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

Simultaneous Wireless Information and Power Transmission (SWIPT) over a point-to-point frequency-selective channel is studied. Leveraging a small-signal model for a nonlinear energy 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 moments of the baseband channel input. 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. The results motivate the design of new modulation for SWIPT and contrast with SWIPT design under linear energy harvesting, for which circularly symmetric Gaussian inputs with water-filling power allocation are optimal.