On the Optimal Power Allocation for Broadcasting in Dense Cooperative Networks

We study the optimal power allocation problem for cooperative broadcast in dense large-scale networks. In our set-up, a single source initiates the transmission and the nodes that receive the message with sufficient signal-to-noise ratio (SNR) retransmit. The goal is to design the transmission order (schedule) and the transmission powers of the relays so that the message reaches to the entire network with the minimum possible power expenditure. In general, finding the best scheduling in cooperative broadcast is known to be NP-complete. In this paper, we show that the optimal scheduling is easily resolved for certain network topologies and channel models. Furthermore, we approximate dense large-scale networks with a continuum of nodes and provide optimal power density for the continuum network under pathloss attenuation