Random Power Control in Poisson Networks

This paper studies power control strategies in interference-limited wireless networks with Poisson distributed nodes. We concentrate on two sets of strategies: single-node optimal power control (SNOPC) strategies and Nash equilibrium power control (NEPC) strategies. 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. We show that under mean and peak power constraints at each transmitter, the SNOPC and NEPC strategies are ALOHA-type random on-off power control policies, whose transmit powers and transmit probabilities depend on the knowledge about the network at each transmitter. Moreover, the resulting NEPC strategies achieve a higher spatial average throughput of the network than constant power transmission. These results suggest that ALOHA can be viewed not only as a MAC scheme but also as a stable and efficient power control scheme.