Elsevier

Ad Hoc Networks

Volume 109, 1 December 2020, 102289
Ad Hoc Networks

GLRT-based spectrum sensing by exploiting Multitaper Spectral Estimation for cognitive radio network

https://doi.org/10.1016/j.adhoc.2020.102289Get rights and content

Abstract

Spectrum sensing is a key technique for future intelligent networks, such as AdHoc network, wireless sensor networks. However, the existing works suffer from high computational complexity, which is a huge challenge for those networks composed of many nodes with the limited computing capabilities. In this paper, we propose a simple and novel method based on the generalized likelihood ratio test(GLRT) criterion and offer a specific algorithm based on maximum value of power spectrum calculated by multitaper spectral estimation. We first derive the statistical characteristics and probability density function of test statistic, and the closed-form expression of detection probability and false-alarm probability are obtained. Then, we carry out some simulations to verify the proposed algorithm by taking BPSK signal as an example. In the simulations, we compare the sensing performance between the proposed algorithm and the existing methods. Both theoretical analysis and simulation results demonstrate the advantages of the proposed algorithm over the existing methods.

Introduction

With the development of wireless communication technology, many types of networks have emerged one after another to meet the requirement of different scenarios [1], [2], [3]. What follow is the serious shortage of spectrum resources due to the current static spectral management policy. In truth, however, some allocated spectrum resources are not fully utilized, which results in serious waste of spectrum resources. Worse yet, traditional methods of improving spectrum efficiency with the fixed spectrum allocation strategy have reached their limit under the constraint of Shannon’s theorem. To deal with the unbalanced utilization of spectrum resources, cognitive radio was proposed by Joseph Mitola. From his point of view, cognitive radio has the ability of autonomous learning and can interact with the surrounding environment to reduce the conflicts of spectrum resources utilization. Later, FCC argued that cognitive radio should dynamically change its transmitter parameters based on the interaction with the surrounding RF environment [4], so cognitive radio has the ability to sense the surrounding RF environment and adaptively adjust transmission parameters. Simon Haykin combined Joseph Mitola’s and FCC’s ideas to propose a cognitive cycle from the perspective of signal processing [5]. In his opinion, cognitive radio is defined as an intelligent communication system, and it learns from the environment with artificial intelligence technology to achieve high spectrum utilization and optimal communication performance. At present, spectrum sensing, channel estimation and resource allocation have become the hot topics of cognitive radio [6], [7].

As an intelligent communication technology, cognitive radio has been applied to various wireless networks as soon as it was proposed, such as wireless sensor networks, AdHoc networks and Internet of things [8], [9], [10], in which spectrum sensing is a fundamental and key technology. With spectrum sensing technology, cognitive radio system can monitor the utilization of spectrum resources in real time and provide dynamic access opportunities for unauthorized users on the premise that authorized users are not interfered. At present, many spectrum sensing algorithms have been reported, and they have different characteristics and are suitable for various scenarios. The matched filtering algorithm is known as an optimal algorithm by maximizing the signal-to-noise of the received signal [11]. Unfortunately, the prior of signal transmission waveform is required. In practice, it is difficult to obtain the prior information in the cognitive radio scenario, so this algorithm is not commonly used. The energy-based spectrum sensing algorithm in the time domain is extensively investigated due to its simplification and acceptable performance [12]. The detection probability, false alarm probability and detection threshold have been derived for various channel conditions [13], [14]. More importantly, the algorithm does not require prior information. Nevertheless, the energy-based algorithm suffers from the SNR wall in the low SNR case and the noise uncertainty [15], [16]. The cyclostationary detection algorithm has been studied in early day. For this algorithm, higher order characteristic information such as the signal cycle frequency can be calculated with the multi-order Fourier transform [17], [18], and so this algorithm has the anti-noise and anti-interference advantages. However, the computational load brought by high complexity is unaffordable for many cognitive nodes with limited power. The eigenvalue-based algorithm is suggested by exploiting the maximum eigenvalue and minimum eigenvalue of random matrix [19], [20]. The basic idea of this method is to carry out eigenvalue decomposition of covariance matrix and utilize the maximum eigenvalue, minimum eigenvalue or their combination to perform spectrum sensing. The success of this algorithm lies in the introduction and application of the classical random matrix theory, which is a typical representative of applying mathematical tools to practice. However, eigenvalue decomposition of matrix is a kind of mathematical operation with a large amount of computation, and it is also not suitable for the cognitive nodes with strict restriction on energy consumption [8], [9], [10].

In the eigenvalue-based detection, the eigenvalue of covariance matrix is the decomposition coefficient of signal energy in the eigenvector space. According to Pasalvar’s theorem, if the sum of eigenvalues is taken as a test statistic, the detection performance should be the same with that of the time-domain energy detection. But cleverly, instead of the sum of eigenvalues, the maximum eigenvalue or the ratio of the maximum eigenvalue to the minimum eigenvalue serves as a test statistic. Compared with the energy-based detection algorithm, the difference between them lies in the maximum value and the average value, and the performance is expected to be better than that of the energy-based detection algorithm. Similarly, the frequency-domain coefficients should also be used as test statistic. In other words, the existence of signal can be demonstrated in the frequency domain, which fits the binary hypothesis model of spectrum sensing. In [21], a detection algorithm by exploiting power spectrum density was first proposed. Unfortunately, this algorithm only accumulates energy from the perspective of frequency domain. According to Pasalvar’s theorem, its detection performance should be identical with that of the time-domain energy-based detection. Later, a method was reported by utilizing the variant of power spectral density [22]. In this method, power spectral density is expressed as quadratic form to obtain the Hermitian quadratic matrix of power spectral density, and then the covariance matrix and the quadratic matrix are multiplied to obtain a new matrix containing the characteristics of signal. Finally, spectrum sensing is realized by eigenvalue decomposition of the new matrix. However, too high computational complexity is unacceptable for sensing nodes that need to be detected quickly and accurately. Inspired by the eigenvalue-based spectrum sensing, the power spectral density at a given frequency should be selected as test statistic to achieve a better performance in the low SNR case and significantly reduce the computational complexity. Taking steps along the idea, we exploit GLRT to derive a test statistic for the received signals with unknown parameters. It is found that the test statistic is the maximum power spectral density S(f0). Correspondingly, spectrum sensing is transferred into calculating the maximum value of power spectral density. Currently, the methods of estimating power spectral density are categorized into parametric methods and nonparametric methods [23]. Parametric methods are composed of AR-based method, ME-based methods and ML-based methods, but they have high computational load or require prior information about signal and noise. Therefore, we select nonparametric methods to estimate power spectral density. For nonparametric methods, the Periodogram method was first proposed by Schuster [24]. However, spectrum leakage is caused due to its implicit rectangular window truncation. Moreover, the statistical average is substituted with a single sample function for this method, so it has large variance. To improve the statistical performance, the Bartlett method and the Welch method are studied. Nonetheless, there is still an inherent contradiction between the resolution and bias due to an implied rectangular window [25]. To counter the shortcomings of these methods, the multitaper method (MTM) was addressed [26]. In this method, the Slepian widow is exploited to achieve a desired solution. In [27], the performance comparison of the MTM and Welch method were discussed in the case of Gaussian white noise, and the results show that the MTM outperforms the Welch method. In [28], the authors put forward the minimum bias window (the MB window) and multisinusoidal window (the MS window) and pointed out that the MS window has a specific expression and excellent approximation to the MB window, which shows excellent advantages in computational complexity and performance. Therefore, we estimate power spectral density with the MS window to achieve the improvement of sensing performance and reduce the computational complexity.

The main contributions of this paper are threefold: (1) The GLRT criterion is adopted to derive a simple and effective algorithm applied in the practical cognitive networks, which offers the insight into the frequency-domain spectrum sensing. (2) To improve the detection performance, the MTM method is employed to estimate the maximum value of power spectral density. (3) The closed-form expression of probability distribution of power spectral density calculated by the MTM method is proved to derive the detection probability and the false-alarm probability.

The structure of this paper is described as follows. In Section 2, we formulate the problem and offer the GLRT-based model. In Section 3, we describe the proposed algorithm and analyze its detection performance and computational complexity. To demonstrate the correctness and validity of the proposed, we carry out some simulations and provide the corresponding simulated results in Section 4. Finally, we conclude the paper in Section 5.

Section snippets

Problem formulation

Spectrum sensing can be formulated as a binary hypothesis test x(n)=w(n)H0h(n)s(n)+w(n)H1where w(n) is the zero-mean Gaussian noise with variance σ2, and h(n) is the channel gain. For a practical signal, the carrier frequency is fixed, and the amplitude and phase are unknown due to the influence of fading and shadow effects, therefore the binary hypothesis test can be rewritten as x(n)=w(n)H0Acos(2πf0n+ϕ)+w(n)H1where A, ϕ and f0 are the amplitude, the phase and the carrier

Spectrum sensing algorithm with multitaper spectral estimation

The idea of the MTM is to add k-order orthogonal windows to the same set of data, then calculate the power spectral density for each window, and finally obtain the power spectral density with the weighted average of these power spectral density. The frequently used windows in the MTM include the sinusoidal window, the Slepian sequence and the MB window, therein the Slepian sequence can concentrate the maximum signal energy, and the MB window can minimize the deviation. However, both of them

Numerical simulations results and analysis

In this section, the correctness of theoretical analysis is verified by means of simulation. In addition, we compare the detection performance of different power spectrum estimation methods including the classical periodogram method and Welch method. In order to show the effect of different window functions on spectrum sensing performance, the Slepian window is added to some simulations.

Conclusion

In this paper, we derive a test statistic based on the GLRT and the Newman-Pearson criterion, which is optimal when the parameters are unknown. And it is proved that the test statistic corresponds to the maximum value of power spectral density. Then, we derive the false-alarm probability and detection probability by exploiting the statistical characteristics of power spectral density. Finally, we carry out some simulations to verify our theoretical results about the chi-square distribution and

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is supported by National Natural Science Foundation of China (NSFC) (61671176) and Civil Space Pre-research Program during the 13th Five-Year Plan (B0111).

The authors would like to thank Haopeng Kang for sharing part of his simulation code.

Yulong Gao is an associate professor in the School of Electronics and Information Engineering, Harbin Institute of Technology. He is also a member of the IEEE communications Society. He received his B.S. degree from Heilongjiang Institute of Science and Technology, China, in 2001, M.S. degree from Harbin Engineering University, China, in 2004, and Ph.D. degree from Harbin Institute of Technology, China, in 2007. From May 2012 to May 2013, he was a visitor in University of Toronto, Canada. His

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    Yulong Gao is an associate professor in the School of Electronics and Information Engineering, Harbin Institute of Technology. He is also a member of the IEEE communications Society. He received his B.S. degree from Heilongjiang Institute of Science and Technology, China, in 2001, M.S. degree from Harbin Engineering University, China, in 2004, and Ph.D. degree from Harbin Institute of Technology, China, in 2007. From May 2012 to May 2013, he was a visitor in University of Toronto, Canada. His current research interests include cognitive radio, intelligent signal processing.

    Chen Wang received the B.S. degree in electronic information engineering from Harbin Engineering University, Harbin, China, in 2019. He is currently working toward the M.S. degree with the Communication Engineering Center, Harbin Institute of Technology. His research interests include direction-of-arrival estimation, sparse arrays, compressive sensing, matrix completion, and Cramer–Rao bound analysis.

    Yanping Chen is a lecturer in the School of Computer and Information Engineering, Harbin University of Commerce. She received her B.S. degree from Harbin University of Commerce, China, in 2005, M.S. degree from Harbin Institute of Technology, China, in 2007, and Ph.D. degree from Harbin Engineering University, China, in 2012. Her current research interests include statistical signal processing and performance analysis of network.

    Xu Bai received his Ph.D in School of Electronics and Information Engineering from Harbin Institute of Technology, HIT, China, in 2008. Afterwards, he joined the Communication Research Centre of HIT, where he worked on projects image processing and wireless communication. From 2013 to 2014, as a visiting Scholar he worked in university of British Columbia, Canada. His research interests include image processing, wireless communication, signal processing in Ground Penetrating Radar, wireless sensor network.

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