Connectivity, Power, and Energy in a Multihop Cellular-Packet System

In this paper, we study a large network of subscriber stations (SSs) with certain common wireless capabilities and base stations (BSs) having direct connections to the wired infrastructure in addition to common wireless capabilities. SSs can communicate with the "outside world" only through the BSs. Connections to SSs without a direct (i.e., a single hop) wireless connection to any BS are established, if possible, through other SSs serving as wireless repeaters. The locations of the SSs and the BSs follow independent homogeneous planar Poisson processes. The propagation channels exhibit signal attenuation with distance and log-normal shadowing. We evaluate exactly the probability of an SS to have a direct wireless connection to any of the BSs and a lower bound on the t-hop (t arbitrary) outage probability of an SS. We then define the minimal hop-count routing algorithm and calculate the mean number of hops for routes connecting SSs to BSs, when a maximum hop-count constraint is imposed. We compute next the probability distribution of the transmit power under the assumption of perfect power control. We conclude by calculating a bound for the total mean transmit energy required to transfer a data packet from an SS to a BS over a minimal hop-count route and show that this energy is significantly lower than the corresponding value in a single-hop network operating at the same outage probability