Capacity Region of MISO Broadcast Channel with SWIPT

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). 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 has not been addressed in the literature and is challenging to solve. By extending the general BC-multiple access channel (MAC) duality [11], 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. Numerical results are presented to validate our proposed algorithm.