Capacity bounds for ad hoc and hybrid wireless networks

We study the capacity of static wireless networks, both ad hoc and hybrid, under the Protocol and Physical Models of communication, proposed in [1]. For ad hoc networks with <i>n</i> nodes, we show that under the Physical Model, where signal power is assumed to attenuate as 1/r<sup>α</sup>, α > 2, the transport capacity scales as Θ(√<i>n</i>) bit-meters/sec. The same bound holds even when the nodes are allowed to approach arbitrarily close to each other and even under a more generalized notion of the Physical Model wherein the data rate is Shannon's logarithmic function of the SINR at the receiver. This result is sharp since it closes the gap that existed between the previous best known upper bound of O(<i>n</i><sup>α-1/α</sup>) and lower bound of Ω(√n). We also show that any spatio-temporal scheduling of transmissions and their ranges that is feasible under the Protocol Model can also be realized under the Physical Model by an appropriate choice of power levels for appropriate thresholds. This allows the generalization of various lower bound constructions from the Protocol Model to the Physical Model. In particular, this provides a better lower bound on the best case transport capacity than in [1]. For hybrid networks, we consider an overlay of μ<i>n</i> randomly placed wired base stations. It has previously been shown in [6] that if all nodes adopt a common power level, then each node can be provided a throughput of at most Θ(1/log <i>n</i>) to randomly chosen destinations. Here we show that by allowing nodes to perform power control and properly choosing ν(1/log <i>n</i>), it is further possible to provide a throughput of Θ(1) to any fraction <i>f</i>, 0 < <i>f</i> < 1, of nodes. This result holds under both the Protocol and Physical models of communication. On the one hand, it shows that that the aggregate throughput capacity, measured as the sum of individual throughputs, can scale linearly in the number of nodes. On the other hand, the result underscores the importance of choosing minimum power levels for communication and suggests that simply communicating with the closest node or base station could yield good capacity even for multihop hybrid wireless networks.