## 1 Introduction
Thus, SU can be selected as UR by USU in either MG. UR selection probability increases. At the same time, the efficient relay selection range (ERSR) is set to maximal value, i.e., ETR. The SU density in the vicinity of USU is not taken into consideration. When one USU locates in the range near the BS, where the density of SU is high, the largest ERSR covers maximum number of SU. Besides, owing to the small path loss, almost all of the SUs in the ETR of USU can be selected as UR. According to the condition of UR selection, each UR ensures that USU he (she) serves receives successfully. So the UR redundancy exists in this range. It is more serious in COM-NOMA than that in CM-OFDMA. The coverage efficiency (coverage efficiency is defined as the ratio of successful users to URs) performance is deteriorated. But in the range near the edge of the cell, where the density of SU is low, there is even no SU in the vicinity of USU, the maxmal ERSR is necessary to cover as many SUs as possible. According the different ranges where the USU locates, it is reasonable to adjust the ERSR. However, in COM-NOMA, the ERSR is fixed and equal to ETR. Besides, when UR forwards data in the manner of D2D, the cooperative users with non-cooperative behavior, such as the selfishness of user, may lead to a sharp decline in network performance [11]. However, one assumption made by all above researches is that every MG user is accommodating. USU can be served by as many URs as requirement. Therefore, from the perspective of system, under this assumption, it is essential to reduce UR redundancy. Especially for wireless sensors network, when sensors are arranged in physical environment, power supply for them is insufficient [12; 13]. Aiming at reducing UR redundancy, we propose a region-division UR selection scheme (termed as RDUR) as an enhanced scheme in COM-NOMA systems. To maximize its coverage efficiency performance, different ERSRs are allocated to different ranges where USU locates. Firstly, the circular coverage area of the cellular is divided into continuous annular areas (AAs). Different ERSRs are assigned to AAs. USUs in the same AA have the same ERSR. Secondly, the ERSR radius set of cellular which maximizes the coverage efficiency is taken to perform UR selection. The main contributions of this paper are summarized as follows:  
* Under the influence of large-scale fading, from cell edge to center, the density of SU experiences a gradual upturn. Considering this, RDUR supplies optional radius for USU's ERSR to reduce the number of unnecessary URs. Simulation results shows that the coverage efficiency increases by at least 14% in comparision to the original UR selection scheme of COM-NOMA systems. The capacity efficiency of the second-stage D2 MD has been improved. RDUR can motivate that smaller ERSRs is allocated to the cell-center AAs in high probability to reduce UR redundancy and larger ERSRs are allocated to the cell-edge AAs in high probability to ensure successful receive. * The number of UR in the ERSR of USU after the first stage of COM-NOMA follows Poisson distribution. The parameter of Poisson distribution is derived. Simulation results show that the analytic result matches well with the simulated one. It verifies that UR redundancy exists in COM-NOMA with original UR selection scheme, when the number of MG user is high (more than 100). * Under different ERSR radius sets, by utilizing the characteristics of Poisson distribution that its parameter is equal to its mathematical expectation, the expressions of UR selection ratio is derived. In this paper, after RDUR, the coverage ratio of the second stage is also given. Through simulation, it is supported that different ERSR assignments can effect the UR selection ratio and coverage ratio. The analytic result accurately reflects simulated one. The rest of this paper is organized as follows. We describe the two-stage COM-NOMA in Section 2. In Section 3, RDUR is proposed. Performance analysis for different ERSR radius sets is in Section 4.