# Efficient User-Serving Scheme in the User-Centric Cell-Free Massive MIMO System
## 1 Introduction  
A massive MIMO system is a technology that can achieve high throughput by using a large antenna array, and it has attracted attention as a recent 5G system and a promising future technology [1, 2, 3]. Because of the structural advantages of massive MIMO, recently, much research has been conducted based on that structure [4, 5]. The cell-free massive MIMO system also uses multiple antennas that are called access points (APs) as a massive MIMO, and the APs are geographically distributed [6, 7, 8]. This structure can also achieve the advantages of the previous massive MIMO such as channel hardening and favorable propagation [9]. Due to this network structure, cell-free massive MIMO is robust against the influence of the surrounding environment and shadow fading; so, it can provide uniform spectral efficiency for all users in the area [8, 10, 11]. The early version of this model was that all APs would serve all users, as in [8]. Since the model in [8] requires a very high amount of computational complexity and fronthaul requirements, which increase in proportion to the number of users [11; 12; 13], the initial cell-free model was non-scalable and difficult to apply in reality [14; 15]. To address this disadvantage, the user-centric cell-free massive MIMO concept appeared [16; 17]. The user-centric model was proposed in [18; 19]. In this model, all APs do not serve all users; so, it requires much lower computational complexity and fronthaul requirements compared to the previous cell-free massive MIMO system [18]. Therefore, it is a feasible and scalable approach in terms of actual implementation and computational complexity even as the number of users increases. In a 5G communication system, power consumption and energy efficiency should be carefully considered in addition to conventional indicators such as error probability and sum rate [13]. The original cell-free massive MIMO model in [8] has limitations in terms of power consumption and energy efficiency, since the complexity increases proportionally as the number of users increases. However, the user-centric cell-free massive MIMO model adopted in this paper can reasonably maintain the complexity of the entire system even if the number of users in the area increases, requiring lower power consumption and ensuring energy efficiency. Basically, both the cell-free massive MIMO system model and the user-centric cell-free massive MIMO model assume that the number of antennas is much larger than the number of users of the massive MIMO [8]. However, in a realistic situation, the number of users can also exist in a non-negligible amount, and when there are many users under the user-centric scheme, there is a high possibility that users who can not receive the service exist. To solve this problem, a user-serving scheme for connecting unserved users was proposed [20]. However, this scheme had the following limitations: it did not consider the case in which the number of APs is similar to the number of users as in [21]. Furthermore, when the number of APs and users is almost the same, there is a possibility that other unserved users may occur. In addition, this scheme used a method of simply selecting the closest AP to an unserved user as [22]. In this case, that can damage the data rate of users that are already served in order to serve the unserved user. Therefore, in this paper, when many users exist in the user-centric cell-free massive MIMO system model, the proposed scheme can efficiently serve the unserved users while maintaining service for existing users. By applying the proposed scheme, it is possible to serve new users at the same time without significantly impairing the throughput of existing users. The main contributions of this paper are outlined as follows:  
* We first derive the downlink spectral efficiency in the user-centric cell-free massive MIMO system, which considers the minimum mean square error (MMSE) estimator channel estimation and equal gain power control [8; 19].