  This paper investigates the optimal transmit beamforming design of
simultaneous wireless information and power transfer (SWIPT) in the multiuser
multiple-input-single-output (MISO) downlink with specific absorption rate
(SAR) constraints. We consider the power splitting technique for SWIPT, where
each receiver divides the received signal into two parts: one for information
decoding and the other for energy harvesting with a practical non-linear
rectification model. The problem of interest is to maximize as much as possible
the received signal-to-interference-plus-noise ratio (SINR) and the energy
harvested for all receivers, while satisfying the transmit power and the SAR
constraints by optimizing the transmit beamforming at the transmitter and the
power splitting ratios at different receivers. The optimal beamforming and
power splitting solutions are obtained with the aid of semidefinite programming
and bisection search. Low-complexity fixed beamforming and hybrid beamforming
techniques are also studied. Furthermore, we study the effect of imperfect
channel information and radiation matrices, and design robust beamforming to
guarantee the worst-case performance. Simulation results demonstrate that our
proposed algorithms can effectively deal with the radio exposure constraints
and significantly outperform the conventional transmission scheme with power
backoff.
