Mobile Information Systems

Volume 2017 (2017), Article ID 7321908, 9 pages

https://doi.org/10.1155/2017/7321908

## A Robust FLOM Based Spectrum Sensing Scheme under Middleton Class A Noise in IoT

^{1}School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China^{2}Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada H3A 0G4

Correspondence should be addressed to Xuemai Gu; nc.ude.tih@iameuxug

Received 14 December 2016; Accepted 16 March 2017; Published 6 April 2017

Academic Editor: Tao Han

Copyright © 2017 Enwei Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Accessibility to remote users in dynamic environment, high spectrum utilization, and no spectrum purchase make Cognitive Radio (CR) a feasible solution of wireless communications in the Internet of Things (IoT). Reliable spectrum sensing becomes the prerequisite for the establishment of communication between IoT-capable objects. Considering the application environment, spectrum sensing not only has to cope with man-made impulsive noises but also needs to overcome noise fluctuations. In this paper, we study the Fractional Lower Order Moments (FLOM) based spectrum sensing method under Middleton Class A noise and incorporate a Noise Power Estimation (NPE) module into the sensing system to deal with the issue of noise uncertainty. Moreover, the NPE process does not need noise-only samples. The analytical expressions of the probabilities of detection and the probability of false alarm are derived. The impact on sensing performance of the parameters of the NPE module is also analyzed. The theoretical analysis and simulation results show that our proposed sensing method achieves a satisfactory performance at low SNR.

#### 1. Introduction

The Internet of Things (IoT) has to construct comprehensive connections among variety of objects distributed over an extensive area. So the resources allocation to this large number of objects has to be resolved carefully to maintain a satisfactory Quality-of-Service (QoS) [1]. Generally, the frequency spectrum is one of the most important resources in wireless communications, and the problem of spectrum scarcity is getting worse as a result of the large number of applications [2]. Therefore, the available spectrum has to be carefully utilized by the IoT to ensure plenty of reliable connections between different objects. Fortunately, Cognitive Radio (CR) allows unlicensed users to utilize licensed bands opportunistically and enable them to reuse the frequency bands that are not heavily occupied by Primary Users (PU). Being able to address the spectrum scarcity issue, CR as a promising solution to exploit the available spectrum for the IoT has been proposed [3–5]. The ability of spectrum sensing to measure or sense the presence and absence of PU signal is essential because the operation of CR starts with detecting spectrum holes [6]. Spectrum Sensing methods proposed for identifying the presence of signal transmissions can be categorized as energy detector (ED) based sensing [7], matched filtering based sensing [8], waveform based sensing [9], cyclostationarity based sensing [10], radio identification based sensing [11], and so forth. Among these methods, ED based approaches are the most commonly used because of their low computational and implementation complexities [12].

Most of the previous studies on spectrum sensing only focused on signals contaminated by Additive White Gaussian Noise (AWGN). However, this assumption fails to model the behavior of certain noise types in IoT applications. Considering the applications of IoT such as Machine to Machine (M2M) networks and smart grids, a key challenge in establishing the IoT is wireless communication in the vicinity of vehicles, machines, or electrical power equipment which often radiates electromagnetic waves from switching power electronics components. In particular, this kind of waves in the form of impulse noise and high power transients disrupt wireless communication [3, 13]. Middleton Class A noise model is one of the widely investigated statistical distributions that are used to model this kind of man-made interference and the narrow band impulsive noise in different systems [14]. Being different from AWGN hypothesis, ED based detector is no longer an optimal detector and it has poor performance. Besides, Generalized Likelihood Ratio Test (GLRT) based detector as the optimal detector has a very complex structure, which will be explained later, when it is used under Middleton Class A noise. Recently, a large number of spectrum sensing approaches under different non-Gaussian noises have been proposed [15–17]. However, the implementation of these detectors in the IoT remains challenging because multiple antennas were used or the noise uncertainty was not considered.

Fractional Lower Order Moments (FLOM) demonstrated its capability in signal processing under non-Gaussian noise in [18]. When FLOM is applied to spectrum sensing, the test statistic has a similar expression as that of ED based sensing. Nevertheless, determination of the threshold also depends on the noise parameters in FLOM based sensing as in the case of ED based sensing, and a small noise uncertainty will cause significant performance loss [19, 20]. To this end, a robust FLOM based sensing method should be studied as a promising solution of spectrum sensing under Middleton Class A noise, especially at low SNR. As is shown in our previous work [21], uncertainty of noise power is really destructive, while small estimation errors on other parameters of the noise do not have a strong effect on spectrum sensing performance. So in this paper, the focus is put on the spectrum sensing method under Middleton Class A noise with Noise Power Estimation (NPE), making the following contributions.(i)We study the problem of spectrum sensing under Middleton Class A noise adopting FLOM based detector and derive the analytical expressions of the probability of false alarm and the probability of detection . Then, we analyze the relationship between the sensing performance enhancement and the noise parameters.(ii)We propose such an NPE based structure to deal with the issue of noise uncertainty that noise-only samples are not necessary in the estimation process. The performance of the proposed structure is analyzed, which relates the accuracy of the estimator to the estimation duration and the order of the estimator.

The following parts of this paper are organized as follows. The signal and noise models are defined in Section 2. In Section 3, FLOM are introduced to spectrum sensing as a suboptimal detector. The NPE based sensing structure is proposed in Section 4 and the derivation and analysis are presented in the same section. Section 5 includes the simulation and the results, and the conclusion is drawn in Section 6.

#### 2. Signal and Noise Models

In spectrum sensing, the PU signal to be sensed is considered as a random process (called Bayesian model) in some works; and it is also considered as an unknown deterministic signal (called classical model) in others [22]. Lacking in the knowledge of the PU signals, we choose Bayesian model and consider a source with a zero-mean Gaussian probability density function (pdf)and is transmitted over a channel impaired by a Middleton Class A noise , whose pdf is where indicates that noise sources contribute to the impulsive event simultaneously and is the corresponding overlap index denoting the average number of impulse noise sources active at any given time. Larger values of make the characteristic of the noise closer to Gaussian noise. Moreover, is the noise power, in which is the Gaussian power and is the impulsive power. is the power ratio of the Gaussian component to the impulsive component, and . Thus, the Middleton Class A noise is totally characterized by the parameters , , and . In addition, the PU signal and the noise are assumed to be mutually independent and SNR is defined by .

#### 3. Spectrum Sensing under Middleton Class A Noise

Depending on the idle state and busy state of the PU, with the presence of the noise, detecting the presence of PU is usually considered as the following binary hypothesis testing problem [23]:in which , is the number of observed samples; is the signal observed by sensing receiver with and denoting the PU signal and the additive impulsive noise respectively. means that the PU signal is absent and means that the PU signal is present.

According to the Neyman-Pearson (NP) theorem, GLRT can maximize detection probability when the probability of false alarm is fixed. So we attempted to use GLRT as an optimal method first. With the signal and noise models described in Section 2, the globally optimal detector can be expressed aswhere is the vector of the received samples. If , it means that the PU signal is present. Otherwise, it means that the PU signal is absent.

Substituting (3) into (4), we havein which denotes statistical expectation.

Obviously, is with respect to the pdf of the PU signal which may not be obtained by unlicensed users. However, CR always operates in low SNR (i.e., ) circumstance, especially in IoT. By making the low SNR assumption, we can obtain a locally optimal detector from the globally optimal detector.

Equation (5) can be simplified by using Taylor series [24],where we drop the time dependence for clarity.

The second term of the right side in (6) equals when taking the expectation. Hence,where we assume .

Then the locally optimal detector under low SNR can be expressed asHere we use for . Obviously, this locally optimal detector only requires the pdf of the noise.

For the case of AWGN, the differential part of (8) can be simplified intoThe locally optimal detector equals the traditional ED. Unfortunately, cannot be easily simplified under Middleton Class A noise hypothesis. From (8), it can be seen that the locally optimal GLRT detector is with respect to the pdf of the noise which contains infinite summation. Moreover, the structure of the detector has to change with the change of the noise parameters which makes the implementation of GLRT detector impossible. Consequently, should be converted into a simpler nonlinear operator so that it can be implemented practically.

Under impulsive noise hypothesis, the presence of impulses increases the false alarm during sensing process. To improve the sensing performance, the impact of randomly appearing large amplitudes in the noise should be reduced. Inspired by the capability of FLOM in signal processing under non-Gaussian noise and the expression of energy detector, we use FLOM as a suboptimal detector and the corresponding test statistic is given in where .

Through fractional power operation, a nonlinear operation, the large impulse amplitude in the noise can be reduced, while the small values almost remain unchanged. As a result, a good sensing performance can be obtained. In addition, with the similar expression of ED, FLOM based detector can be implemented practically when the parameter is determined.

#### 4. FLOM Based Spectrum Sensing with Noise Power Estimation

##### 4.1. FLOM Based Spectrum Sensing

As for the FLOM based detector, the structure is shown in Figure 1. According to the central limit theorem [25], when is large enough, the metric in (10) can be approximated as a Gaussian random variable,in which