Analytical level crossing rates and average fade durations for diversity techniques in Nakagami fading channels

Using a unified methodology, we derive analytical expressions for the level crossing rates (LCR) and average fade durations (AFD) for three diversity reception techniques and a general Nakagami fading channel. We provide novel analytical expressions for selection combining (SC) and equal-gain combining (EGC), and rederive, in a more general manner, the case of maximal-ratio combining (MRC). Our general results reduce to some specific cases previously published. These results are used to examine the effects on the concerned quantities of the diversity technique, the number of receiving branches and the severity of fading. It is observed that as the Nakagami m-parameter and the diversity order increase, the behavior of the combined received envelope for EGC follows closely the one for MRC, and distances itself from SC.