Connectivity, Power and Energy in a Multihop Cellular Packet System

We study large networks of subscriber stations (SSs) with certain common wireless capabilities, and base stations (BSs) having direct connection to the wired infrastructure in addition to common wireless capabilities. SS nodes 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 through other SSs serving as wireless repeaters. The locations of the SSs and BSs are assumed given by a homogeneous planar Poisson process. We evaluate exactly the probability of a potential SS to have a "working" wireless connection to any of the BSs as a function of the densities of the BSs and SSs and the parameters of the wireless links, including random lognormal fading. We derive a lower bound on the t-hop (t arbitrary) outage probability of an SS. We then define the "minimal hop-count router", and calculate the mean number of hops for routes connecting SSs to BSs, and the effect on maximum hop constraints on this mean. We next compute the probability distribution of the transmit power under the assumption of perfect power control. We conclude by calculating an expression for the total mean transmit energy required to transfer a data packet from an SS to a BS and show that this energy is significantly lower than the corresponding value required in a single-hop network operating at the same outage probability. Multi-hoping can therefore save SS battery power and reduce the system's self interference effects.