Power allocation in the energy harvesting full-duplex Gaussian relay channels

In this paper, we propose a general model to study the full-duplex non-coherent decode-and-forward Gaussian relay channel with energy harvesting (EH) nodes, called NC-EH-RC, in three cases: i) no energy transfer (ET), ii) one-way ET from the source (S) to the relay (R), and iii) two-way ET. We consider the problem of optimal power allocation in NC-EH-RC in order to maximize the total transmitted bits from S to the destination in a given time duration. General stochastic energy arrivals at S and R with known EH times and amounts are assumed. In NC-EH-RC with no ET, the complicated min-max optimization form along with its constraints make the problem intractable. It is shown that this problem can be transformed to a solvable convex optimization form; however, convex optimization solution does not provide the structural properties of the optimal solution. Therefore, following an alternative perspective, we investigate conditions on harvesting process of S and R where we find optimal algorithmic solution. Further, we propose some suboptimal algorithms and provide some examples, in which the algorithms are optimal. Moreover, we find a class of problems for NC-EH-RC with one-way ET from S to R, where the optimal algorithmic solution is devised. For NC-EH-RC with two-way ET, we propose general optimal algorithmic solution. Furthermore, the performance of the proposed algorithms are evaluated numerically and compared with optimal numerical convex optimization tools.