On lossy source-channel transmission in Energy Harvesting communication systems

Continuous-time lossy source transmission in an Energy Harvesting (EH) communication system is studied. In particular, the distortion performance for the transmission of a Gaussian source and compound Poisson energy arrivals is considered. Based on the convexity of the distortion function and Jensen´s inequality, a lower bound on the average distortion is established in terms of the capacity of the battery and parameters such as the distribution of energy arrivals and the variance of the source. Moreover, a calculus of variations technique is used to derive an adaptive transmission power policy as well as an adaptive mismatch factor. More specifically, the structure of a locally optimal achievable power policy is characterized as the solution to a first order non-linear ordinary differential equation (ODE). Also for the mismatch factor, a closed-form formula as a function of the battery charge via the LambertW function is derived.