## 1 Introduction  
In the future industrial internet of things (IIoT), a large number of devices including monitoring sensors and execution control units will be deployed to support factory automation and industry control system [1]. Massive periodic/non-periodic data will be transferred to a centralized control unit or adjacent devices via an industry wireless network, including video monitoring information, sensing data, operation instructions. However, due to the limited capacity and throughput of the current cellular system, it is insufficient in supporting future IoT applications with a tremendous number of devices and heterogeneous information traffic [2]. Massive machine-type communication (mMTC), as one of three typical application scenarios in the 5 th-generation (5G) network, is investigated to support communication among a massive number of devices, which provides a feasible solution for future industrial IoT (IIoT) [3]. Due to limited spectrum resources in the cellular system, massive devices access the wireless network in a spectrum-sharing manner in which multiple devices are allocated in the same spectrum at the same time. Thus, the co-channel interference among devices restricts the number of devices connected to the cellular system. Effective interference management plays a vital role in mMTC to support the simultaneous access of more devices. The features and challenges of mMTC in IoT are as follows. First, devices in IoT need to exchange information with their neighbor devices frequently. In other words, the communication is performed between adjacent devices [4]. Second, the coding blocklengths for IoT are usually short, to reduce the transmission delay. The transmission rate cannot be estimated by the conventional Shannon's capacity, which assumes an infinite blocklength [5]. Third, a massive number of devices in IoT need to be supported. Thus, efficient resource allocation in mMTC needs to be investigated to address these challenges. A wide range of works have contributed to the resource allocation problem in mMTC. In [6], the authors establish an interference model and a formulate resource allocation problem between users and machine-type communication (MTC) gateways in mMTC burst scenarios. In [7], the authors investigated the access management issues for MTC devices with heterogeneous quality of service (QoS) in the same cellular network. This work does not consider bandwidth utilization because transmission opportunities are reserved for a group of MTC devices at the same time. The authors in [8] propose two relay schemes and transmission protocols to specifically stimulate system capacity. In a multi-cell MTC system, [PERSON] et al. [9] establishes the interference model and analyzes the signal-to-interference-plus-noise-ratio (SINR) distributions and drives efficient resource allocation schemes. In [10], the authors propose a dynamic resource allocation algorithm based on the estimation of the number of MTC devices to handle massive and dynamic MTC devices while satisfying the random access delay requirement of MTC devices. To achieve effective resource utilization, a resource allocation metric based on statistical priority is proposed in [11]. In this way, effective resource utilization is achieved by letting MTC devices send a reduced set of their data. In [12], the authors consider a connectivity maximization problem for narrowband IoT with non-orthogonal multiple-access (NOMA). However, articles [6; 7; 8; 9; 10; 11; 12] assume that all devices communicate with the base station or centralized controller directly and do not consider the communications between adjacent devices. D2D technology, as another promising technology in 5G, can establish communication between adjacent nodes, which can improve the spectrum efficiency and offload the load of Base Station (BS). D2D communication is introduced to mMTC system to stimulate spectrum efficiency and support more mMTC devices accessed with limited spectrum resources.