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

TL;DR

This paper characterizes the capacity of complex AWGN channels under nonlinear power constraints, showing when Gaussian or time-sharing distributions achieve capacity, and applies these results to optimize simultaneous wireless information and power transfer (SWIPT).

Contribution

It provides a comprehensive analysis of capacity-achieving distributions under nonlinear power constraints and introduces new bounds for SWIPT rate-power tradeoffs using experimentally validated models.

Findings

Capacity under power constraints equals that with only average power constraint.

Optimal input distributions can be Gaussian or time-sharing, depending on constraints.

Input distributions with restricted delivered power outperform Gaussian inputs in the RP region.

Abstract

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.