  We first consider an energy harvesting channel with fading, where only the
transmitter harvests energy from natural sources. We bound the optimal long
term throughput by a constant for a class of energy arrival distributions. The
proposed method also gives a constant approximation to the capacity of the
energy harvesting channel with fading. Next, we consider a more general system
where both the transmitter and the receiver employ energy harvesting to power
themselves. In this case, we show that finding an approximation to the optimal
long term throughput is far more difficult, and identify a special case of unit
battery capacity at both the transmitter and the receiver for which we obtain a
universal bound on the ratio of the upper and lower bound on the long term
throughput.
