  In this paper, we study information-theoretic limits for simultaneous
wireless information and power transfer (SWIPT) systems employing a practical
nonlinear radio frequency (RF) energy harvesting (EH) receiver. In particular,
we consider a three-node system with one transmitter that broadcasts a common
signal to separated information decoding (ID) and EH receivers. Owing to the
nonlinearity of the EH receiver circuit, the efficiency of wireless power
transfer depends significantly on the waveform of the transmitted signal. In
this paper, we aim to answer the following fundamental question: What is the
optimal input distribution of the transmit waveform that maximizes the rate of
the ID receiver for a given required harvested power at the EH receiver? In
particular, we study the capacity of a SWIPT system impaired by additive white
Gaussian noise (AWGN) under average-power (AP) and peak-power (PP) constraints
at the transmitter and an EH constraint at the EH receiver. Using Hermite
polynomial bases, we prove that the optimal capacity-achieving input
distribution that maximizes the rate-energy region is unique and discrete with
a finite number of mass points. Furthermore, we show that the optimal input
distribution for the same problem without PP constraint is discrete whenever
the EH constraint is active and continuous zero-mean Gaussian, otherwise. Our
numerical results show that the rate-energy region is enlarged for a larger PP
constraint and that the rate loss of the considered SWIPT system compared to
the AWGN channel without EH receiver is reduced by increasing the AP budget.
