# Anomaly Detection in IoT Communication Network Based on Spectral Analysis and Hurst Exponent
## 2 Literature Review
The authors in [11] presented many studies that have been conducted on this subject, including those by [PERSON] (1900), [PERSON] (1995), [PERSON] (1941), and [PERSON] (1963). The main feature of fractal geometry is its ability to describe the irregular or fragmented shape of natural features and as other complex objects which traditional Euclidean geometry cannot analyze. This phenomenon is often expressed by the spatial or temporal laws of statistical scaling and is characterized by the maintenance of the power-law of real physical systems. This concept allows for simple, geometric interpretation and is often found in various fields such as geophysics, biology and fluid mechanics. Fractal geometry is widely used in general problems with image analysis, especially in medicine. It is applied in different ways with different results [11]. In recent years, the analysis of long-term temporal relationships has become more critical. The topics of self-similarity and long-range dependence (LRD) in time series have become trendy fields of research [12]. The most commonly used measure of self-similarity is the value of Hurst coefficient, H, introduced by hydrologist [PERSON]. [PERSON] based on the observation of Nile level fluctuation. The closer the H value is to 1, the more clearly the phenomenon shows a self-similar character [3]. A recent analysis of the traffic measurements from different communication networks showed that traffic is long-range dependent or fractal (self-similar). These developments revolutionized the understanding of network traffic by explaining the difference between theoretical performance estimates and performance measured in practice. In network traffic, long-range dependence corresponds to the slow decaying autocorrelation function and the heavy-tailed behavior of the probability density function. There are various statistical techniques for estimating the Hurst parameter. By definition, the LRD phenomenon is related to the maintenance of the power-law of some second-order statistics (variance, covariance, etc.) of the process concerning the duration of observation. Many Hurst estimators are therefore based on the idea of measuring the slope of the linear adjustment on a log-log graph. Estimators of Hurst parameters can be divided into two categories: those operating in the time domain and those operating in the frequency domain. However, traditional estimators can be seriously biased. The rescaled range (R/S) estimator has poor statistical performance, with a high deviation and suboptimal variance. The estimator of discrete discomfort is only asymptotically impartial. An asymptotic set-up is not sufficient for a good estimator, which must be impartial, robust, and efficient [9]. Our article aims to emphasize the superiority of the Hurst parameter estimator based on a multifractal spectrum. Therefore, Hurst's exponent can be considered a quantitative method of describing, e.g., traffic in computer networks or the IoT, determining its characteristics that describe overloads or states deviating from the accepted standards. In other words, changes in the intensity and characteristics of the traffic are significant for each other. In [13], a systematic literature review (SLR) of the Intrusion Detection Systems (IDS) in the IoT environment has been presented. Then detailed categorizations of the IDSs in the IoT--anomaly-based, signature-based, specification-based, and hybrid; centralized, distributed, and hybrid; simulation and theoretical; and denial of service attack, Sybil attack, replay attack, selective forwarding attack, wormhole attack, black hole attack, sinkhole attack, jamming attack, and false data attack--were also provided by using standard features. The authors discussed the advantages and disadvantages of the selected mechanisms, and directions for future trends were also provided. LRD is a relatively new statistical concept in time series analysis and has been empirically shown to exist in many fields such as engineering, astronomy, finance, statistics, and hydrology.