We study the problem of finding optimal transmission policies in a point-to-point energy harvesting communication system with continuous energy arrivals in causal setting. In particular, we investigate bounds on the long-term achievable average throughput and corresponding power policies, where energy packets of random size arrive at the transmitter at random times, modelled as a compound Poisson dam.In this work, we also account for battery life and quality of service of the users. We thus formulate non-linear constrained maximization problems. Specifically, we limit the instantaneous battery depletion rate (i.e., transmission power) as well as its variation to account for prolonging the battery life. Moreover, we limit the variation of instantaneous throughput to maintain it to a constant level to account for improving the quality of service.Using the theory of calculus of variations as a powerful mathematical tool, we derive necessary conditions in the form of first order non-linear ODEs, for local and thus global optimality of solutions to the optimization problems. We also obtain numerical as well as analytical upper bounds for the problem of constrained proper functions of transmission power. Numerically solving the ODEs for the case of a Gaussian channel, we also compute achievable throughputs and locally optimal power policies as a function of battery capacity and remaining battery charge, respectively.
展开▼
