  In this paper, we study the waveform and passive beamforming design for
intelligent reflecting surface (IRS)-aided wireless power transfer (WPT).
Generalized multi-user and low complexity single-user algorithms are derived
based on alternating optimization (AO) framework to maximize the weighted sum
output DC current, subject to transmit power constraints and passive
beamforming phases unit modulus constraints. The input signal waveform and IRS
passive beamforming phase shifts are jointly designed as a function of users'
individual frequency-selective channel state information (CSI). The energy
harvester nonlinearity is explored and two IRS deployment schemes, namely
frequency selective IRS (FS-IRS) and frequency flat IRS (FF-IRS), are modeled
and analyzed. This paper highlights the fact that IRS can provide an extra
passive beamforming gain on output DC power over conventional WPT designs and
significantly influence the waveform design by leveraging the benefit of
passive beamforming, frequency diversity and energy harvester nonlinearity.
Even though FF-IRS exhibits lower output DC current than FS-IRS, it still
achieves substantially increased DC power over conventional WPT designs.
Performance evaluations confirm the significant benefits of a joint waveform
and passive beamforming design accounting for the energy harvester nonlinearity
to boost the performance of single-user and multi-user WPT system.
