Average level crossing rate and fading duration of multiuser single relay cooperation wireless uplinks

We investigate the average Level Crossing Rate (LCR) and Average Fading Duration (AFD) of multiuser single relay cooperation wireless uplinks over independent and non-identically distributed (i.ni.d) Ray-leigh fading channels. We first present the statistical analyses of the first-hop equivalent envelope. Then, we investigate the LCR and AFD of an equivalent end-to-end envelope, and present the closed-form solutions to LCR and AFD, which are given with integral forms. Finally, we derive the Laplace approximations of LCR and AFD as well as the upper and lower bounds. The numerical results of LCR show that the upper bound is tight. For multiuser systems with different number of mobile users, the analyses indicate that the LCRs are approximately the same at the low level of the envelope. However, at the high level of the envelope there are reasonable differences among the curves of LCRs. Due to that fact that AFD is the inverse function of LCR, the results for AFD are the opposite.