ALOHA Performs Delay-Optimum Power Control

As a fundamental source of delay in wireless networks, the local delay is defined as the mean time, in number of time slots, until a packet is successfully received (decoded) over a link. This paper shows that with mean power and peak power constraints at each node, power control can significantly reduce the local delay. We show that, for links with Rayleigh fading and random length, there exists a simple power control strategy, which turns out to be optimal in reducing the local delay. This strategy acts as an ALOHA-type random on-off power control policy whose parameters depend on the link distance. The optimal power control policy as well as its variations are compared with constant power transmission and other simple random power control policies.