Energy harvesting communication system with a finite set of transmission rates

A point-to-point communication system in which the transmitter is equipped with an energy harvesting (EH) device and a rechargeable battery of limited size is considered. The harvested energy profile is assumed to be known in advance, that is, the problem is studied in the offline optimization framework. A practical communication system is considered, in which the possible transmission rates, and equivalently, power levels, belong to a finite set of discrete values. This problem is formulated as a convex optimization problem, which can be solved numerically. In order to provide further insights into the nature of the optimal transmission policy, an alternative solution is provided based on the solution of the continuous version of this problem, which itself has a "shortest path" interpretation. We propose an optimal algorithm, which permits us to easily build the solution of the discrete case from the continuous case, using an equivalence notion between different transmission policies, and several equivalence-preserving transformations.