## 1 Introduction
A feasible attempt was proposed in [43], where a power optimization problem for NOMA systems is formulated mathematically, and its NP-hardness is proved. For tackling the problem, the authors in [43] identify a convex problem by relaxation and then propose an efficient \"relax-then-adjust\" algorithm. Although their schemes can approximately solve the power optimization problem, considering the minimization of energy consumption may not obtain a spectrum efficient result [44]. A more reasonable objective was formulated in [45], where the near-optimal power allocation schemes and suboptimal closed-form solutions were proposed to maximize the system energy efficiency, which is defined by ergodic capacity under unit power consumption. However, the number of users is fixed as two in this work, which conflicts with the NOMA concept. If the desired number of simultaneous transmission users increases, the algorithms will not be available anymore. This drawback significantly limits its practical application in NOMA systems. Focusing on maximizing global energy efficiency, we present a new technique for energy utilization in NOMA systems. The objective is to maximize the NOMA systems' energy efficiency and fully utilize the systems' power budget to enhance wireless transmission performance. We optimize the user clustering strategy and power allocation scheme jointly, which are two of the most basic designs positively affecting the performance of NOMA systems [46]. Specifically, the energy efficiency maximization in downlink NOMA systems is formulated as an optimization problem to achieve the optimal user clustering and power allocation under the constraints of maximal transmission power, minimum data transmission rate requirement, and SIC requirement. Since this problem is NP-hard, we first exploit a quick suboptimal clustering method to assign each user to a subchannel to find an approximate solution with much low complexity. By employing the Lagrangian multiplier method with Karush-Kuhn-Tucker optimality conditions in each subchannel, system energy allocation is further modeled as a dynamic programming model to obtain an optimal solution. As the Lagrangian multiplier method's closed-form expressions are obtained, and our dynamic programming model only involves a small number of steps, it can be efficiently solved in practice. Our solution is compared with representative schemes in terms of energy efficiency. Experimental results show that it can achieve a noticeable improvement in energy utilization. The main contributions of this paper are summarized as follows:  
* By studying the novel NOMA concept's transmission mechanism, an energy-efficient technique is proposed to optimize the user clustering and power allocation designs. * We perform analysis for user clustering results and apply a clustering strategy to group users with a low-complexity. In our solution, the number of users assigned to the same subchannel is not limited. * We introduce the Karush-Kuhn-Tucker optimality conditions to obtain a closed-form result of power allocation in each subchannel via the Lagrangian multiplier method. * We further formulate the target problem as a dynamic programming model, generating an optimal overall system power allocation. The rest of this paper is organized as follows. Section 2 formulates the energy efficiency maximization problem for downlink NOMA systems. Section 3 presents our user clustering and power allocation co-design technique in detail. Section 4 shows the experimental results with discussion. Section 5 concludes this paper.