Energy detector´s performance evaluation in a relay based cognitive radio network: Area under the ROC curve (AUC) approach

In this paper, energy detector´s performance is analyzed for the two-hop relay network using the area under the receiver operating characteristic (ROC) curve (AUC) in contrast to the ROC based analysis. AUC provides summary measures for the performance of a system. It provides meaningful performance analysis as it varies only from 0.5 to 1. In the worst case scenario, the practical detector´s performance can be no less than 0.5 and the best can be 1. A simple generalized AUC framework is developed based on the canonical series representations of the generalized Marcum Q-function of real order in conjunction with the k^th order derivative of the moment generating function (MGF) of signal to noise ratio (SNR) of the channel. The framework is then applied to analyze the energy-detection performance for single and multiple two-hop relay networks. For multiple two-hop relay networks, the receiver combining techniques are analyzed in particular maximum ratio combining (MRC) and square-law combining (SLC) as the representative of various combining techniques. Different factors such as the sampling number, number of relays and fading severity influencing the energy sensing have been analyzed. Proposed approach is simple in terms of computation and performance analysis and the results can be used readily for selecting proper cognitive radio operating parameters. Also the solution is capable of handling the half odd-integer bandwidth-time product (u) and the half odd-integer Nakagami-m fading severity index (m).