Optimal power allocation for a renewable energy source

Battery powered transmitters face energy constraint, replenishing their energy by a renewable energy source (like solar or wind power) can lead to longer lifetime. We consider here the problem of finding the optimal power allocation under random channel conditions for a wireless transmitter, such that rate of information transfer is maximized. Here a rechargeable battery, which is periodically charged by renewable source, is used to power the transmitter. All of above is formulated as a Markov Decision Process. Structural properties like the monotonicity of the optimal value and policy derived in this paper will be of vital importance in understanding the kind of algorithms and approximations needed in real-life scenarios. The effect of curse of dimensionality which is prevalent in Dynamic programming problems can thus be reduced. We show our results under the most general of assumptions.