This paper investigates energy-efficient resource allocation problem for the wireless power transfer (WPT) enabled multi-user massive multiple-input multiple-output (MIMO) systems. In the considered systems, the sensor nodes (SNs) are firstly powered by WPT from the power beacon (PB) with a large scale of antennas. Then, the SNs use the harvested energy to transmit the data to the base station (BS) with multiple antennas. The problem of optimizing the energy efficiency objective is formulated with the consideration of maximum transmission power of the PB and the quality of service (QoS) of the SNs. By adopting fractional programming, the energy-efficient optimization problem is firstly converted into a subtractive form. Then, a joint power and time allocation algorithm based on the block coordinate descent and Dinkelbach method is proposed to maximize energy efficiency. Finally, simulation results show the proposed algorithm achieves a good compromise between the spectrum efficiency and total power consumption.

In this letter, we study the resource allocation for the downlink cooperative non-orthogonal multiple access (NOMA) systems based on the amplifying-and-forward protocol relay transmission. A joint power allocation and amplification gain selection scheme are proposed. Fractional programming and the iterative algorithm based on the Lagrangian multiplier are used to allocate the transmit power to maximize the energy efficiency (EE) of the systems. Simulation results show that the proposed scheme can achieve higher energy efficiency compared with the minimum power transmission (MPT-NOMA) scheme and the conventional OMA scheme.

In this letter, we consider the power allocation scheme with rate proportional fairness to maximize energy efficiency in the downlink the non-orthogonal multiple access (NOMA) systems. The optimization problem of energy efficiency is a non-convex optimization problem, and the fractional programming is used to transform the original problem into a series of optimization sub-problems. A two-layer iterative algorithm is proposed to solve these sub-problems, in which power allocation with the fixed energy efficiency is achieved in the inner layer, and the optimal energy efficiency of the system is obtained by the bisection method in the outer layer. Simulation results show the effectiveness of the proposed algorithm.

Considering worse-case channel uncertainties, we investigate the robust energy efficient (EE) beamforming design problem in a K-user multiple-input-single-output (MISO) interference channel. Our objective is to maximize the worse-case sum EE under individual transmit power constraints. In general, this fractional programming problem is NP-hard for the optimal solution. To obtain an insight into the problem, we first transform the original problem into its lower bound problem with max-min and fractional form by exploiting the relationship between the user rate and the minimum mean square error (MMSE) and using the min-max inequality. To make it tractable, we transform the problem of fractional form into a subtractive form by using the Dinkelbach transformation, and then propose an iterative algorithm using Lagrangian duality, which leads to the locally optimal solution. Simulation results demonstrate that our proposed robust EE beamforming scheme outperforms the conventional algorithm.