Abstract
We study the optimum designs of a wireless ad hoc network that employs a random multiple access protocol and operates in an interference-limited environment. The nodes are assumed to form a homogeneous Poisson point process (PPP). With the random multiple access protocol, each node transmits with a certain probability, the value of which is critical to system performance. A higher transmission probability means more transmission opportunities for a node, but at the cost of more interference from other nodes in the network due to more simultaneous transmissions. For half-duplex nodes that cannot transmit and receive at the same time, a higher transmission probability will also decrease the probability that a node is in the receiving mode. The objective of this paper is to identify the optimum transmission probabilities of the ad hoc network. Two performance metrics are considered, the connectivity probability and the random access transport capacity (RATC), which are derived as closed-form expressions of system parameters by considering the effects of channel propagations, interference, and the stochastic geometric of node distributions. The optimum transmission probabilities that can maximize the connectivity probability or RATC are then obtained for half-duplex and full-duplex systems, respectively.
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