Elsevier

Signal Processing

Volume 93, Issue 5, May 2013, Pages 1118-1125
Signal Processing

Fuzzy likelihood ratio test for cooperative spectrum sensing in cognitive radio

https://doi.org/10.1016/j.sigpro.2012.12.005Get rights and content

Abstract

Efficient and reliable spectrum sensing is an essential requirement in cognitive radio networks. One challenge faced in the spectrum sensing is the existence of the noise power uncertainty. This paper proposes a cooperative spectrum sensing scheme using fuzzy set theory to mitigate the noise power uncertainty. In this scheme, the noise power uncertainty in each Secondary User (SU) is modeled as a Fuzzy Hypothesis Test (FHT). We deploy the likelihood ratio test on the FHT to derive a fuzzy energy detector with a threshold that depends on the noise power uncertainty bound. The fusion center combines the received local hard decisions from the SUs and makes a final decision to detect the absence/presence of a Primary User (PU). We compare the performance of the proposed algorithm with some classical threshold-based energy detection schemes using receiver operating characteristic and detection probability versus the signal to noise ratio curves via Monte Carlo simulations. The proposed algorithm outperforms the cooperative spectrum sensing with a bi-thresholds energy detector and a simple energy detector.

Highlights

► Applying fuzzy hypothesis test model for noise power uncertainty in cognitive radio. ► Deploying likelihood ratio test on the fuzzy model for local Spectrum Sensing (SS). ► The threshold values of local SS detectors are computed and tabulated offline. ► Using a fusion center for combining local hard decisions for Cooperative SS (CSS). ► The proposed method outperforms the simple and bi-thresholds energy detectors in CSS.

Introduction

Cognitive Radio (CR) technology has been introduced to alleviate the spectrum scarcity through opportunistically access of Secondary Users (SUs) to licensed spectrum bands. In a CR network, SUs must accurately sense the spectrum holes, use those for their transmissions and vacate the frequency band as soon as the Primary Users (PUs) start their transmissions [1], [2], [3]. The main challenge in such systems is to avoid the harmful interference from SUs imposed on the PUs in their vicinity through spectrum sensing. The basic idea behind the spectrum sensing is to detect the weak signal of a PU. To alleviate some practical concerns of spectrum sensing such as multipath fading and hidden PUs, cooperative spectrum sensing has been proposed [4]. In centralized cooperative spectrum sensing, each SU sends its local sensing results to a fusion center. The fusion center combines the received local information and makes a final decision to detect the absence/presence of the PU. In recent years, cooperative spectrum sensing schemes have been extensively studied in cognitive radio networks [5], [6]. In [7], the authors provide a comprehensive survey in the area of spectrum sensing, in particular in the context of cooperative approaches. To improve the detection probability, many signal detection algorithms are used in such cooperative spectrum sensing (e.g. [6]). In most detection techniques, the noise power is supposed to be known a priori for threshold setting. However due to the noise power variations, the power of the noise is not known precisely which yields the noise uncertainty in the signal detection process. Due to the noise uncertainty and sensing time limitations, obtaining the accurate noise power is not an easy task, thus the performance of such detection methods is susceptible to the noise power uncertainty. There are two types of the noise uncertainty; receiver device and environment noise uncertainties [8]. The receiver device noise uncertainty is caused by the time-varying thermal noise and the nonlinearity of the receiver components. Transmissions from other users, on the other hand, are the sources of the environment noise uncertainty. To achieve a desired performance in an energy detection-based system in the presence of the noise power uncertainty, the received Signal to Noise Ratio (SNR) must be more than a prespecified threshold level [9].

There exists some literature on the noise power uncertainty in cooperative spectrum sensing [10], [11], [12]. The study in [10] proposes a covariance and eigenvalue-based cooperative spectrum approaches in the presence of the noise uncertainty. However, the scheme in [10] has more complexity than common methods for cooperative spectrum sensing such as the energy detector. The authors in [11] propose an energy detector-based cooperative spectrum sensing method that uses three thresholds for local sensing. The methods proposed in [10], [11] use soft decision combining mechanisms, however, the approaches occupy more bandwidth of the control channel for sending local sensing results. Some literature surpass this soft decision concern through utilizing a hard decision combining approach with a bi-thresholds energy detector in SUs (e.g. [12]).

Throughout this paper, we address the hard decision-based cooperative spectrum sensing in the presence of the noise power uncertainty and utilize fuzzy set theory concepts [13] as a mathematical framework to model such uncertainty. In this scheme, the noise power uncertainty in each SU is modeled as a Fuzzy Hypothesis Test (FHT). We deploy the Likelihood Ratio Test (LRT) on the FHT [14] to derive a fuzzy energy detector with a threshold that depends on the noise power uncertainty. The local sensing results of SUs are sent to a fusion center and are combined to make a final decision to detect the absence/presence of the PU. We compare the performance of the proposed algorithm with some classical threshold-based energy detection schemes using the Receiver Operating Characteristic (ROC) and the detection probability versus the signal to noise ratio curves via Monte Carlo simulations. The proposed algorithm outperforms the cooperative spectrum sensing with a bi-thresholds energy detector in [12] and a simple energy detector.

The rest of the paper is organized as follows. Section 2 provides an overview of the system model, the FHT concept and the likelihood ratio test for FHT. In Section 3, we derive a detector using LRT for FHT at each SU and deploy this detector for the proposed cooperative spectrum sensing approach. Simulation results are presented in Section 4. Finally, Section 5 provides a brief summary and conclusions.

Notations: Throughout this paper, we use boldface lower case letter to denote vector. A Gaussian random variable with mean m and variance σ2 is represented by N(m,σ2). Also, we use E[.] as the expectation operator, sup(.) for representing the supremum, and P{.} for the probability of the given event. The signs “” and “” mean “almost smaller” and “almost greater”, respectively. Finally Q(.) is the complementary cumulative distribution function, which calculates the tail probability of a zero mean and unit variance Gaussian variable, i.e. Q(x)=x(1/2π)exp(t2/2)dt.

Section snippets

System model

In this work, we consider a homogeneous cognitive radio network in the sense that all the SUs use the same protocol for local spectrum sensing. The network consists of M secondary users indexed by {i=1,,M} that monitor the frequency band of the interest as shown in Fig. 1. The spectrum sensing problem for the ith SU can be represented by the binary hypothesis test as follows:H0:xi[k]=wi[k],H1:xi[k]=si[k]+wi[k]for k=0,1,,N1, where N is the number of samples, xi[k] and si[k] are the baseband

Local spectrum sensing at SUs

In this section, we provide an efficient algorithm to encounter the noise power uncertainty using the FHT. To achieve this goal, we reconsider the conventional detection using the energy detector for local spectrum sensing at each SU. For such energy detector, the decision rule is given byUik=0N1|xi[k]|2H0H1ηi,where Ui and ηi are the test statistic and the detection threshold in the ith SU, respectively. According to the central limit theorem, Ui is approximated by the Gaussian random

Simulation results

In this section, we evaluate the performance of the proposed algorithm using the Receiver Operating Characteristic (ROC) and the detection probability versus SNR curves by Monte Carlo simulations. In our simulation, we assume that the number of SUs (M) is equal to 5 and the number of samples (N) is equal to 200. In addition, ρi and SNRi indicate the noise power uncertainty bound and the SNR at the ith SU, respectively. Fig. 3 shows the ROC curves of a single SU for the proposed fuzzy method

Conclusion

In this paper, a cooperative spectrum sensing algorithm based on the fuzzy hypothesis test was proposed to confront the noise power uncertainty. We derived the detector using the likelihood ratio test for the fuzzy hypothesis test at each SU. It was shown that the obtained detector is an energy detector except that its threshold depends on the noise power uncertainty. A fusion center receives the local hard decisions from the SUs and fuses them using the “AND” and “OR” rules for final decision.

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