Average Fade Duration for Amplify-and-Forward Relay Networks in Fading Channels

We analyze the level crossing rate and the average fade duration of amplify and forward multihop relay networks. We first calculate exact closed-form expressions for these statistics when the individual links are affected by log-normal fading with arbitrary autocorrelation. Based on these expressions, we formulate a log-normal approximation to the product of N Nakagami-m independent random processes. In particular, through a proper matching of the mean, variance and the autocorrelation function, we show that the product of N Nakagami-m stochastic processes can be closely approximated by a single log-normal process. This allows us to accurately approximate the crossing statistics for the cascaded Nakagami-m fading channel in closed-form. Using this analytical framework we characterize the dynamics of the equivalent multihop channel gain for different correlation models, and study the influence of the number of hops and the relay mobility in these second order statistics.