## 1 Introduction  
As enhancements of devices' capabilities to record and play video continue to progress, demands to cope with the mobile multimedia data traffic also increase [1; 2; 3]. The demands have affected not only the cellular networks, but also sensor networks. Wireless multimedia sensor networks (WMSNs), wireless sensor networks (WSNs) for targeting the multimedia data, have been developed [4]. A sensor that can collect multimedia data is called a multimedia sensor in WMSN. The multimedia sensor can be used in various areas such as transmitting multimedia, checking traffic, and monitoring nature, people, and machines [5; 6]. The WMSN uses multimedia sensing technologies to monitor peripheral situations and sends collected data to an aggregator for reporting [7]. An application in WMSN may require several months of operating lifetime [8]. Since WMSN consists of sensors, the WMSN technologies have been developed to ensure Quality of Service (QoS) and to overcome limited computing power and energy of sensors [4; 5; 9; 10]. As these problems of limitation are reduced, the WMSN can be applied to future smart cities, security systems, or industries [11]. In WMSN, it is important to communicate efficiently and to achieve high throughput because large multimedia data are transmitted such as high resolution image, audio, and video stream [12]. Therefore, reliable and efficient wireless communication should be offered between sensor and data aggregator [13; 14]. Many problems are considered that can occur in WMSN such as deployment costs, energy-efficient routing, network coverage, and connectivity [15; 16; 17]. One of the fundamental deficiencies that cause these problems is a centralized structure. All generated data were finally sent to a central aggregator (CA) in previous studies. Unlike the typical WSN system, the amount of traffic is very large in WMSN. It is a significant burden for the CA, and it can degrade the overall performances of WMSN. Thus, device-to-device ( D2D) communication should be considered in WMSN. The D2D communication in WMSN can be used for various services such as live streaming services and mobile aggregating systems. For the case of the streaming service, local streaming broadcast to personal devices in a stadium can be considered. The data can be broadcast to local networks. To reduce the dense overhead to the central system, the traffic should be distributed as much as possible. In the services, D2D links of WMSN can be considered. Additionally, mobile aggregating is one of the candidates to use D2D links for WMSN, which means that sensor networks use a mobile device as an aggregator [18; 19]. To support the mobile aggregator, multi-hop communication should be considered, where a D2D link is adopted. We focus on a D2D WMSN with a cellular link and a D2D link as shown in Figure 1. There are two types of D2D links: overlaying and underlaying types [20; 21]. The overlaying system is one in which a fraction of frequency resources is allocated to the D2D link. There is no interference between the uplink and D2D link, but bandwidth efficiency is degraded. Otherwise, the underlaying system is one in which a D2D link shares the same channel resources with the uplink. It means that the two links are based on a non-orthogonal system. The underlaying system can be regarded as a fault-tolerance mechanism such as [22; 23], which maximizes performance while allowing some faults of links. Recently, studies of the D2D link underlaying system consider QoS requirements. The authors of [24; 25] consider the minimum QoS requirement to avoid the dissatisfaction of the minimum SINR. In addition, the authors of [26] propose a radio resource allocation scheme that considers the intra cell interference and increases the throughput of whole cell. The study in [27] covers the various uplink resource allocation algorithms for the optimal allocation of the subcarriers and transmission powers in the SC-FDMA cellular networks.