Identification of spectrum sharing opportunities for a finite field secondary network through an exact outage expression under Rayleigh fading

A closed-form expression for the outage probability at a receiver in the primary network due to a uniform annular sector distribution of secondary transmitters is derived in a Rayleigh fading environment. This may include an exclusion region, and a finite or infinite outer radius. Conversely, under a given constraint on the outage probability, spectrum sharing opportunities are analyzed with respect to the field size and are shown to be significantly dependent on the exclusion region. Conditions are obtained for which an infinite field size assumption can or cannot lead to the loss of spectrum sharing opportunity. Additionally, the spectrum sharing gains (the maximum average number of secondary transmitters) are derived for the secondary network for different spatial deployments. It is worth mentioning that other than networks sharing spectrum, the derived results are applicable to any set of interferers from the same network or other networks around any receiver of study.