  We consider the classical AWGN channel where the channel input is constrained
to an amplitude constraint that stochastically varies at each channel use,
independent of the message. This is an abstraction of an energy harvesting
transmitter where the code symbol energy at each channel use is determined by
an exogenous energy arrival process and there is no battery for energy storage.
At each channel use, an independent realization of the amplitude constraint
process is observed by the transmitter causally. This scenario is a
state-dependent channel with perfect causal state information at the
transmitter. We derive the capacity of this channel using Shannon's coding
scheme with causal state information. We prove that the code symbols must be
selected from a finite set in the capacity achieving scheme, as in the case of
Smith. We numerically study the binary on-off energy arrivals where the
amplitude constraint is either zero or a non-zero constant.
