The effect of Gaussian error in selection diversity combiners

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Abstract
Selection diversity combining (SDC) is one of the simplest and most commonly implemented diversity mechanism for mitigating the detrimental effects of deep fades experienced on wireless channels. While SDC improves the mean combined signal‐to‐noise ratio (SNR) over that of a single branch with increasing diversity order, its main advantage is the reduction of the probability of deep fades. The effect of Gaussian errors in the branch gain estimates on the SDC receiver performance is investigated by deriving new closed‐form expressions for the probability density function, cumulative distribution function and the moment generating function of the combiner output SNR statistic. Mathematical expressions for quantifying the degradation in the mean combined SNR, outage probability and the average symbol error rate of a broad class of binary and multilevel modulation schemes owing to imperfect branch SNR estimates in Rayleigh fading are also derived. It is shown that combiner errors affect the mean combined SNR negligibly in comparison to their effect on the deep fades. Copyright © 2001 John Wiley & Sons, Ltd.