## 1 Introduction  
Recently, there is growing interest in device-to-device (D2D) communication technologies capable of directly transmitting data between devices without going through a base station or other infrastructure [1; 2; 3; 4; 5; 6]. D2D communication technology has the advantage of being able to communicate even when there is no base station around or the base station is not operational for various reasons. It can also improve the efficiency of spectrum utilization and help to solve traffic overload problems of the base stations from the surge of mobile traffic. Furthermore, due to the proximity of devices, D2D communication can reduce the transmission power of devices, which is important for many applications including the Internet of things (IoT) or sensor devices [7; 8; 9]. D2D communication is considered one of the key technologies for 5G communication systems for enabling IoT, vehicle to everything (V2X), public safety, data offloading, and social-aware communications [10; 11; 12; 13]. Orthogonal frequency-division multiple access (OFDMA) is one of the most widely used multiple access technologies in cellular communication systems [14]. OFDMA allows flexible and efficient use of frequency resources by allocating sub-channels, which is comprised of subcarriers, to each user. OFDMA is also widely used in D2D communication systems to maintain the similarities with cellular communication systems and to ensure transmission distance [15; 16; 17; 18]. D2D underlay systems operate cellular and D2D communications on the same sub-channel of the OFDMA system [19; 20; 21]. Although the performance of D2D underlay systems can be improved by maximizing frequency reuse, complicated interference management may be required. Above all, if the interference channel measurement and the interference control are not perfect, D2D communication may not be guaranteed or the performance of the cellular system may be degraded. In this paper, we consider a D2D overlay system that uses different sub-channels for cellular and D2D communications. Theoretically, signals on different sub-channels in OFDMA systems are orthogonal and not interfered with each other. However, in an actual system, there is non-negligible interference from other sub-channels that results from in-band emissions [22; 23; 24; 25]. Unlike a cellular communication system in which a base station (BS) is centered on a cell, a D2D communication system operates in a distributed manner, and the interference from other sub-channels can be considerable, especially when the number of sub-channels in OFDMA systems is large. This paper assumes a D2D overlay system to focus on the effects of other-channel interference and does not consider co-channel interference. However, if a D2D underlay system is considered in order to increase frequency reuse, control for co-channel interference is also required. Efficient interference management schemes for co-channel interference can be found in many papers [26; 27; 28; 29; 30] and can be used in addition to the techniques discussed in this paper. This work deals with the interference from other sub-channels in OFDMA-based D2D systems. This journal article extends the conference paper [31] by considering several different scenarios of D2D configurations, while the preliminary version of this paper focused on a single limited scenario with limited assumptions. It also includes more details on the system model, assumptions and numerical analysis, as well as additional simulation results. One of the most widely used communication configurations in D2D communication systems is group-casting [32; 33; 34]. In group-casting, one transmitter within a group transmits data to the remaining devices in the group. However, if the transmitter is at the edge of the group or near the edge, the direct transmission from the transmitter can cause a high outage probability, and a relay in the right position can be used to reduce the outage [35; 36; 37].