Characterization of the fundamental properties of wireless CSMA multi-hop networks

A wireless multi-hop network consists of a group of decentralized and self-organized wireless devices that collaborate to complete their tasks in a distributed way. Data packets are forwarded collaboratively hop-by-hop from source nodes to their respective destination nodes with other nodes acting as intermediate relays. These networks can be used to collect and exchange data for a variety of applications in both civilian and military elds. Existing and future applications in wireless multi-hop networks will greatly bene t from better understanding of the fundamental properties of such networks. This thesis is concerned with wireless multi-hop networks operating with distributed Media Access Control (MAC) protocols Carrier Sense Multiple Access (CSMA) protocols. In recent decades, CSMA protocols have become prevailing with widespread adoption. In this thesis we explore two fundamental properties of wireless CSMA multi-hop networks, connectivity and capacity. We start o with investigating the connectivity of wireless CSMA multi-hop networks. A network is said to be connected if and only if there is at least one (multi-hop) path between any pair of nodes in the network. Despite that interference is a major performance-limiting factor, the research results reported in the literature is very limited on the connectivity properties of wireless multi-hop networks where the impact of interference is taken into account. Therefore in this thesis we investigate the critical transmission power for asymptotic connec-