## 1 Introduction  
With the proposal of the industrial 4.0 strategy, advanced technologies such as the Internet of Things, edge computing, and Big Data have emerged to provide technical support for the development of intelligent manufacturing [1; 2; 3; 4]. The Industrial Internet of Things connects machines, objects, and people in factories [5; 6]. Edge computing transfers data processing, application running, and even the realization of some functional services from the network center to the nodes on the edge of the network. It solves the disadvantage that cloud computing cannot support computing-intensive and delay-sensitive tasks and enables data processing and analysis in intelligent factories. In order to support the intelligent interconnection and application of all kinds of equipment in the industrial field more effectively, edge calculation should be made close to or embedded in all kinds of sensor, robot, instrument, and other equipment nodes of industrial wireless networks [7]. In order to better access or embed edge computing on various device nodes of industrial wireless networks, the characteristics of the Industrial Internet of Things should be studied. As a typical case of the fifth generation mobile communication (5G) mMTC (massive machine type of communication) scenario, the Industrial Internet of Things (IIoT) has become the key competitiveness of the country and has attracted extensive attention in academic and industrial fields [8]. Wireless technology, as the information transmission channel in the IIoT system, plays a significant role in the industrial field. At present, improving production efficiency and realizing energy saving and emission reduction are the main strategic tasks of manufacturing industry. With the development of the industrial internet, intelligent manufacturing will run through all aspects of enterprise production and operation, bringing profound changes to the development of manufacturing industry. IIoT connects mechanical equipment, people, and items together and enables them to exchange data. It will be widely used in automobile manufacturing and other industrial scenarios. However, the electromagnetic noise in the industrial environment is significantly different from that in other typical environments such as office areas [9]. When the machine is working, different types of electromagnetic noises will be emitted due to the increase of temperature, mechanical vibration, spark discharge, and other physical phenomena. Moreover, there are many kinds of electromagnetic noise distributed at any random position in the factory, and the frequency distribution range is very large [10]. Electromagnetic noise causes electromagnetic interference to the industrial environment, which reduces the signal-to-noise ratio of the communication system and affect the communication quality and the capacity of the communication system. Noise is usually considered as additive white Gaussian noise in general scenes. However, the noise characteristics in IIoT scenes are quite different from the additive white Gaussian noise (AWGN) hypothesis [11]. First, the noise generated by machines, motors, and other equipment may have a non-flat power spectrum, so the noise in the IIoT scene does not always meet the characteristics of white noise [12]. Second, the frequency domain impulse noise generated by welding equipment in infrared environments does not obey the time domain Gaussian distribution, so the noise in IIoT scenes does not always obey the Gaussian distribution. Third, the noise process in IIoT scenes is not always stationary, and there often exist sudden noises. In addition, in order to prolong the service life, equipment in industrial applications is in a low power transmission mode, which makes them vulnerable to industrial noise generated by machines, motors, and other equipment [13]. Therefore, it is meaningful to study the wireless network design of the Industrial Internet of Things. At present, previous scholars had carried out research on electromagnetic noise in the factory environment.