  In this paper, we study the fundamental limits of simultaneous information
and power transfer over a Rayleigh fading channel, where the channel input is
constrained to peak-power constraints that vary in each channel use by taking
into account high-power amplifier nonlinearities. In particular, a three-party
communication system is considered, where a transmitter aims simultaneously
conveying information to an information receiver and delivering energy to an
energy harvesting receiver. For the special case of static PP constraints, we
study the information-energy capacity region and the associated input
distribution under: average-power and PP constraints at the transmitter, an HPA
nonlinearity at the transmitter, and nonlinearity of the energy harvesting
circuit at the energy receiver. By extending Smith \' mathematical framework,
we show that the optimal input distribution under those constraints is discrete
with a finite number of mass points. We show that HPA significantly reduces the
information energy capacity region. In addition, we derive a closed\-form
expression of the capacity achieving distribution for the low PP regime, where
there is no trade-off between information and energy transfer. For the case
with time-varying PP constraints, we prove that the optimal input distribution
has a finite support by using Shannon\'s coding scheme. Specifically, we
numerically study a particular scenario for the time-varying PP constraints,
where the PP constraint probabilistically is either zero or equal to a non-zero
constant.
