The General Solution for Crossing Rates and Fade Durations of Selection Combining

General and compact expressions for level crossing rate and average fade duration of selection combining are derived. The expressions can be directly applied to any multibranch, correlated, non-identical, and unbalanced fading environment for which the joint statistics of the envelopes and each of their time derivatives are known. The general solutions specialize to simpler calculations for some particular cases. In the derivation process, novel, generalized, joint crossing rate concepts, consistent with the statistical theory, are introduced. Simple bounds for the quantities investigated are also attained, and they are written in terms of the individual branch measures.