On Capacity-Achieving Distributions for Complex AWGN Channels Under Nonlinear Power Constraints and Their Applications to SWIPT

摘要

The capacity of deterministic, complex and discrete time memoryless AdditiveWhite Gaussian Noise (AWGN) channel under three constraints, namely, channelinput average power, channel input amplitude and delivered power at the channeloutput is considered. The delivered power constraint is modelled as a linearcombination of even-moment statistics of the channel input being larger than athreshold. It is shown that the capacity of an AWGN channel under transmitaverage power and receiver delivered power constraints is the same as thecapacity of an AWGN channel under an average power constraint, however,depending on the two constraints, it can be either achieved or arbitrarilyapproached. It is also shown that under average power, amplitude and deliveredpower constraints, the optimal capacity achieving distributions are discretewith a finite number of mass points. To establish the results, the confluenthypergeometric functions as well as the output rate of decay of complexGaussian channels are utilized extensively. As an application, a simultaneousinformation and power transfer (SWIPT) problem is studied, where anexperimentally-validated nonlinear model of the harvester is used. Relying onsmall signal analysis approximation, a general form of the deliveredDirect-Current (DC) power in terms of system baseband parameters is derived forindependent and identically distributed (iid) inputs. It is shown that thedelivered power depends on higher order statistics of the channel input. Bydefining the rate-power (RP) region, two inner bounds, one based on complexGaussian inputs and the other based on convexifying the optimizationprobability space, are obtained.