performance comparison of spectrum sensing ...

COMPARACIÓN DEL DESEMPEÑO DE TÉCNICAS DE MEDICIÓN DEL ESPECTRO EN REDES DE RADIO COGNITIVA PERFORMANCE COMPARISON OF SPECTRUM SENSING TECHNIQUES FOR COGNITIVE RADIO NETWORKS Luis Miguel Gato Diaz1, Liset Martínez Marrero2, Jorge Torres Gómez3 1 CUJAE, Cuba, [email protected] , Calle Trébol, Edif. 50A, Apt.6 Entre 92 y 96. Habana del Este. La Habana. 2 CUJAE, Cuba, [email protected] 3 CUJAE, Cuba, [email protected]

RESUMEN: La Radio Cognitiva ha emergido como una tecnología prometedora para mejorar la eficiencia en el uso del espectro y superar el problema de escasez espectral realizando un acceso oportuno a canales vacantes temporalmente. Para los usuarios cognitivos, varias han sido las técnicas de medición del espectro que se han propuesto para detectar las señales de los usuarios primarios. En este artículo se realiza una comparación de desempeño entre las distintas técnicas de medición del espectro para redes de radios cognitivos operando en canales caracterizados por ruido blanco aditivo Gaussiano. Palabras Clave: Radio Cognitiva, comparación de desempeño, medición del espectro.

ABSTRACT: Cognitive Radio has emerged as a promising technology to improve the spectrum utilization efficiency and overcome spectrum scarcity problem by performing an opportunistic access to temporary vacant channels. For cognitive users, several spectrum sensing techniques have been proposed to detect primary user signals. In this paper, a performance comparison among different spectrum sensing techniques for cognitive radio networks under AWGN channel is provided. KeyWords: Cognitive Radio, performance comparison, spectrum sensing.

1. INTRODUCTION In the context of wireless communications, spectrum sensing alludes to the ability of some devices to be sensitive to the state of one or more portions of the radio spectrum. The main utility of spectrum sensing consists on detecting and characterizing other users. The most relevant application in the last years have been to find usage opportunities of temporary vacant channels.

Due to the fast growing of the new communication technologies, and the requirement of higher data rates for multimedia type applications, the spectrum allocation has been exhaustive. Besides, the traditional static and exclusive spectrum allocations policies lead to the main problem faced nowadays in wireless communications: spectrum scarcity. As a result, innovative techniques that can offer new ways of exploiting the available licensed spectrum are

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needed. A new paradigm for wireless communication devices called Cognitive Radio [1], [2] has emerged to optimize the employment of the radio spectrum. Through the use of temporary vacant channels it is possible to improve the spectrum utilization [3]. Furthermore, the parameters of the transmitter and the receiver are adaptively adjusted in order to avoid interference and achieve a higher throughput. Several current technologies perform spectrum sensing in some way, although they are not properly cognitive radios, for example: Bluetooth (WPAN – IEEE 802.15.1) [4] and WLAN – IEEE 802.11k [5]. The IEEE 802.22, the working group on wireless regional area networks (WRAN), is developing a wide variety of standards to enable spectrum sharing in white spaces of the television frequency bands, by using cognitive radio technology. The detection problem for spectrum sensing is stated as a binary hypothesis test [6]. Formally, this is modelled as the problem of decide between the “signal absent” hypothesis, denoted by 𝐻0 , and the “signal present” hypothesis, denoted by 𝐻1 :

optimal solution in terms of the output signal-tonoise-ratio (SNR). However, prior knowledge of the SoI is required [7]. On the other hand, non-coherent detection also referred as blind detection, does not require prior knowledge of the primary signals parameters. Energy detection (ED) is the most widely used technique for blind detection [8]. Nevertheless, the incapability of distinguishing between different types of signals, the vulnerability to uncertainty in noise variance estimation, and the poor performance under low SNR regimes, represent an important limitation in practice [9]. On the other hand, the use of cyclostationary detection (CD) is reported to mitigate the limitations of ED [8]. A summary of the most used techniques for spectrum sensing in cognitive radio networks is shown in Figure 1. Except for matched filter, the other techniques are considered in the IEEE 802.22 standards for wireless regional area networks.

𝐻0 : 𝑥[𝑛] = 𝜔[𝑛] (1) 𝐻1 : 𝑥[𝑛] = 𝑠[𝑛] + 𝜔[𝑛] where 𝑥[𝑛] denotes the received signal, 𝑠[𝑛] denotes the signal of interest (SoI), and 𝜔[𝑛] represents additive white Gaussian noise (AWGN). This notation is valid for every detection technique, the only difference among different approaches lies on the decision statistic used for distinguishing between both hypotheses. Two parameters are defined to characterize the performance of the detector: the probability of detecting a SoI (𝑃𝑑 ), which is the probability of choose 𝐻1 when the signal is present, and the probability of false alarm (𝑃𝑓𝑎 ), which is the probability of choose 𝐻1 when the signal is absent. The test statistic used to discriminate between 𝐻0 and 𝐻1 , depends on the detection technique employed.

2. THE MAIN SPECTRUM SENSING TECHNIQUES From the perspective of signal detection, the spectrum sensing techniques can be classified as coherent detection or non-coherent detection [7]. In the former case, the SoI is detected using a generated signal, this is conformed taking into account the modulation parameters like the carrier frequency and phase, the order of the modulation, the shape and duration of pulses, etc. Matched filter provides the

Figure 1. Classification of spectrum sensing techniques.

2.1 Matched filter based spectrum sensing An important kind of systems are those in which a deterministic known signal is detected in presence of noise. In such scenario, it is possible to design a filter that maximizes the output SNR by reducing the output noise power. This kind of filter is called matched filter [10].

Let 𝑠[𝑛] be a digital signal transmitted by a primary user (PU). If the communication channel is characterized by AWGN, then the impulse response of the corresponding matched filter is: ℎ[𝑛] = {

𝑘 · 𝑠[𝑁 − 1 − 𝑛], 0,

for 𝑛 = 0,1, … , 𝑁 − 1 otherwise.

(2) where 𝑘 is a not zero arbitrary constant, and 𝑁 is the length of the received signal in number of samples. The finite impulse response (FIR) filter is made up by a reflected and delayed copy of the SoI.

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Gato, Luis; Martínez, L.; Torres, J. | “COMPARACIÓN DE DESEMPEÑO DE TÉCNICAS DE MEDICIÓN DEL ESPECTRO EN REDES DE RADIO COGNITIVA”

Figure 2 shows a block diagram for describing a matched filter detector.

Figure 2. Block diagram describing a matched filter detector.

For a matched filter of length 𝑁, the expressions of 𝑃𝑑 and 𝑃𝑓𝑎 are: 𝑃𝑓𝑎 = 𝑄 (

𝛾 2𝐸 √𝜎𝜔 𝑁

)

(3)

and 𝑃𝑑 = 𝑄 ( where 𝑄(𝑎) =

𝛾−𝐸𝑁 2𝐸 √𝜎𝜔 𝑁

∞ 1 ∫ √2𝜋 𝑎

)

𝑒 −𝑡

(4) 2 /2

𝑑𝑡 is the standard Gauss-

ian complementary cumulative distribution function, 𝐸𝑁 is the energy of the SoI at the output of the matched filter of 𝑁 coefficients, and 𝜎𝜔2 is the noise power. Figure 3a) shows several receiver operating characteristic (ROC) curves of a cognitive radio using matched filter of 𝑁 = 1024 coefficients for spectrum sensing under different SNRs. The ROC curves represent 𝑃𝑑 as a function of 𝑃𝑓𝑎 . For a more extensive study of the detection performance under low SNR regimes, figure 3b) shows the probability of detection for different 𝑃𝑓𝑎 values.

2.2 Cyclostationary feature detector The spectrum sensing techniques that perform cyclostationary feature detection exploit the periodicities introduced to the communication signals due to

several processes like codification, modulation and sampling [11]. Cyclostationarity is a common property in sinusoidal carriers, pulse trains, spreading codes, hopping sequences and cyclic prefixes used in some signals with synchronization purposes. These periodicities can be detected using an appropriate cyclostationary model. Let 𝑥[𝑛] be a primary user signal with second order periodicities [11], it’s autocorrelation sequence 𝑅𝑥𝑥 [𝑛, 𝑛 + 𝑚] is periodic in time domain for every lag value 𝑚. Therefore, it can be expressed by a Fourier series of the form: 𝛼 [𝑚]𝑒 𝑗2𝜋𝛼𝑛 𝑅𝑥𝑥 [𝑛, 𝑛 + 𝑚] = ∑𝛼 𝑅𝑥𝑥

(5)

𝛼 [𝑚] where 𝑅𝑥𝑥 are the corresponding Fourier coefficients associated to the cyclic frequencies 𝑚 𝛼∈{ } . 𝑁 𝑚=0,1,…,𝑁−1

These Fourier coefficients can be computed using equation (6): 𝛼 [𝑚] 𝑅𝑥𝑥 =

1 2𝑀+1

−𝑗2𝜋𝛼𝑛 ∑𝑀 𝑛=−𝑀 𝑥[𝑛]𝑥[𝑛 + 𝑚]𝑒

(6)

Because of its similarity with the conventional autocorrelation function, the set of these coefficients is called cyclic autocorrelation. Extrapolating the Wiener-Khinchin theorem for the power spectral density function, the cyclic power spectral density or spectral correlation density is obtained by Fourier transform of the cyclic autocorrelation. The cyclostationary signals transmitted by primary users exhibit spectral correlation that is not present in stationary noise or interference [12]. Figure 4) shows a block diagram describing the cyclostationary feature detector for spectrum sensing.

Figure 3. Performance of a cognitive radio using a matched filter of N = 1024 coefficients. (a) ROC curves for different SNRs and a Pfa = 0,1. (b) Curves of Pd vs. SNR for different Pfa values.

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2.3 Energy detector based spectrum sensing

Figure 4. Block diagram describing a cyclostationary feature detector for spectrum sensing.

Let 𝑠[𝑛] = 𝐴𝑐𝑜𝑠(2𝜋𝑓0 𝑛/𝑓𝑠 + 𝜃), a primary user signal transmitted through a AWGN channel with noise power 𝜎𝜔2 , and let 𝐴, 𝑓0 , and 𝜃 be the amplitude, carrier frequency and phase of the PU signal respectively, and 𝑓𝑠 is the sampling frequency of the receiver. For every threshold 𝛾 the corresponding 𝑃𝑓𝑎 and 𝑃𝑑 can be computed as follows: 𝑃𝑓𝑎 = 𝑒 −𝛾

2 /2𝜎 2 𝜈

√2𝜂

𝑃𝑑 = 𝑄 (

where 𝜎𝜈2 = 𝜂=

𝑁𝐴2 2 2𝜎𝜔

2 𝜎𝜔

2𝑁+1

𝜎𝜔

(7)

𝛾

, )

(8)

𝜎𝜈

, the SNR of the received signal is ∞

, and 𝑄(𝑎, 𝑏) = ∫𝑏 𝑡𝑒 −

𝑡2 +𝑎2 2

𝐼0 (𝑎𝑡) 𝑑𝑡 is the

generalized standard Gaussian complementary cumulative distribution function, where 𝐼0 is the zero-order Bessel function of first kind. Figure 5a) shows several receiver operating characteristic (ROC) curves of a cognitive radio using a cyclostationary feature detector with 𝑁 = 1024 samples of the received signal under different SNRs and expecting a 𝑃𝑓𝑎 = 0,1. For a more extensive study of the detection performance, in figure 5b) the probability of detection have been plotted for low SNRs, from -20 to -10 dB, and for different 𝑃𝑓𝑎 values.

If an estimate of the noise power is available, the technique with lowest computational cost for spectrum sensing is to detect the PU signal by computing the energy of the received signal [9, 13]. This has been the most studied technique, and the performance of cognitive radios using energy detectors has been tested under multiple conditions, including AWGN and fading channels [4]. One of the challenges of ED-based spectrum sensing techniques is to select an appropriate threshold, since it is very vulnerable to uncertainty in noise power estimation [4]. In general, the energy detector (ED) presents a poor performance under low SNR regimes and interference condition, with respect to coherent techniques [4]. This is an important limitation with regard to spread spectrum signal detection. Both the SoI and noise are modeled as realizations of zero-mean, white, Gaussian, wide sense stationary random processes, with variances 𝜎𝑠2 and 𝜎𝜔2 , respectively. By using the likelihood ratio test [6], the optimal decision statistic for the energy detector can be expressed as [14]: 1

𝐸 = ∑𝑁−1 𝑛=0 ( 𝑁

𝑥[𝑛] 2 𝜎𝜔

)

(9)

Figure 6) shows a block diagram describing the energy detector for spectrum sensing.

Figure 6. Block diagram describing an energy detector for spectrum sensing.

From the decision statistic in equation 9), and using the Neyman-Pearson theorem, both the probability of

Figure 5. Performance of a cognitive radio using a cyclostationary feature detector with N = 1024 samples of the received signal. (a) ROC curves for different SNRs and a Pfa = 0,1. (b) Curves of Pd vs. SNR for different Pfa values.

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detection and the probability of false alarm can be obtained [14]: 𝑁 2

𝑃𝑓𝑎 = 1 − 𝐹 (𝛾, , ) 2 𝑁

𝑁 2

𝑃𝑑 = 1 − 𝐹 (𝛾, , (1 + 𝜂)) 2 𝑁

where

𝐹(𝑡, 𝑎, 𝑏) =

(10)

(11)

𝑡 1 ∫ 𝜏 𝑎−1 𝑒 −𝜏/𝑏 𝑑𝜏 𝑏 𝑎 Γ(𝑎) 0

is

the

Gamma cumulative distribution function with shape parameter 𝑎 and scale parameter 𝑏. In equation 11), the SNR at the output of the bandpass filter has been denoted by 𝜂. Equations 10) and 11) apply only for ideal conditions, with perfect knowledge of the noise power. However, these expressions are limited under practical conditions where some degree of uncertainty in noise power estimation is present. For an estimated noise variance 𝜎̂𝜔2 ∈ [ 𝜎𝜔2 /𝜌 , 𝜌 𝜎𝜔2 ] characterized with an uncertainty 𝜌 ≠ 1, exists a minimal SNR value for which the detector performance does not converge to expressions 10) and 11). As a result, for a fixed 𝑃𝑓𝑎 the performance is worse than expected. An approximation for this SNR wall, for 𝑁 ≫ 10 and low SNR regimes, is [15]:

𝜂𝑚𝑖𝑛 ≈ (

𝜌2 −1 𝜌

2

) + √ (𝑄 −1 (𝑃𝑓𝑎 ) − 𝑄 −1 (𝑃𝑑 ) ) 𝑁

(12) where 𝑄 −1 is the inverse of the standard Gaussian complementary cumulative distribution function. Numerical analysis show that the noise power is usually estimated with an uncertainty of 𝜌𝑑𝐵 = ±1 dB, due to calibration error, thermal noise changing, estimate error and other factors [16].

Figure 7a) shows several receiver operating characteristic (ROC) curves of a cognitive radio using an energy detector with 𝑁 = 1024 samples under different SNRs and expecting a 𝑃𝑓𝑎 = 0,1. For a more extensive study of the detection performance, in figure 7b) have been plotted the probability of detection for low SNRs, from -20 to 10 dB, and for different 𝑃𝑓𝑎 values. The black line represents the SNR wall of the receiver an uncertainty 𝜌𝑑𝐵 = ±1 dB.

3. OTHER SPECTRUM SENSING TECHNIQUES Although the most used techniques for blind spectrum sensing in cognitive radio networks are those based on the energy detector, other techniques have been proposed, in order to overcome the main limitations of the ED. For example, in the IEEE 802.22 standard for cognitive wireless regional area networks [17], a decision statistic for spectrum sensing is obtained from the eigenvalues of the correlation matrix of the received signal. Three main techniques based on eigenvalues are: MED (Maximum eigenvalue detection), MME (Maximum-minimum eigenvalue detection) and the energy to minimum eigenvalue ratio [18]. Analytical expressions for evaluate the performance of cognitive radios based on eigenvalue detectors are not straightforward. Nevertheless, numerical results has been obtained under specific conditions [19]. Figure 8) shows a comparison of the performance between the energy detector and an eigenvalue detector for a fixed 𝑃𝑓𝑎 = 0.1, under noise power uncertainty of 1 dB and using 10000 samples of the received signal. For illustration purposes with regard to the effect of noise uncertainty, the performance of the ED under perfect knowledge of the noise power (i.e., 𝜌𝑑𝐵 = 0 dB) has been plotted too.

Figure 7. Performance of a cognitive radio using an energy detector with N = 1024 samples of the received signal. (a) ROC curves for different SNRs and a Pfa = 0,1. (b) Curves of Pd vs. SNR for different Pfa values.

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5. REFERENCES 1. Mitola J, Maguire G. Cognitive radio: Making software radios more personal. IEEE Personal Communications. 1999;6(4):13-18. 2. Haykin S. Cognitive Radio: Brain-empowered wireless communications. IEEE Journal on Selected Areas in Communications. 2005;23(2):201-220. 3. McHenry M. Frequency Agile Spectrum Access Technologies. FCC Workshop on Cognitive Radio; 2003. p. 1-4. 4. Yucek T, Arslan H. A survey of spectrum sensing algorithms for Cognitive Radio applications. IEEE Communications Surveys and Tutorials. 2009;11(1):116-130. Figure 8. Performance comparison between an eigenvalue detector and an energy detector.

Another technique used for spectrum sensing in cognitive radios networks is to perform multi resolution spectral analysis using wavelets. Some authors [20] have proposed to use wavelets for detecting transitions in the spectrum, corresponding to the switch between an idle and a busy channel. They reported a good performance under low SNR regimes. The main advantage of this approach is the capability of perform wide-band spectrum sensing. Additionally, the use of wavelets can achieve a performance close to a cyclostationary feature detector, according to some authors [21]. The IEEE 802.22 standard for cognitive wireless regional area networks also includes this technique for performing a fast and raw spectrum sensing.

4. CONCLUSIONS With the purpose of increasing the spectrum utilization efficiency, several spectrum sensing techniques have been proposed by different authors during the last few years, most of them for achieving spectrum awareness in Cognitive Radio networks. In this paper, a performance comparison of the main spectrum sensing techniques under similar conditions has been conducted. The highest performance is achieved by those networks whose cognitive users perform matched filterbased spectrum sensing. However, The primary user signal must be known to perform coherent detection. The other solutions are suboptimal, but they allow a more relaxed detection scheme, with partial information about the primary user signals, or no information at all. A trade-off between complexity and detection performance is present.

5. Panaousis E, Frangoudis P, Ververidis C, Polyzos G. Optimizing the channel load reporting process in IEEE 802.11k-enabled WLANs. Dept. of Computer Science of the Athens University of Economics and Business; 2008. 6. Kay S. M. Fundamentals of Statistical Signal Processing: Detection Theory. vol. II of Signal Processing Series. Prentice Hall; 1993. 7. Wang B, Liu K. J. Advances in cognitive radio networks: A survey. IEEE Journal of Selected Topics in Signal Processing. 2011 Feb;5(1):5– 23. 8. Bagwari A, Tomar G. Multiple energy detection vs. cyclostationary feature detectionspectrum sensing technique. Fourth International Conference on Communication Systems and Network Technologies. 2014;p. 178{181. 9. Satheesh A, Sruthi S, Kumar H. Spectrum sensing techniques A comparison betweenenergy detector and cyclostationarity detector. International Conference on Control Communicationand Computing (ICCC). 2013;p. 388-393. 10. Cabric D, Mishra SM, Brodersen RW. Implementation issues in spectrum sensing for cognitive radios. In: Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004. 2004. p. 772– 776 Vol.1. 11. Gardner W. Statistical Spectral Analysis: A Nonprobabilistic Theory. Prentice-Hall; 1988. 12. Gardner W. Measurement of Spectral Correlation. IEEE Transaction on Acoustics, Speech,and Signal Processing. 1986;ASSP34(5):1111-1123.

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Gato, Luis; Martínez, L.; Torres, J. | “COMPARACIÓN DE DESEMPEÑO DE TÉCNICAS DE MEDICIÓN DEL ESPECTRO EN REDES DE RADIO COGNITIVA”

13. Akyildiz IF, Lo BF, Balakrishnan R. Cooperative Spectrum Sensing in Cognitive Radio Networks: A Survey. Phys Commun. 2011 Mar;4(1):40–62. 14. Chen Y. Improved energy detector for random signals in Gaussian noise. IEEE Transactions on Wireless Communications. 2010;9(2):558-563.

Zhao Y, et al. Wavelet transform for spectrum sensing in Cognitive Radio networks. IEEE International Conference on Audio, Language and Image Processing (ICALIP). 2014;p. 565569.

ABOUT THE AUTHORS

15. Tandra R, Sahai A. SNR Walls for Signal Detection. IEEE Journal of Selected Topics inSignal Processing. 2008;2(1):4-17. 16. Li Z, et al. A Study of SNR Wall Phenomenon under Cooperative Energy Spectrum Sensing. IEEE - 22nd International Conference on Computer Communications and Networks (ICCCN). 2013;p. 1-5. 17. Shellhammer S. Spectrum sensing in IEEE 802.22. Qualcom Inc. 2010. 18. Yousif E, Ratnarajah T. On the Design and Throughput Analysis of a New MME Detector Using Bartlett's Method. IEEE International Symposium on Information Theory. 2014;p.3107-3111. 19. Dikmese, S. Enhanced spectrum sensing techniques for Cognitive Radio systems., Thesis for the degree of Doctor Science in Technology. University of Tampere, 2015. 20. Tian Z, Giannakis G. Compressed Sensing for Wideband Cognitive Radios. IEEE International Conference on Acoustics, Speech, and Signal Processing. 2007;p. 1357-1360.

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Luis Miguel Gato Diaz. Telecommunications and Electronics Engineer, CUJAE, 2015. Currently working on Spectrum Sensing Algorithms, Cognitive Radio platforms and Cooperative Communications. Email: [email protected].

Liset Martínez Marrero. Telecommunications and Electronics Engineer, CUJAE, 2013. Currently working on Spectrum Sensing Algorithms, Cognitive Radio platforms, Cooperative Communications, Energy Efficiency Algorithms and Energy Harvesting Solutions. Email: [email protected] . Jorge Torres Gómez. Dr.C. Telecommunications and Electronics Engineer, CUJAE, 2009. Currently working on Spectrum Sensing Algorithms, Cognitive Radio platforms, Cooperative Communications, Energy Efficiency Algorithms and Energy Harvesting Solutions. Email: [email protected].