Large Overlaid Cognitive Radio Networks: From Throughput Scaling to Asymptotic Multiplexing Gain

We study the asymptotic performance of two multi-hop overlaid 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 λ^(p) and the secondary network consists of Poisson distributed cognitive radio users with density λ^(s) = (λ^(p))^β (β > 0, β ≠ 1) that utilize the spectrum opportunistically. Both networks are decentralized and employ ALOHA medium access protocols where the secondary nodes are additionally equipped with range-limited perfect spectrum sensors to monitor and protect primary transmissions. We study the problem in two distinct regimes, namely β > 1 and 0 <; β <; 1. We show that in both cases, the two networks can achieve their corresponding stand-alone throughput scaling even without secondary spectrum sensing (i.e., the sensing range set to zero); this 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 the asymptotic multiplexing gain, which captures the effect of inter-network interferences with different spectrum sensing setups. With this metric, we clearly demonstrate that spectrum sensing can substantially improve the overlaid cognitive network performances when β > 1. On the contrary, spectrum sensing turns out to be unnecessary when β <; 1 and employing spectrum sensors cannot improve the network performances.