  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.
