Analysis of Wireless Ad-Hoc and Sensor Networks in Finite Regime

In the past, many analytic results for wireless networks have been reported for the case where the number of nodes n in the network tends to infinity (large-scale networks). These include connectivity, coverage, and capacity. These results have not been extended for small or moderate values of n, although in many practical networks n is not very large. In this paper, we first show that previous asymptotic results provide poor approximations for the finite networks (small-scale networks). We then aim to develop a framework to analytically study network properties without assuming that n is large. We provide a set of differences between small-scale and large-scale analysis. We consider wireless networks in which the location of the nodes is random. We study routing algorithms, coverage, connectivity and capacity of finite wireless networks. We provide easily computable expressions for different network properties. With validation from simulations, we show that these analytic expressions give very good estimates of these quantities for finite wireless networks. Our investigation suggests that the small- scale networks posses unique characteristics that require a new framework for analysis and design.