Energy efficiency optimization for multi-user MISO swipt systems

This paper considers a power splitting based multi-user multiple-input-single-output (MISO) downlink system with simultaneous wireless information and power transfer. Assuming that the most common zero-forcing (ZF) beam-forming scheme is employed by the base station, we aim to maximize the system energy efficiency in bits per Joule by joint beamforming and power splitting (PS) under both the signal-To-interference-plus-noise ratio constraints and energy harvesting constraints. The energy efficiency optimization (EEO) problem is nonconvex and very hard to solve. In this paper, by exploiting the problem structure, we first simplify the EEO problem to a joint transmit power allocation and receive power splitting problem. Then, with a tactful reformulation, we propose a Lagrangian relaxation (LR) method coupled with Dinkelbach method to address the simplified EEO problem. It is proven that the proposed LR method can guarantee at least a feasible solution, which is a notable advantage over the existing methods. Finally, numerical results validate the excellent efficiency of the proposed algorithms.