The energy harvesting multiple access channel with energy storage losses

This work considers a Gaussian multiple access channel with two energy harvesting transmitters with lossy energy storage. The power allocation policy maximizing the average weighted sum rate given the energy harvesting profiles is found. In particular, it is shown that the optimal policy has a double-threshold structure on each of the transmit powers, while the two transmit powers interact through the multivariate achievable rate function which determines the thresholds. For the special case of sum rate maximization in a Gaussian MAC channel, it is shown that the thresholds apply to the sum power, and the optimal policy consists of three thresholds, rather than four, which enables the user with a more efficient battery to be given priority in energy storage.