## 1 Introduction  
With the advancement of high-traffic mobile broadband services, the amount of mobile data has increased sharply. It has been estimated that mobile data will grow tenfold in the next five years [1]. The upcoming 3 GPP 5G standard is designed to provide several gigabits per second throughput to users [2]. Therefore, limited spectrum resources need to be utilized more efficiently. However, it is reported that 20% popular video services produce 80% data [3], which causes the frequency band to be occupied by the same service repeatedly. Spectrum resources cannot be fully utilized. Fortunately, with the multicast technology, when multiple users request the same service, they are accessed to the same time-frequency resource. Therefore, it is worthwhile to confirm that multicast technology is effective in solving this problem. The two-stage cooperative multicast (CM) that can jointly solve the bottleneck problem (In conventional multicast, system throughput is limited by the user with the worst channel condition.) of conventional multicast and the low coverage ratio problem of opportunistic multicast scheme (OMS) has been extensively researched in recent years. In the first stage, with OMS, BS only successfully transmits data to those multicast group (MG) users who own good channel conditions (termed as successful users (SUs)). Remaining MG users with bad channel conditions are termed as unsuccessful users (USUs). In the second stage, user-to-user collaboration is carried out. Through the UR selection scheme, some SUs are selected as user relays (URs) to forward their reception signals to USUs using device-to-device (D2D) technology. It is worth mentioning that when the first-stage coverage ratio is fixed, the performance improvement of CM is mainly decided by the UR selection scheme in the second stage. Current researches on CM are mainly based on two access technologies, orthogonal frequency division multiple access (OFDMA) and non-orthogonal multiple access (NOMA). In the OFDMA-based CM (termed as CM-OFDMA) [4; 5; 6; 7; 8; 9], user-to-user collaboration is carried out only in a single MG. Users in a single MG are sparsely distributed in the cell. To ensure the cooperation between users who are far apart, the small efficient transmission range (ETR) of user's device in D2D technology is not considered as a restriction to perform UR selection. In [4], all of the SUs are selected as URs to serve USUs. When one UR is far away from USU, due to the large path loss, he/she contributes little to the reception signal-to-noise ratio (SNR) of the USU. This causes a waste of energy. A try-best UR selection scheme is proposed in [5]. Every USU selects the nearest SU as his (her) UR. Under the assumption that SU should be closer to the BS than USU, those SUs with low average SNR are closer to USUs. They are selected as URs [6]. Several URs are placed on the fixed positions in the cell. In order to minimize system average outage probability, optimal locations are found to place these URs in the proposed genie-aided CM scheme [7]. A user-autonomous relay selection scheme is proposed in [8], in which users decide whether to participate in relay transmission in the second stage. In [9], a location-aware relay selection scheme is proposed. In order to select the least URs to achieve greater system coverage ratio than the threshold, each USU selects UR from the SUs in a certain probability. However, the method that makes USU choose UR according to the probability is not given. Above researches only take the requirement of USU into consideration. In the second-stage D2D transmission, the small ETR restricts the cooperation among users. The UR far away from the USU can not guarantee successful reception. It results in UR redundancy. This point is neglected. An NOMA-based CM is investigated in [10] (termed as COM-NOMA), in which with NOMA technology two MG are regarded as one quasi-MG to implement OMS in the first stage. Inter-group cooperation and intra-group cooperation are realized in the second stage.