This paper determines the optimum secondary user power allocation and ergodic multicast rate of point-to-multipoint communication in a cognitive radio network in the presence of outage constraints for the primary users. Using tools from extreme value theory (EVT), it is first proved that the limiting distribution of the minimum of independent and identically distributed (i.i.d.) signal-to-interference ratio (SIR) random variables (RVs) is a Weibull distribution, when the user signal and the interferer signal undergo independent and non-identically distributed (i.n.i.d.) κ − µ shadowed fading. This limiting distribution is then used for determining the optimum transmit power of a secondary network in an underlay cognitive radio network subject to outage constraints at the primary network in a generalized fading scenario. Furthermore, the asymptotic ergodic multicast rate of secondary users is analyzed for varying channel fading parameters.
Index Termsextreme value theory, κ − µ shadowed fading, outage probability, cognitive radio
I. INTRODUCTIONWith the advances in wireless technology, the presence of wireless devices has become ubiquitous. Furthermore, with the advent of the Internet of Things (IoT), the number of connected devices accessing the spectrum is set to increase in the coming times. With the upcoming increase in devices and hence increasing the traffic, it will be very hard to find free spectrum.Cognitive radio (CR) is one of the promising techniques mitigating spectrum scarcity in wireless communication systems [1]-[4]. In cognitive radio networks (CRNs), there are three popular modes of spectrum sharing between primary users (PU) and secondary users (SU) -underlay, overlay and interweave [5]- [8]. As a further development, the authors of [9], [10] have studied the security aspects of a CR system in the presence of eavesdroppers.Throughout this paper, we consider the underlay mode, in which the secondary network is allowed to access the spectrum allocated to the primary network provided that the interference caused by the SU transmitter does not unduly deteriorate the performance of the primary network.An important problem in CRNs is the choice of power policy at the SU-Tx (transmitter), so that the interference at the PU-Rx (receiver) remains below an admissible threshold. Several authors [11]-[15] have studied the performance of underlay CRNs under various interference constraints. In [16], different-power adaptive transmit antenna selection (TAS) schemes were analyzed for the underlay CRN. Furthermore, the authors of [17] have determined the optimal rate sharing parameters for both the SU and the PU, so that the achievable rates were maximized.Similarly, recent contributions [18], [19] have also considered the performance of an interferencelimited underlay CRN relying on continuous power adaptation at the SU. In [19], the secondary transmitter is assumed to transmit information to the specific SU, having the kth highest signalto-interference ratio (SIR). The authors of [18] have also investigated t...
