Transmit power policy and ergodic multicast rate analysis of cognitive radio networks in generalized fading

This paper determines the optimum secondary user (SU) power allocation and ergodic multicast rate of point-to-multipoint communication in a cognitive radio network (CRN) in the presence of various quality of service (QoS) constraints for the primary users (PUs). 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 signals undergo independent and non-identically distributed (i.n.i.d.) kappa -mu shadowed fading. Also, the rate of convergence of the actual minimum distribution to the Weibull distribution is derived. This limiting distribution is then used for determining the optimum transmit power of a secondary network in an underlay CRN subject to three different QoS constraints at the primary network in a generalized fading scenario. Furthermore, the optimum transmit power and the asymptotic ergodic multicast rate of SUs is analyzed for varying channel fading parameters.