Joint Transmit Signal and Beamforming Design for Integrated Sensing and Power Transfer Systems

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 design 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 a non-convex optimisation problem for a general number of EH receivers and a single sensing target (ST) and solve the problem via a grid search over the pulse duration, semidefinite relaxation (SDR), and successive convex approximation (SCA). The average harvested power is shown to monotonically increase with the pulse duration when the average transmit power budget is large. We discuss the trade-off between sensing performance and power transfer of the 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.