# Anomaly Detection in IoT Communication Network Based on Spectral Analysis and Hurst Exponent
## 2 Literature Review  
Network traffic can be stored both as an increasing number and as a sequence of intervals between adjacent events. The oldest model of the stream is the Poisson process. As a result of research on real network traffic, an internal correlation in streams was observed. The model based on the Poisson process did not take into account this feature of the generated traffic. Thus, subsequent models were developed that more accurately reflected the real character of the traffic flow in the network. However, many of them are characterized by autocorrelation, which disappears very quickly (exponentially). These are the so-called processes of short memory. The Poisson process has been used to model incoming connections in telecommunication networks due to its analytical simplicity. However, it is unsuitable for new types of network traffic that have emerged from basic internet protocols such as Transmission Control Protocol (TCP) and applications such as TELNET and FTP (File Transfer Protocol). New applications, such as video streaming, bring with them new traffic models that are necessary for traffic engineering. A detailed study of the different traffic characteristics in the IoT network is still not available, so in our work, we deal with this problem. The studies presented in [4] showed that models using Poisson's decomposition are not able to accurately reflect the explosiveness of TCP/IP traffic. Only the use of models of self-similar traffic enables the realistic rendering of TCP/IP traffic. Self-similarity is a phenomenon that retains the statistical properties of the model despite changes in the applied time scale. The most visible feature in the characteristics of network traffic that indicate the occurrence of self-similarity is the occurrence of densities and dilutions at intervals between events and the lack of blurring of this feature despite the use of several different time scales (e.g., seconds, minutes, and hours) [5; 8]. Meanwhile, the development of new network services has caused traffic to change its characteristics. Currently, network traffic, especially in IoT infrastructure, is characterized by a much stronger, long-distance correlation. Nowadays, the internet is based on the Internet Protocol (IP), which is managed by the Internet Engineering Task Force (IETF). The use of IP addresses to identify connected devices and traffic has become entirely natural. Therefore, one might think that a similar analogy could also be used in IoT for compliance purposes, but this is not so obvious. The industry has developed many other wireless communication technologies and networks to meet the needs of IoT applications, leading to numerous interoperability problems. Many providers have started without support for IPv6 but are slowly integrating it, which will allow us to apply our traffic analysis methods. Network traffic in the IoT contains a sequence of packets with incremented timestamps that represent a time series. Time series data represent a set of values obtained from sequential measurements in time. The traffic time series can also be used to monitor security. An analysis of anomalies in network traffic patterns can be used to detect the irregular behavior of intelligent devices caused by failures or security breaches. Currently, the IoT ecosystem offers many devices with a low-security level, which poses a high threat to the IoT system and enables distributed denial of service attacks (DDoS). Monitoring network activity from these devices to centralized hosts (or any other destination) is significant in ensuring the early detection of intrusions [9]. Network traffic contains much useful information about the type of devices, users and applications used. Therefore, an analysis of this traffic is useful not only in detecting intrusions but also in identifying applications, classifying the use of services in applications, etc. [10]. The idea of describing natural phenomena through the study of statistical scaling laws is not new.