White spaces refer to the unused frequency voids across time or space. The vast existence of white spaces has been validated by many measurements and is widely regarded as an undesirable consequence of the fixed spectrum licensing policy. In this paper, we apply stochastic geometry to study the spatial distribution of white spaces in the presence of a random primary network with homogeneous nodes. We show that with a self-interfering constraint on the primary network, a large portion of the total area will be detected as the white space regardless of the density of the primary transmitters. Our finding suggests that the existence of white spaces is not merely a by-product of the artificial spectrum licensing policy but also an inherent phenomenon of wireless communication systems. Two main causes of the white spaces are the self-interfering constraint and random network topology. Our model also suggests that power control and topology-aware spectrum management are the keys to eliminate white spaces and improve the overall spectrum utilization.
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