  The capacity of a complex and discrete-time memoryless additive white
Gaussian noise (AWGN) channel under three constraints, namely, input average
power, input amplitude and output delivered power is studied. The output
delivered power constraint is modelled as the average of linear combination of
even moments of the channel input being larger than a threshold. It is shown
that the capacity of an AWGN channel under transmit average power and receiver
delivered power constraints is the same as the capacity of an AWGN channel
under an average power constraint. However, depending on the two constraints,
the capacity can be either achieved by a Gaussian distribution or arbitrarily
approached by using time-sharing between a Gaussian distribution and On-Off
Keying. As an application, a simultaneous wireless information and power
transfer (SWIPT) problem is studied, where an experimentally-validated
nonlinear model of the harvester is used. It is shown that the delivered power
depends on higher order moments of the channel input. Two inner bounds, one
based on complex Gaussian inputs and the other based on further restricting the
delivered power are obtained for the Rate-Power (RP) region. For Gaussian
inputs, the optimal inputs are zero mean and a tradeoff between transmitted
information and delivered power is recognized by considering asymmetric power
allocations between inphase and quadrature subchannels. Through numerical
algorithms, it is observed that input distributions (obtained by restricting
the delivered power) attain larger RP region compared to Gaussian input
counterparts.
