Novel results for the performance of single and double stages cognitive radio systems through Nakagami-m fading and log-normal shadowing

Previously reported results presented approximate expressions for the performance of cognitive radio systems through Nakagami fading and log-normal shadowing. In this article, exact expressions for the Receiver Operating Characteristics of cognitive radio system are derived analytically for a single stage and a double stage system. By single stage, it is assumed that the secondary users are close to the fusion centre therefore, they can be considered directly coupled to it. For the second stage system the secondary users are considered far from the fusion centre, thus another communication link is assumed between the secondary users and the fusion centre with similar characteristics as the first link. In both scenarios Nakagami fading and log-normal shadowing are assumed. Results for integer and non-integer Nakagami fading parameter ‘m’ are obtained. Depicted results show that better performance is obtained with the increase of the number of secondary users and increase of ‘m’. Deterioration due to shadowing is also indicated.