# Energy-Efficient User Pairing for Downlink NOMA in Massive MIMO Networks
## 1 Introduction
### Background  
An algorithm of low computational complexity is proposed in [20] to solve the user scheduling, link selection, and power allocation problems for D2D cellular networks with NOMA technology. The proposed algorithm achieves high data rates and converges in a limited number of iterations. NOMA and OMA are compared for a large number of BS antennas in [21]. Karush-Kuhn-Tucker (KKT) conditions are used to derive closed-form solution for maximizing the sum rate of downlink NOMA system [22]. Moreover, the pairing of two users of different channel conditions is accomplished using the Hungarian algorithm. The work in [23] studies the joint power allocation and user association for EE maximization in multi-cell multi-carrier NOMA (MCMC-NOMA) networks. A new binary variable matrix for the association is introduced in [24] to allow dynamic pairing for NOMA-assisted downlink networks. The work in [25] applies a clustering strategy of low complexity and introduces KKT optimality conditions to obtain a closed-form result of power allocation for EE maximization in downlink NOMA systems. The stochastic algorithm, two-stage greedy randomized adaptive search (GRASP), and two-stage stochastic sample greedy (SSD) are three heuristic solutions proposed in [26] to optimize the problem of efficient dynamic power and channel allocation (DPCA) for users in the downlink multi-channel NOMA (MC-NOMA) systems. An efficient joint multi-resource-block optimization scheme is proposed in [27] to achieve an optimal weighted achievable rate (WAR) for NOMA-based maritime communications. A NOMA-assisted ambient backscatter communication (AmBC) system is proposed in [28] to increase the achievable sum rate. The work in [29] decomposes the multi-dimensional resource allocation problem for MIMO-NOMA systems into beamforming, user clustering, and power allocation. At first, a fractional transmitting power control (FTPC) is applied. Then, optimal user clustering is considered. Finally, power allocation is introduced as a difference of convex (DC) programming problem to be solved by successive convex approximation (SCA). Hybrid spatial division multiple access (SDMA) and NOMA are combined in [30] for optimal power allocation in sectored cells for sum-throughput maximization. Integer linear programming is adopted in [31] for user pairing, and particle swarm optimization is used for power allocation in NOMA systems in 5G networks. The work in [32] classifies users according to their status into cell-center users, high-rate edge users, and low-rate edge users to participate in many-to-many subchannel-user matching problems to form joint transmission coordinated multi-point (JT-CoMP) subchannels and dynamic point selection CoMP (DPS-CoMP) subchannels. The work in [33; 34; 35; 36] introduced the power allocation solution for maximizing the EE in power domain NOMA. Dynamic power allocation and four different pairing methods for NOMA in heterogeneous networks were introduced in [37]. The EE maximization for an uplink NOMA-assisted mmWave mMIMO system was considered in [38], and a hybrid analog-digital beamforming scheme was proposed to reduce the number of radio frequency chains at the BS. In [39], EE maximization of an uplink hybrid system with NOMA integrated with OMA (HMA) was achieved, and a minimum required rate is pre-defined for each user to guarantee the quality of service. The problem is decoupled into the user-resource block association subproblem, and the power allocation subproblem and (joint user-RB PA) algorithm is proposed. User clustering, sub-channel allocation, and power allocation are jointly considered in the EE optimization problem for the uplink multi carrier-NOMA network in [40]. A user pairing algorithm that ensures the cluster fairness in terms of the sum rate gain is proposed in [41], and a comparison between MIMO-NOMA and MIMO-OMA when users have pre-defined quality of service (QoS) requirements is also conducted.