  Second order statistics provides a dynamic representation of a fading channel
and plays an important role in the evaluation and design of the wireless
communication systems. In this paper, we present a novel analytical framework
for the evaluation of important second order statistical parameters, as the
level crossing rate (LCR) and the average fade duration (AFD) of the
amplify-and-forward multihop Rayleigh fading channel. More specifically,
motivated by the fact that this channel is a cascaded one and can be modeled as
the product of N fading amplitudes, we derive novel analytical expressions for
the average LCR and the AFD of the product of N Rayleigh fading envelopes (or
of the recently so-called N*Rayleigh channel). Furthermore, we derive simple
and efficient closed-form approximations to the aforementioned parameters,
using the multivariate Laplace approximation theorem. It is shown that our
general results reduce to the corresponding ones of the specific dual-hop case,
previously published. Numerical and computer simulation examples verify the
accuracy of the presented mathematical analysis and show the tightness of the
proposed approximations.
