# SWIPT Signalling over Frequency-Selective Channels with a Nonlinear Energy Harvester: Non-Zero Mean and Asymmetric Inputs

## TL;DR

This paper investigates SWIPT over frequency-selective channels with nonlinear energy harvesters, showing that non-zero mean Gaussian inputs outperform zero mean inputs in maximizing the rate-power region.

## Contribution

It derives a general power expression considering nonlinear harvesters and develops an optimization algorithm for power allocation with non-zero mean Gaussian inputs.

## Key findings

- Non-zero mean Gaussian inputs expand the RP region.
- Asymmetric power allocation improves performance.
- Nonlinear energy harvesting alters optimal input distributions.

## Abstract

Simultaneous Wireless Information and Power Transfer (SWIPT) over a point-to-point frequency-selective Additive White Gaussian Noise (AWGN) channel is studied. Considering an approximation of the nonlinearity of the harvester, a general form of delivered power in terms of system baseband parameters is derived, which demonstrates the dependency of the delivered power on higher order moment of the baseband channel input distribution. The optimization problem of maximizing Rate-Power (RP) region is studied. Assuming that the Channel State Information (CSI) is available at both the receiver and the transmitter, and constraining to non-zero mean Gaussian input distributions, an optimization algorithm for power allocation among different subchannels is studied. As a special case, optimality conditions for zero mean Gaussian inputs are derived. Results obtained from numerical optimization demonstrate the superiority of non-zero mean Gaussian inputs (with asymmetric power allocation in each complex subchannel) in yielding a larger RP region compared to their zero mean and non-zero mean (with symmetric power allocation in each complex subchannel) counterparts. This severely contrasts with SWIPT design under linear energy harvesting, for which circularly symmetric Gaussian inputs are optimal.