## 2 System Model  
### Device-To-Device (D2D) Group-Casting  
In the paper, we considered a case where one transmitter in a D2D group transmits data to the remaining devices in the group, as shown in Figure 1. The signal transmitted from the transmitter is broadcast to all other devices in the group. However, especially when the transmitter is at the edge of the group or near the edge, the success probability of the receivers may not be large enough, and a relay can be used to improve the success rate. The relay sends the received data to the other devices in the group.  
We also considered a D2D overlay system that uses different sub-channels for cellular and D2D communications, as shown in Figure 2. Different D2D groups can be assigned to different sub-channels to reduce the interference between each other, or they can be allocated to the same sub-channel if they are geographically separated or some contention resolution mechanism such as listen-before-talk (LBT) is employed. In this paper, we assumed that co-channel interference occurring in the same sub-channel can be resolved or ignored, and we focused on other-channel interference from other sub-channels.  
In general, D2D communication uses the uplink, and other-channel interference from D2D transmitters to the BS can be resolved by limiting the transmit power of D2D transmitters. If we reduce the transmit power of D2D transmitters, however, the effect of the other-channel interference from the cellular system to D2D receivers can become more severe. In this paper, we analyzed other-channel interference from cellular devices to D2D receivers.  
Figure 1: Device-to-device (D2D) group-casting with a relay.  
Figure 2: Other-channel interference.  
This paper considered a D2D group-casting system with a focus on interference from other sub-channels. In this paper, we ignored other performance-degradation effects such as collisions between intra-group devices, insufficient signal power due to fading, or co-channel interference from other D2D groups or cellular devices on the same sub-channel. We assumed that received signal power was sufficiently larger than the noise power, and fading effects can be ignored because there was sufficient diversity in the channels. We also assumed that smart resource management techniques can be used to solve the collisions in the same D2D group and to alleviate the co-channel interference from other D2D groups or cellular devices in the same sub-channel. Nevertheless, it may be difficult to avoid the interference from other sub-channels, unless very complicated resource management schemes over multiple sub-channels are used.  
In this paper, we only considered interference from D2D or cellular devices on other sub-channels for the cause of reception failures, assuming that there is one D2D or cellular transmitter in each sub-channel in the target cell area. The interference from other sub-channels is very weak compared to co-channel interference, thus, only receivers near the other-channel interferers are affected. However, the interference from other sub-channels cannot be ignored, especially when the transmission power of devices in other sub-channels is high or the number of sub-channels is large. In order to alleviate performance degradation from the interference, a relay can be used, and we considered three different scenarios using a relay.