Closed-form evaluation of area under the ROC of cooperative relay-based energy detection in cognitive radio networks

In this article, we develop a closed form evaluation of the area under receiver operating characteristics (ROC) curve (AUC) when employed in the analysis of cooperative amplify-and-forward (CAF) relay-based energy detection. The developed analytical expression for AUC results into finite kth order derivative of the moment generating function of the end-to-end signal-to-noise ratio. The resulting closed-form expressions can be easily generalized across different fading channels and multi-relay system. We first consider a single amplify-and-forward (AF) relay based sensing and later extend the framework to multi-relay system. Both options of maximum ration combining (MRC) and square-law combining are analysed. We found out that direct sensing performs better than single relay sensing under certain scenario. However, the sensing performance is greatly enhanced when both direct and relay based sensing are combined to form a CAF relay detection system. Also, we show that MRC CAF relay sensing outperforms their corresponding SLC CAF relay sensing.