Level Crossing Rates of Envelop Processes for Multihop Fading Channels with Amplify-and-Forward Relays

The analytical average level crossing (LCR) of the envelope process for multihop fading channels with the amplify-and-forward (AF) relay is derived by using the counting functional, where the fading factors of different hops are assumed to be independent. The evaluation of the analytical LCR involves integrals that are difficult to compute. To evaluate the LCR, the lower bound and the upper bound on the LCR are derived. The cases of Rayleigh and Rician fading channels are considered, where the lower bound and the upper bound are assessed. Numerical results are presented for different fading parameters.