Cognitive opportunistic relaying systems with mobile nodes: average outage rates and outage durations

In the existing literature about cognitive radio opportunistic relaying (CR-OR) systems, the first-order statistics such as outage probability are investigated widely. However, for the second-order statistics, such as average outage duration (AOD) and average outage rate (AOR), there is not open works, still. To obtain a comprehensive cognition on the behaviour of mobile communication systems, this study focuses on the second-order statistical properties of CR-OR systems. There are two CR-OR schemes considered, in which the canonical amplify-and-forward (AF) and reactive decode-and-forward (RDF) are employed, respectively. Since the equivalent end-to-end signal-to-noise ratio (SNR) of AF CR-OR is complicated such that it is very difficult to obtain the closed-form solution to AOR of AF CR-OR schemes, the high SNR approximation in AF CR-OR schemes is employed. For the two schemes, first the closed-form solutions to AORs and AODs are obtained by using appropriate mathematical proof. Based on the derivations, the comparison analyses about AORs and AODs of the two schemes are provided. The comparison results show that, under high SNR approximation, the AF CR-OR scheme achieves the same AOR and AOD as RDF CR-OR. Finally, the impact of system parameters on AORs and AODs is provided.