Energy efficiency of decode-and-forward for wideband wireless multicasting

In this paper, we study the minimum energy per bit required for communicating a message to all the destination nodes in a wireless network. The physical layer is modeled as an additive white Gaussian noise (AWGN) channel affected by circularly symmetric fading. The fading coefficients are known at neither transmitters nor receivers. We provide an information-theoretic lower bound on the energy requirement of general multicasting in arbitrary networks as the solution of a linear program, when no restrictions are placed on the bandwidth or the delay. We study the performance of decode-and-forward operating in the noncoherent wideband scenario, and compare it with the lower bound, for a variety of network classes where all nonsource nodes are destinations. For three-terminal networks with one source and two cooperative destination nodes, the energy expenditure of decode-and-forward is shown to be at most twice the lower bound and optimal in many cases. We also show that for arbitrary networks with k nodes, the energy requirement of decode-and-forward is at most k-1 times that of the lower bound regardless of the magnitude of channel gains. In networks that can be represented as directed acyclic graphs (DAGs), we establish the minimum energy per bit, also achieved by decode-and-forward. In addition, we also study regular networks where the energy consumption of decode-and-forward is shown to be almost order optimal in many situations of interest.