Cognitive networks achieve throughput scaling of a homogeneous network

We study two distinct, but overlapping, networks which operate at the same time, space and frequency. The first network consists of n randomly distributed primary users, which form either an ad hoc network, or an infrastructure supported ad hoc network in which l additional base stations support the primary users. The second network consists of m randomly distributed secondary or cognitive users. The primary users have priority access to the spectrum and do not change their communication protocol in the presence of secondary users. The secondary users, however, need to adjust their protocol based on knowledge about the locations of the primary users so as not to harm the primary network´s scaling law. Base on percolation theory, we show that surprisingly, when the secondary network is denser than the primary network, both networks can simultaneously achieve the same throughput scaling as a standalone ad hoc network.