Higher order statistics for lognormal small-scale fading in mobile radio channels

Lognormal small-scale fading has recently been reported in a number of indoor propagation studies. However, until now, no method of generating higher order statistics for this distribution in short-term fading channels has appeared in the literature. In this letter, we present a lognormal fading model which is based on the Bessel-derived autocorrelation function frequently used in Rayleigh-, Rice-, and Nakagami-fading simulators. In addition, we present exact, closed-form expressions for the level crossing rate and average fade duration (AFD) observed in lognormal small-scale fading channels for arbitrary mu and sigma. The accepted ability of the lognormal distribution to approximate Nakagami second-order statistics for high values of the Nakagami-m parameter is used in combination with simulated data, generated using a rank-matching approach, to validate the new model. Theoretical second-order distributions are also compared with empirical measurements obtained for mobile indoor on-body propagation channels. In all cases, the theoretical equations and test data are in good agreement.