On the First- and Second-Order Statistics of Selective Combining over Double Nakagami-m Fading Channels

This paper studies the statistical properties of selective combining (SC) diversity schemes over double Nakagami-m fading channels. It is assumed that all diversity branches follow independent and identically distributed (i.i.d.) double Nakagami-m fading processes, where the serial concatenated Nakagami-m processes making up the double Nakagami-m fading branches are assumed to be independent, but not necessarily identically distributed. Starting from already known statistics on double Nakagami-m processes, analytical expressions are derived for the cumulative distribution function (CDF), probability distribution function (PDF), level- crossing rate (LCR), and average duration of fades (ADF) of SC diversity schemes. A general expression is derived for the moments of the instantaneous signal-to-noise ratio (SNR). By using the general expression, we study the mean SNR, amount of fading (AoF), and the diversity gain. The derived expressions include also the corresponding results for double Rayleigh, double one-sided Gaussian, and one-sided Gaussian×Rayleigh channels as special cases. A good agreement is observed between theory and simulation, which confirms the validity of the obtained analytical expressions.