  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 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
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.
