Minimum energy per bit for Gaussian broadcast channels with common message and cooperating receivers

This paper considers a three-terminal communication problem with one source node which broadcasts a common message to two destination nodes over a wireless medium. The destination nodes can cooperate over bidirectional wireless links. We study the minimum energy per information bit for this setup when there is no constraint on the available bandwidth. The physical link between any pair of nodes is affected by additive white Gaussian noise and circularly symmetric fading. The channel states are assumed to be not known at the transmitters. We show information-theoretic converse bounds on the minimum possible energy expenditure per information bit. These bounds are then compared against the achievable energy per bit using a decode-and-forward scheme which is shown to be weaker than the converse bounds by a factor of at most two for all cases of channel gains. For many cases of channel gains, decode-and-forward achieves the minimum energy per bit exactly. For the cases where the performance of decode-and-forward does not meet the converse bounds, we propose another scheme based on estimate-and-forward, assuming only phase-fading which is known at the receivers. For the particular cases of symmetric channel gains, we show that estimate-and-forward improves upon decode-and-forward, and is weaker than the converse bounds by at most a factor of 1.74.