Asymptotic Performance of ALOHA-Based Cognitive Overlaid Networks

We study the asymptotic performance of two overlaid wireless ad-hoc networks that utilize the same temporal, spectral, and spatial resources based on random access schemes. The primary network consists of Poisson distributed legacy users with density $n$ and the secondary network consists of Poisson distributed cognitive radio users with density $m = n^{β}$ ($β > 1$) that utilize the spectrum opportunistically. Both networks are emph{decentralized} and deploy ALOHA protocols where the secondary users are equipped with range-limited emph{perfect} spectrum sensors to monitor and protect primary transmissions. First, we show that both networks can achieve their corresponding stand-alone throughput scaling even without secondary spectrum sensing (i.e., sensing range set to zero), which implies the need for a more comprehensive performance metric than just throughput scaling to evaluate the influence of the overlaid interactions. We thus introduce a new criterion, termed as the emph{asymptotic multiplexing gain}, which captures the effect of spectrum sensing and inter-network interferences.