ALOHA performs optimal power control in Poisson networks

This paper studies power control strategies in interference-limited wireless networks with Poisson distributed nodes. We focus on the case where each transmitter knows its distance to its desired receiver but does not know the topology of the rest of the network. We study three sets of strategies: the single-node optimal power control (SNOPC) strategy, the Nash equilibrium power control (NEPC) strategy, and the globally optimal power control (GOPC) strategy. SNOPC strategies maximize the expected throughput of the power controllable link given that all the other transmitters do not use power control. Under NEPC strategies, no individual node of the network can achieve a higher expected throughput by unilaterally deviating from these strategies. The GOPC strategy maximizes the throughput of a typical node in the network. This paper shows that under mean and peak power constraints at each transmitter, all of the three strategies are ALOHA-type random on-off power control policies in bipolar networks. For links of iid random distances, we show both SNOPC and NEPC strategies are ALOHA-type random on-off policies. These results suggest that ALOHA can be viewed not only as a MAC scheme but also as an efficient and stable power control scheme.