Multiple access and two-way channels with energy harvesting and bi-directional energy cooperation

This paper considers the multiple access and two-way channels with energy harvesting transmitters that can cooperate by transferring energy to each other. Specifically, the jointly optimal transmit power allocation and energy transfer policies that achieve the sum-capacity in both models are found. These models were first considered in previous work with unidirectional energy transfer, and optimal policies were found using a two-dimensional water-filling algorithm. In this paper, the bi-directional extension of the energy cooperation model is considered. Using an equivalent energy transfer efficiency representation, it is found that in the optimal policy, a node cannot simultaneously send and receive energy. It is shown that a class of power policies termed procrastinating policies include at least one optimal policy, leading to the insight that the resulting power allocation problem can be solved by a one-dimensional directional water-filling algorithm. It is observed that in the multiple access channel, a node either transfers no energy, or transfers all of its energy to a single user to achieve sum-capacity. For the two-way channel, the optimal policy is found to have a directional water-filling interpretation with two non-mixing fluids whenever optimal energy transfer is non-zero.