Optimal Transmission Power for Single- and Multi-Hop Links in Wireless Packet Networks With ARQ Capability

In this paper, we rigorously investigate the energy minimization problem for wireless packet networks with automatic repeat request (ARQ) capability. We first formulate the problem for the single-hop case under constrained packet delay and reliability and derive the necessary and sufficient condition for the optimal transmission power at each ARQ stage. We formulate a global rule of optimal transmission power control that achieves optimality regardless of the delay and reliability constraints. Then we extend it to encompass the multi-hop case by dividing the overall problem into two subproblems-energy determination for each ARQ stage and energy distribution among the constituent nodes. We show that the optimality condition established for the single-hop case is also applicable to solve the energy determination problem in the multi-hop case, rendering an optimal solution to the energy distribution problem. Numerical examples reveal that a significant amount of energy is saved by adopting the optimal transmission power and the performance gain is strongly correlated with the decreasing property of the frame error rate