When Power Adaptation is Useless or Harmful

We consider the design of optimal strategies for joint power adaptation, rate adaptation and scheduling in a multi-hop wireless network. Most existing strategies for ad-hoc networks control either power and scheduling, or rates and scheduling, but not the three together as we do. We assume the underlying physical layer allows finegrained rate adaptation (like in 802.11a/g, HDR/CDMA, UWB). Our goal is to find properties of the power control in an optimal joint design. In the linear regime (i.e when the rate of a link can be approximated by a linear function of signal-to-noise ratio, SNR), we prove analytically that it is always optimal to use the simple 0 − P MAX power control (when a node is sending it uses the maximum transmitting power allowed). This holds in both important networking scenarios: high rate networks where the goal is to maximize rates under power constraints, and low power networks where the goal is to minimize average consumed power while meeting minimum rate constraints. Moreover, we prove that, when maximizing rates, 0−P MAX is the only possible optimal power control strategy. Outside the linear regime, we do not know what the optimal power control is. We show that in the power minimization scenario, in some cases, rate adaptation and 0 − P power control performs much worse than power adaptation. Nevertheless, we conjecture, and we demonstrate numerically that when maximizing rates, even outside the linear regime, 0− P MAX is very close to the optimal power control, and the rate adaptation with 0 − P outperforms power adaptation with fixed link rates.