  We consider communication over the AWGN channel with a transmitter whose
battery is recharged with RF energy transfer at random times known to the
receiver. We assume that the recharging process is i.i.d. Bernoulli. We
characterize the capacity of this channel as the limit of an $n$-letter maximum
mutual information rate under both causal and noncausal transmitter knowledge
of the battery recharges. With noncausal knowledge, it is possible to
explicitly identify the maximizing input distribution, which we use to
demonstrate that the capacity with noncausal knowledge of the battery recharges
is strictly larger than that with causal knowledge. We then proceed to derive
explicit upper and lower bounds on the capacity, which are within 1.05
bits/s/Hz of each other for all parameter values.
