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

AWGN Channel under Time-Varying Amplitude Constraints with Causal Information at the Transmitter