Outage Probability in Arbitrarily-Shaped Finite Wireless Networks

This paper analyzes the outage performance in finite wireless networks. Unlike most prior works, which either assumed a specific network shape or considered a special location of the reference receiver, we propose two general frameworks for analytically computing the outage probability at any arbitrary location of an arbitrarily-shaped finite wireless network: (i) a moment generating function-based framework which is based on the numerical inversion of the Laplace transform of a cumulative distribution and (ii) a reference link power gain-based framework which exploits the distribution of the fading power gain between the reference transmitter and receiver. The outage probability is spatially averaged over both the fading distribution and the possible locations of the interferers. The boundary effects are accurately accounted for using the probability distribution function of the distance of a random node from the reference receiver. For the case of the node locations modeled by a Binomial point process and Nakagami-$m$ fading channel, we demonstrate the use of the proposed frameworks to evaluate the outage probability at any location inside either a disk or polygon region. The analysis illustrates the location dependent performance in finite wireless networks and highlights the importance of accurately modeling the boundary effects.Comment: accepted to appear in IEEE Transactions on Communication

Stochastic Geometry for Modeling, Analysis and Design of Future Wireless Networks

This thesis focuses on the modeling, analysis and design of future wireless networks with smart devices, i.e., devices with intelligence and ability to communicate with one another with/without the control of base stations (BSs). Using stochastic geometry, we develop realistic yet tractable frameworks to model and analyze the performance of such networks, while incorporating the intelligence features of smart devices. In the first half of the thesis, we develop stochastic geometry tools to study arbitrarily shaped network regions. Current techniques in the literature assume the network regions to be infinite, while practical network regions tend to be arbitrary. Two well-known networks are considered, where devices have the ability to: (i) communicate with others without the control of BSs (i.e., ad-hoc networks), and (ii) opportunistically access spectrum (i.e., cognitive networks). First, we propose a general algorithm to derive the distribution of the distance between the reference node and a random node inside an arbitrarily shaped ad-hoc network region, which helps to compute the outage probability. We then study the impact of boundary effects and show that the outage probability in infinite regions may not be a meaningful bound for arbitrarily shaped regions. By extending the developed techniques, we further analyze the performance of underlay cognitive networks, where different secondary users (SUs) activity protocols are employed to limit the interference at a primary user. Leveraging the information exchange among SUs, we propose a cooperation-based protocol. We show that, in the short-term sensing scenario, this protocol improves the network's performance compared to the existing threshold-based protocol. In the second half of the thesis, we study two recently emerged networks, where devices have the ability to: (i) communicate directly with nearby devices under the control of BSs (i.e., device-to-device (D2D) communication), and (ii) harvest radio frequency energy (i.e., energy harvesting networks). We first analyze the intra-cell interference in a finite cellular region underlaid with D2D communication, by incorporating a mode selection scheme to reduce the interference. We derive the outage probability at the BS and a D2D receiver, and propose a spectrum reuse ratio metric to assess the overall D2D communication performance. We demonstrate that, without impairing the performance at the BS, if the path-loss exponent on cellular link is slightly lower than that on D2D link, the spectrum reuse ratio can have negligible decrease while the average number of successful D2D transmissions increases with the increasing D2D node density. This indicates that an increasing level of D2D communication is beneficial in future networks. Then we study an ad-hoc network with simultaneous wireless information and power transfer in an infinite region, where transmitters are wirelessly charged by power beacons. We formulate the total outage probability in terms of the power and channel outage probabilities. The former incorporates a power activation threshold at transmitters, which is a key practical factor that has been largely ignored in previous work. We show that, although increasing power beacon's density or transmit power is not always beneficial for channel outage probability, it improves the overall network performance