In this paper, we present performance analysis for underlay cognitive decode-and-forward relay networks with the Nth best relay selection scheme over Nakagami-m fading channels. Both the maximum tolerated interference power constraint and the maximum transmit power limit are considered. Specifically, exact and asymptotic closed-form expressions are derived for the outage probability of the secondary system with the Nth best relay selection scheme. The selection probability of the Nth best relay under limited feedback is discussed. In addition, we also obtain the closed-form expression for the ergodic capacity of the secondary system with a single relay. These expressions facilitate in effectively evaluating the network performance in key operation parameters and in optimizing system parameters. The theoretical derivations are extensively validated through Monte Carlo simulations. Both theoretical and simulation results show that the fading severity of the secondary transmission links has more impact on the outage performance and the capacity than that of the interference links does. Through asymptotic analysis, we show that the diversity order for the Nth best relay selection scheme is min(m1, m3) × (M - N) + m3, where M denotes the number of cognitive relays, and m1and m3represent the fading severity parameters of the first-hop transmission link and the second-hop transmission link, respectively.

In underlay cognitive radio networks, imperfect channel knowledge will have an adverse effect on the performance of both the primary users (PU) and the secondary users (SU) owing to the interference power constraint of PU. This paper investigates the performance of a cognitive relay network (CRN) with imperfect channel state information (CSI) of the interference links over Nakagami-m fading channels. Interference probability is defined to characterize the interference caused by SU to PU due to CSI imperfection. Closed-form expressions for both the interference probability of the primary user and the outage probability of the secondary system are derived and validated by simulations. It is proved that the interference probability of the primary user is always 0.5 under the condition of imperfect CSI when no power control mechanism is adopted. The effects of CSI imperfection, channel fading severity, interference probability of PU and transmit power of PU on the outage performance of the secondary system are also analyzed.