# Transmit Power Policy and Ergodic Multicast Rate Analysis of Cognitive Radio Networks in Generalized Fading

## TL;DR

This paper analyzes the optimal power allocation and ergodic multicast rate in cognitive radio networks under generalized fading, using extreme value theory to derive limiting distributions and outage constraints.

## Contribution

It introduces a novel application of EVT to derive the Weibull distribution for minimum SIR in generalized fading, optimizing secondary user power and multicast rate.

## Key findings

- Limiting distribution of minimum SIR is Weibull under generalized fading.
- Derived convergence rate of the minimum SIR distribution to Weibull.
- Provided optimal transmit power policy for secondary users under outage constraints.

## Abstract

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.