  Simultaneous Wireless Information and Power Transfer (SWIPT) is subject to
nonlinearity at the energy harvester that leads to significant changes to
transmit signal designs compared to conventional wireless communications. In
this paper, the capacity of a discrete time, memoryless and complex Additive
White Gaussian Noise (AWGN) channel in the presence of a nonlinear energy
harvester at the receiver is studied. Considering the two common nonlinear
energy harvester models introduced in the literature, two sets of constraints
are considered. First the capacity is studied under average power (AP), peak
amplitude (PA) and receiver delivery power (RDP) constraints. The RDP
constraint is modelled as a linear combination of even-moment statistics of the
channel input being larger than a threshold. It is shown that the capacity of
an AWGN channel under AP and RDP constraints is the same as the capacity of an
AWGN channel under an AP constraint, however, depending on the two constraints,
it can be either achieved or arbitrarily approached. It is also shown that
under AP, PA and RDP constraints, the amplitude of the optimal inputs is
discrete with a finite number of mass points. Next, the capacity is studied
under AP, PA and output outage probability (OOP) constraints. OOP is modelled
as satisfying a certain probability inequality for the amplitude of the
received signal being outside of a given interval. Similarly, it is shown that
the amplitude of the optimal input is discrete with a finite number of mass
points.
