Throughput Analysis of Wireless Ad-Hoc Cognitive Radio Networks

In this dissertation we consider the throughput performance of cognitive radio networks and derive the optimal sensing and access schemes for secondary users that maximizes their sum-throughput while guaranteeing certain quality of service to primary networks. First, we consider a cognitive radio network where secondary users have access to N licensed primary frequency bands with their usage statistics and are subject to certain inter-network interference constraint. In particular, to limit the interference to the primary network, secondary users are equipped with spectrum sensors and are capable of sensing and accessing a limited number of channels at the same time. We consider both the error-free and erroneous spectrum sensing scenarios, and establish the jointly optimal random sensing and access scheme, which maximizes the secondary network expected sum throughput while honoring the primary interference constraint. We show that under certain conditions the optimal sensing and access scheme is independent of the primary frequency bandwidths and usage statistics; otherwise, they follow water-filling-like strategies. Next, 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) that utilize the spectrum opportunistically. Both networks 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 ; 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 interference . With this metric, we clearly demonstrate that spectrum sensing can substantially improve the overlaid cognitive networks performance when β > 1. On the contrary, spectrum sensing turns out to be redundant when β < 1 and employing spectrum sensors cannot improve the networks performance. Finally, we present a methodology employing statistical analysis and stochastic geometry to study geometric routing schemes in wireless ad-hoc networks. The techniques developed in this section enable us to establish the asymptotic connectivity and the convergence results for the mean and variance of the routing path lengths generated by geometric routing schemes in random wireless networks