A Cumulant-Based Investigation of the Impact of Secondary Users´ Field Size on Spectrum-Sharing Opportunities

Previous works studied the effect of different system parameters on spectrum-sharing opportunities where secondary users access the spectrum of primary users (PUs). However, a parameter that has received little attention is the spatial size of the field of secondary users. Usually, the field size is assumed to be infinite. Using results developed for infinite fields might be too pessimistic, leading to missing spectrum-sharing opportunities. This paper studies the effect of field size on spectrum-sharing opportunities. We verify that asymptotic results obtained for infinite fields are applicable for finite but relatively large fields (when the radial depth of the field is much greater than the minimum distance to the PU) as well. We also demonstrate that, in some cases, however, asymptotic results are too pessimistic, hiding some spectrum-sharing opportunities. Moreover, this paper shows that, in certain situations, a small reduction in the field size may create spectrum-sharing opportunities, while in certain other situations, a huge increase in the field size may not eliminate spectrum-sharing opportunities. Our study is based on a cumulant-based characterization of the aggregate interference power generated by secondary users. A number of recent papers in literature have dealt with cumulants of the aggregate interference, but only under specific scenarios. We introduce a more comprehensive method to determine the cumulants under various system and channel conditions. These cumulants are utilized to understand the dynamics of the aggregate interference power, approximate its distribution, and, hence, investigate the spectrum-sharing opportunities.