Delay-constrained distortion minimization for energy harvesting transmission over a fading channel

Distortion minimization for an energy harvesting sensor node communicating over a fading channel is studied. Slotted transmission is considered such that, new source samples and energy packets arrive at the beginning of each time slot (TS), and the fading channel state changes from one TS to the next. A delay constraint is imposed requiring each source sample to be reconstructed at the destination d TSs after its arrival. Assuming independent Gaussian samples with variances changing over TSs, total distortion is minimized under the offline optimization framework, i.e., energy arrivals, source variances and channel gains are assumed to be known non-causally. Optimal compression rates and transmission powers are found and some properties of the optimal strategy are discussed. A two-dimensional water-filling interpretation of the optimal solution is provided for a battery-run node with d = 1.