Optimal probing control for wireless transmission when the payload is negligible

A mobile electronic device needs to periodically connect to a stationary receiver, but the information to transfer is minimal. One such example is the electronic bracelet used in house arrest, where the main purpose is to inform the receiver that the person is in the house. Because the mobile device does not know its current distance from the receiver, it has incentive to first send a low-strength signal to conserve its battery energy. If the low-strength signal fails to reach the receiver, the mobile device then gradually increases its signal strength until a successful connection occurs. By formulating the problem as a dynamic program, we characterize the structure of the optimal probing policy and develop an algorithm to compute it. We also consider a discrete approximation that can be easily implemented in practice. Numerical examples show promising improvement of the derived policy over naive heuristic policies, and that the derived policy is robust when there are small errors in estimating the distribution of the distance between the mobile device and the receiver.