  Wireless powered sensor networks (WPSNs) have emerged as a key development
towards the future self-sustainable Internet of Things (IoT) networks. To
achieve a good balance between self-sustainability and reliability, partially
WPSNs with a mixed power solution are desirable for practical applications.
Specifically, most of the sensor nodes are wireless powered but the key sensor
node adopts traditional wire/battery power for reliability. As a result, this
paper mainly investigates optimal design for the partially WPSNs in which
simultaneous wireless information and power transfer (SWIPT) is adopted in the
downlink. Two scenarios with space division multiple access (SDMA) and time
division multiple access (TDMA) in the uplink are considered. For both the
SDMA-enabled and TDMA-enabled partially WPSNs, joint design of downlink
beamforming, uplink beamforming and time allocation is investigated to maximize
the uplink sum rate while guaranteeing the quality-of-service (i.e., satisfying
the downlink rate constraint) at the key sensor node. After analyzing the
feasibility of uplink sum rate maximization problems and the influence of the
downlink rate constraint, semi-closed-form optimal solutions for both
SDMA-enabled and TDMA-enabled WPSNs are proposed with guaranteed global
optimality. Complexity analysis is also provided to justify the advantage of
the proposed solutions in low complexity. The effectiveness and optimality of
the proposed optimal solutions are finally demonstrated by simulations.
