Higher Order Statistics in Switch and Stay Diversity Systems

Abstract

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 thresholdbased techniques such as DF or SSC, the output SNR is a discontinuous random process and hence classic Rice approach to calculate the LCR is not applicable. Thus, we use an alternative formulation in terms of the one and two-dimensional 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, finding an insightful connection between the asymptotes of the LCR and the fading diversity order.

Free space optical communications with distributed switch‐and‐stay combining

“…The expressions for optimal rate adaptation (ORA), channel inversion with fixed rate (CIFR) and truncated inversion with fixed rate (TIFR) are derived, but performance analysis of the optimal power and rate adaptation (OPRA) in terms of capacity is missing. The higher order statistics for SSC systems, where receivers are equipped with multiple antennas, has been developed in [17].…”

“…Selection of a branch is based on the threshold value of SNR and no co‐phasing or channel state information (CSI) is required, this has become practically feasible with the use of adaptive and intelligent systems. Recently, distributed schemes have surpassed the performance of stand‐alone SSC techniques [17]. FSO appears very promising for backhaul transmission amongst infrastructure elements in cellular networks [1] and is very less affected by different fading conditions as compared with RF due to its LOS transmission property.…”