  Integrating different functionalities, conventionally implemented as
dedicated systems, into a single platform allows utilising the available
resources more efficiently. We consider an integrated sensing and power
transfer (ISAPT) system and propose the joint optimisation of the rectangular
pulse-shaped transmit signal and the beamforming vector to combine sensing and
wireless power transfer (WPT) functionalities efficiently. In contrast to prior
works, we adopt an accurate non-linear circuit-based energy harvesting (EH)
model. We formulate and solve a non-convex optimisation problem for a general
number of EH receivers to maximise a weighted sum of the average harvested
powers at the EH receivers while ensuring the received echo signal reflected by
a sensing target (ST) has sufficient power for estimating the range to the ST
with a prescribed accuracy within the considered coverage region. The average
harvested power is shown to monotonically increase with the pulse duration when
the average transmit power budget is sufficiently large. We discuss the
trade-off between sensing performance and power transfer for the considered
ISAPT system. The proposed approach significantly outperforms a heuristic
baseline scheme based on a linear EH model, which linearly combines energy
beamforming with the beamsteering vector in the direction to the ST as its
transmit strategy.
