# A Correlation-Based Sensing Scheme for Outlier Detection in Cognitive Radio Networks
## 1 Introduction  
The services provided for the rapid growth of the applications, such as computers, laptops, ipads, internet of things (IoT), etc., have increased the demand of the spectrum, which results in spectrum shortage. According to the Federal Communication Commission (FCC), most of the spectrum is underutilized, even in the crowded region, the spectrum utilization is between 15% and 85% [1]. To tackle the issue of the spectrum underutilization, cognitive radio technology (CRT) has emerged as a strong candidate for exploiting the spectrum [2]. The main functionality of CRT is to determine the availability of the spectrum for the secondary users (SUs). For achieving the spectrum availability and efficient utilization of the spectrum, the SUs need to continuously monitor the available spectrum to find the spectrum holes and vacate the spectrum whenever the primary user (PU) appears in the network [3]. The spectrum sensing is performed to determine the presence or absence of the PU in the network. Different detection techniques, such as matched filter detection, cyclostationary feature detection, energy detection, etc., have been proposed in the literature [4, 5]. Every detection technique has their own features. For example, feature detection is optimal, when the PU information is available at the SU. When the SU has no prior information about the PU, then the energy detection technique is the optimal detection technique. The SU has only knowledge about the local noise power. The received signal energy is utilized to decide about the existence of the PU in the network. Various techniques are used to efficiently utilize the scarce spectrum by merging the underlay and overlay methods in hybrid cognitive radio networks [6]. However, spectrum sensing is highly vulnerable to fading and hidden terminal problems between the PU and the SUs [7; 8]. Thus, the decision of the spectrum sensing performed by a single SU is neither sufficient nor reliable for final decision about the presence of the PU in the network. To overcome the problem of the single SU sensing, researchers take advantages of cooperative spectrum sensing (CSS) for the enhancement of spectrum sensing. In CSS, each single SU gathers information about the PU channel, and shares its local sensing information with the FC, which accumulates the sensing information from the SUs and declares the global decision about the presence of the PU in the network [9; 10]. In CSS, the SUs send information to the FC in two ways. In the first scenario, the SU sends a single bit of information to the FC, which is also known as the hard-decision rule. In the second scenario, which is called the soft combination rule, the SU sends a sampled energy value to the FC [11; 12]. However, the existence of malicious users (MUs), or outliers, in the network highly degrades the performance of CSS. Various attacks, which highly degrade the performance of the networks, have been studied in the literature. Two common attacks are primary user emulation attacks (PUEAs) and spectrum sensing data falsification (SSDF) attacks [13; 14]. In SSDF attacks, the MUs falsify the sensing results, which influences the sensing results in two ways. First, it decreases the probability of detection, which ultimately decreases the spectrum utilization. Second, it increases the probability of misdetection and the probability of false alarm, which increases interference in the network. Thus, overall performance of CSS is degraded by the SSDF attacks. To mitigate the effects of these attacks, several schemes have been proposed [15; 16; 17]. In Reference [18], the impact of incorrect information of the sensing system was formulated as detection performance and sensing efficiency; additionally, an authentication code length was proposed to reduce the system overhead. The authors of [19] proposed a MU suppression scheme, which consists of an improved energy detector followed by a statistical algorithm implemented at the FC.