Finite-State Markov Chain Models for the Intensity of Nakagami Fading

Abstract

For the design, analysis, and simulation of communication systems with Nakagami-m fading channels, it is very convenient to model the fading by finite-state Markov chains in which the states represent fade levels or signal-to-noise ratios in decibels. Our approach to the development of such Markov chain models is to work with the intensity of the fading process, which is proportional to the logarithm of squared envelope of the faded signal. We demonstrate that all the parameters of the Markov chains can be determined from the bivariate distribution of the intensity of the Nakagami-m fading process. Several analytical results are derived from the bivariate distribution of the intensity, including expressions for the chain’s transition probabilities for both adjacent and nonadjacent states and the asymptotic distribution of the intensity for deep fades. For several values of m, we verify the accuracy of our Markov chain models as simulation tools by comparisons of the state probabilities and level-crossing rates obtained from simulations of the Markov chain with those obtained from our analytical expressions.