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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.

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) [

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 [

Fractional Lower Order Moments (FLOM) demonstrated its capability in signal processing under non-Gaussian noise in [

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

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

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 [

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 [

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

Substituting (

Obviously,

Equation (

The second term of the right side in (

Then the locally optimal detector under low SNR can be expressed as

For the case of AWGN, the differential part of (

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

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

As for the FLOM based detector, the structure is shown in Figure

Structure of FLOM based detector.

The

Assuming that the noise

Then it can be easily concluded that

Figure

Distribution comparison of the test statistics of FLOM detector and energy detector with

The optimal value of

The probability of false alarm

The threshold is normally chosen to satisfy a target

Substituting (

As shown in (

As mentioned above, FLOM based sensing outperforms ED based methods. However, the noise power fluctuation is generally encountered in practice. So the noise power uncertainty should be considered to ensure the implementation of the sensing method. If the estimated noise power is assumed to be in an interval

Due to the

From (

Figure

SNR walls with different

To keep a satisfactory sensing performance, the real time value of noise power should be used to determine the threshold in every sensing period. Fortunately, we found that the higher order moment of the samples can be a maximum likelihood (ML) noise power estimator, although it is not able to act as a good sensing statistic. In this paper, an adaptive threshold sensing structure is adopted with a higher order moment detector as a real time noise power estimator and updating thresholds during each sensing process. From the structure of the NPE based detector shown in Figure

Structure of FLOM detector with noise power estimation module.

The statistic of the noise power estimator is shown in

Due to the fact that the expectations of

It is worth mentioning that the estimated noise power

Substituting (

Utilizing the threshold

The previous discussion indicates that PW also obeys Gaussian distribution with a large

Substituting (

In this section, we give the simulations and analysis of the theoretical results in Section

Let

Probability of detection

From another perspective, Figure

ROC curves of FLOM detector with

The detection ability of the FLOM detector under different SNR is plotted in Figure

Probability of detection

The performance of the NPE based FLOM sensing approach must be related to the estimation accuracy, so the relationship between

Figure

Ideal probability of detection

It is worth mentioning that the number of observed samples has impact on the energy consumption and the sensing time. As an example, the proposed sensing structure works well at

Cognitive Radio can be a helpful technology for utilizing and allocating frequency spectrum in the IoT. The utilization of the FLOM can successfully achieve spectrum sensing task for CR under Middleton Class A noise in the IoT. We derive the analytical expressions of the probability of false alarm

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by Hydro-Quebec, the Natural Sciences and Engineering Research Council of Canada, and McGill University in the framework of the NSERC/Hydro-Quebec/McGill Industrial Research Chair in Interactive Information Infrastructure for the Power Grid.