Impact of Secondary Users' Field Size on Spectrum Sharing Opportunities

Previous works studied the effect of many system parameters on spectrum sharing opportunities where secondary users access the spectrum of primary users. 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 the field size on spectrum sharing opportunities. We verify that asymptotic results obtained for infinite fields are applicable for finite but relatively large fields as well, i.e., when the radial depth of the field is much greater than the minimum distance to the primary user. We demonstrate that in some cases, however, asymptotic results are too pessimistic hiding some spectrum sharing opportunities. Moreover, the 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 results also suggest the possibility of a secondary network to concurrently share the spectrum with a primary user without the need for spectrum sensing techniques or other cognitive radio functionalities.