A unified approach to performance evaluation of switched diversity in independent and correlated fading channels

This paper outlines a unified approach to performance evaluation of a broad class of coherent, differentially coherent and noncoherent digital communication systems, with dual-branch switched diversity (SWC) reception over generalized fading channels. The moment generating function (MGF) of the signal power at the output of the SWC combiner and the first-order derivative of the MGF with respect to the switching threshold are derived. These expressions are obtained for the general case of correlated fading and nonidentical diversity branches, and hold for any common fading distributions (e.g., Rayleigh, Nakagami-m, Rician, Nakagami-q). The optimum switching threshold (in a minimum error rate sense) is obtained by solving a nonlinear equation which is formed by using the first-order derivative of the MGF. This nonlinear equation can be simplified for several special cases: (a) closed-form expressions for the optimal switching threshold are derived for three generic forms of the conditional error probability by assuming independent and identically distributed diversity branches; and (b) a closed-form formula for the optimal switching threshold is derived for the non-coherent binary modulation formats in correlated Rayleigh or Nakagami-m fading with identical fading statistics.