shadowing effects are modeled as a log-normally distributed random process affecting the received power, and the transition probabilities are derived as functions of the variance and autocorrelation function of shadowing; (ii) via an empirical approach, in which the transition matrix is calculated by directly measuring the changes in signal strengths. We test the assumptions of our Markovian model using signal strength measurements collected over an 802.16e (WiMAX) network and a wireless multi-hop network deployed by Rice University. We compare the steady state and transient performance of the model with those computed using the empirically derived transition matrix and those observed in the actual traces themselves.

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