# Adaptive Clustering of Users in Power Domain NOMA
###### Abstract
The paper focused on the beamforming method and used the well-known user-clustering method [20] based on paring users with the maximum channel gain difference. Although providing a significant increase in spectral efficiency, NOMA systems also increase energy consumption. Therefore, in [21], a solution for user clustering and power allocation was studied to maximize the energy efficiency under maximal transmission power, minimum data transmission rate requirement and SIC requirement. The clustering method has two steps: initially, pairs of users with the most significant differences between channel gains are formed, and each group is associated with a cluster. By Lagrange multipliers, each power coefficient is determined. The authors in [22] studied joint power control and user clustering for downlink NOMA to minimize the total power consumption by considering the transmission power and the decoding power of the users, which is ignored in many works. The problem is transformed into an equivalent problem with tractable constraints. Then, an optimization algorithm dealt with the reformulated problem using re-weighted \(t_{1}\)-norm minimization and majorization-minimization techniques. The user clustering effects and power allocation in downlink and uplink NOMA systems were investigated by [23]. In this work, users are clustered in groups of two, four and six users, according to the difference in their channel's gain, prioritizing users with the best channel conditions. In each group, the power coefficients of the users are optimized by Lagrange multipliers. In [24], the authors investigated the impact of user clustering over the reachable diversity order in a downlink NOMA system. A joint user clustering and subcarrier allocation scheme was proposed with enhanced minimum diversity order. In the worst case, this method allows the user with the highest outage probability to reach the same order of diversity that would be obtained using an exhaustive search scheme. Adopting a different approach from other works, the authors in [25] proposed a user clustering scheme in a hybrid downlink NOMA system based on a genetic algorithm. The objective was to maximize the overall system throughput with no limit of users in every cluster. In the simulations, it was observed in several scenarios that the proposed scheme approached the optimal solution for any number of users present in a cluster. A joint optimization design of beamforming and power allocation in the downlink NOMA-based satellite-terrestrial integrated network (STIN) operating at mmWave band was proposed in [26]. A multiuser downlink framework was presented to integrate a system where satellite networks exploit multicast communication and coexist with a cellular network that implements NOMA. For this, a new user pairing scheme was presented based on channel gain and correlation. The new method obtained the optimal solution of beamforming weight vectors and power coefficients, thus, improving the computational efficiency. In [27], a clustering model was proposed using the method of pairing two users or three users together and combining the signal-to-noise ratio (SNR) levels to decide on two or three pairings in order to ensure the quality of service (QoS) for users. The method is divided into two stages, the first clustering using the users' spatial location information by the K-means algorithm. Then, maintenance of these clusters is conducted to separate those users that do not satisfy the clustering conditions and then attempt to rejoin or transmit them by OMA. The results showed that the proposed model guarantees the quality of service requirements. An adaptive multi-user clustering algorithm was proposed in [28]. The proposed model uses a combination of the traditional model with an adaptation step. The traditional model consists of ordering users by channel gain value and grouping more users with higher gain values with those with lower gain values.