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Summary: PREPARED FOR IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS (1ST REVISION) 1
On the Average Crossing Rates in Selection
Diversity
Hong Zhang, Student Member, IEEE, and Ali Abdi, Member, IEEE
Abstract
This letter presents new results on the average crossing rate of the combined signal of a selection
diversity in Rayleigh fading channels. Exact closed-form expressions are derived for the inphase zero
crossing rate, inphase rate of maxima, phase zero crossing rate, and the instantaneous frequency zero
crossing rate of the output of the selection combiner. The utility of the new theoretical formulas, validated
by Monte Carlo simulations, are brie y discussed as well.
Index Terms
Zero crossing rate, selection combining, Rayleigh channels, fading channels, instantaneous fre-
quency.
I. INTRODUCTION
Diversity combining techniques are often used to combat the effect of fading and selection
combining (SC) is one of the simplest diversity methods [1]. It is well known that the average
crossing rate represents the fading rate and effectively quanti es the impact of the diversity
combiner on channel uctuations [2]. Another application is speed/Doppler estimation which is
important for many applications such as handoff, adaptive modulation and equalization, power
control, etc. [1] [7] [11] [12]. However, to the best of our knowledge, only the envelope level
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