Energy efficiency optimization for MISO SWIPT systems with zero-forcing beamforming

This paper considers a power splitting based multiuser multiple-input-single-output (MISO) downlink system with simultaneous wireless information and power transfer, where each single antenna receiver splits the received signal into two streams of different power for decoding information and harvesting energy separately. Assuming that the most common zero-forcing (ZF) beamforming 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 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, whilst devising a nearly closed-form solution for the subproblems involved in the Dinkelbach method. It is proven that the proposed LR method is optimum under some condition and can guarantee at least a feasible solution, which is a notable advantage over the existing methods. Besides, we develop a low complexity EEO algorithm by proportionally distributing the total power to users. Finally, numerical results validate the excellent efficiency of the proposed algorithms.