Capacity Region of MISO Broadcast Channel for Simultaneous Wireless Information and Power Transfer

This paper studies a multiple-input single-output (MISO) broadcast channel (BC) featuring simultaneous wireless information and power transfer (SWIPT), where a multi-antenna access point (AP) delivers both information and energy via radio signals to multiple single-antenna receivers simultaneously, and each receiver implements either information decoding (ID) or energy harvesting (EH). In particular, pseudo-random sequences that are {\it a priori} known and therefore can be cancelled at each ID receiver is used as the energy signals, and the information-theoretically optimal dirty paper coding (DPC) is employed for the information transmission. We characterize the capacity region for ID receivers under given energy requirements for EH receivers, by solving a sequence of weighted sum-rate (WSR) maximization (WSRMax) problems subject to a maximum sum-power constraint for the AP, and a set of minimum harvested power constraints for individual EH receivers. The problem corresponds to a new form of WSRMax problem in MISO-BC with combined maximum and minimum linear transmit covariance constraints (MaxLTCCs and MinLTCCs), which differs from the celebrated capacity region characterization problem for MISO-BC under a set of MaxLTCCs only and is challenging to solve. By extending the general BC-multiple access channel (MAC) duality, which is only applicable to WSRMax problems with MaxLTCCs, and applying the ellipsoid method, we propose an efficient algorithm to solve this problem globally optimally. Furthermore, we also propose two suboptimal algorithms with lower complexity by assuming that the information and energy signals are designed separately. Finally, numerical results are provided to validate our proposed algorithms.