Higher Order Statistics in Switch and Stay Diversity Systems

We analyze the level crossing rate (LCR) and the average fade duration of the output signal-to-noise ratio (SNR) in switch-and-stay combining (SSC) systems. By using a common approach, we study these higher order statistics for two different kinds of configurations: 1) colocated diversity, i.e., receiver equipped with multiple antennas, and 2) distributed diversity, i.e., relaying link with multiple single-antenna threshold-based decode-and-forward (DF) relays. Whenever using threshold-based techniques such as DF or SSC, the output SNR is a discontinuous random process, and hence, the classic Rice approach to calculate the LCR is not applicable. Thus, we use an alternative formulation, in terms of the 1-D and 2-D cumulative distribution functions of the output SNR. Our results are general and hold for any arbitrary fading distribution at the different diversity branches with any arbitrary time correlation model. Moreover, we develop a general asymptotic framework to calculate these higher order statistics in high average SNR environments that only needs the univariate probability density function (PDF), finding an insightful connection between the asymptotes of the LCR and the fading diversity order.