Error performance for equal-gain combiners over Rayleigh fading channels

Introduction: Diversity is one of the most commonly used techniques in mobile radio for combatting signal fading. Moreover, equal-gain combining (EGC) has been accepted as an attractive diversity tool due to its improved error performance and the simplicity of its implementation [1]. Two effective techniques have been proposed for the evaluation of error probability (ERRP) in equal-gain combiners in Rayleigh fading channels. The first such useful approach was made by Beaulieu [2] where the ERRP was obtained through the determination of the probability density function (PDF) of the sum of L Nakagami signals arriving in the L branches of the combiner and Rayleigh fading was treated as a special case. The proposed closed forms contain two kinds of confluent hypergeometric functions. Zhang [3, 4] presented a simpler approach, and the ERRP for coherent and non-coherent modulation schemes was derived directly from the characteristic function (CHF) of the decision variable using a special lemma (Gil-Palaez) and avoiding the lengthy process of deriving the PDF of the sum of L Rayleigh variates. This is an important result since the proposed closed formulation is much simpler than formulations in previously published techniques, but it also needs the calculation of a confluent hypergeometric function. In this Letter an alternative approach for the evaluation of ERRP in BPSK systems with EGC diversity and additive uncorrelated white noise is proposed. The ERRP is evaluated directly using the definition and the properties of the characteristic function of a random variable and a final closed formula is derived. This formula is very simple, can be evaluated using the Hermite numerical integration method and does not require any complicated calculations (such as the confluent hypergeometric functions in previous techniques).