Probabilistic-constrained robust secure transmission for energy harvesting over MISO channels

In this paper, we consider a system supporting simultaneous wireless information and power transfer (SWIPT), where the transmitter delivers private message to a destination receiver (DR) and powers to multiple energy receivers (ERs) with multiple single-antenna external eavesdroppers (Eves). We study secure robust beamformer and power splitting (PS) design under imperfect channel state information (CSI). The artificial noise (AN) scheme is further utilized at the transmitter to provide strong wireless security. We aim at maximizing the energy harvested by ERs subject to the transmission power constraint, a range of outage constraints concerning the signal-to-interference-plus-noise ratio (SINR) recorded at the DR and the Eves, as well as concerning the energy harvested at the DR. The energy harvesting maximization (EHM) problem is challenging to directly solve, we resort to Bernstein-type inequality restriction technique to reformulate the original problem as a tractable approximated version. Numerical results show that our robust beamforming scheme outperforms the beamforming scheme relying on the worst-case design philosophy.