Energy optimization in wireless broadcasting through power control

We consider the problem of optimally controlling transmission power in a time-slotted wireless broadcast network. Fixed-length packets and AWGN channels are considered, and a simple ARQ scheme (Send-and-Wait) is used for error control. Packets are retransmitted until a minimum QoS requirement is met for each packet. Transmission powers are chosen from a finite set depending on the number of nodes that have received the packet successfully. The goal is to minimize the total energy expended for each successful packet transmission. The system is studied when the transmitter chooses between two distinct powers, and the results are then extended to multiple powers. It is observed that the optimal policy is always of the separation type. Also, the effect of varying the QoS requirement on the energy and service time is studied.