Optimal Threshold of Welch's Periodogram for ... - Semantic Scholar
EW2013 1569717137 European Wireless 2013, 16 – 18 April, 2013, Guildford, UK
ISBN 978-3-8007-3498-6
© VDE VERLAG GMBH • Berlin • Offenbach, Germany
Optimal Threshold of Welch’s Periodogram for Sensing OFDM Signals at Low SNR Levels Nan Wang, Yue Gao School of Electronic Engineering and Computer Science Queen Mary University of London, London E1 4NS, UK Email: [email protected] Abstract—Spectrum sensing is one of the key technologies to realize dynamic spectrum access in cognitive radio systems, especially being able to reliably detect primary user signal in low signal-to-noise ratio (SNR) levels. In this paper, a new optimal threshold setting algorithm based on the conventional Welch’s energy detection algorithm is proposed to achieve an efficient trade-off between the detection probability and false alarm probability for OFDM signals at the low SNR levels. The proposed optimal threshold algorithm in the Welch’s method demonstrates a better spectrum sensing performance at the low SNR levels. The relationship between the spectrum utilization and optimal threshold is derived. The effect of spectrum utilization on the performance of spectrum sensing is also analyzed.
was considered in [9] to minimize the total error sensing probability. All these work has assumed that the impact factor (weighted factor or spectrum utilization) is a constant value in their derivation or simulations, e.g. 50%. However, the effect of varying impact factors on the performance of spectrum sensing should be considered. In addition to the requirements of the detection probability and false alarm probability, another major challenge for the spectrum sensing is the ability of detecting signal at low SNR levels. However, due to the noise uncertainty, the sensing performance at low SNR levels deteriorates rapidly for the conventional spectrum sensing techniques such as matched filters, energy detectors and even cyclostationary detectors. The sensing performance of Welch’s energy detector was studied for detecting the OFDM signals used in LTE femtocell scenarios at SNR = -11dB in [10]. In [11], spectrum sensing using cyclostationaryity detector was studied for OFDM signals used in DVB-T signals. The minimum sensing level achieved in [11] was -14dB, which still has a big gap compared to the sensing requirement of DTV signals, e.g. -18dB [12]. Therefore, a very challenging task associated with each sensing technique is to detect signals at low SNR levels while optimize the trade-off between the detection and false alarm probability. In this paper, an optimal threshold setting algorithm is proposed to minimize the error decision probability at low SNR levels for different spectrum utilizations. The proposed optimal threshold is also implemented with Welch’s algorithm for the sensing of OFDM signals at the SNR ranging from 20dB to -10dB. Furthermore,variable spectrum utilizations are analyzed with regard to the performance of spectrum sensing. The remainder of this paper is organized as follows: The principle of conventional fixed threshold based Welch’s algorithm is described in Section II. The proposed optimal threshold determination algorithm is described in Section III. The downlink LTE signals used for testing our proposed sensing algorithm are presented in Section IV. In section V, simulations of both proposed and conventional algorithm to detect OFDM signals are compared and analyzed. The conclusions are drawn in Section VI.
I. I NTRODUCTION Cognitive Radio (CR) is being viewed as a new intelligent wireless communication technology to solve the inefficiency of the fixed spectrum assignment policy [1], [2]. The spectrum sensing is one of the most challenging tasks in CR systems as it requires precise accuracy and low complexity for dynamic spectrum access [3]. In the field of spectrum sensing, the performance metric is usually measured as a trade-off between selectivity and sensitivity, and can be specified by the levels of detection probability and false alarm probability. The higher the detection probability, the better the primary user can be protected. The lower the false alarm probability, the more chances a channel can be utilized by a secondary user. A detection probability of 90% and a false alarm probability of 10% have been regarded as the target requirements for all the sensing algorithms [4]. Generally, the performance of spectrum sensing depends greatly on the setting of detection threshold. Most conventional spectrum sensing methods adopt a fixed threshold to distinguish the primary user from noise. For example, an experimental value is set in [5] by the measurements of the noise power. However, it is difficult to guarantee the detection probability and false alarm probability with the fixed threshold setting method, especially when the noise power fluctuates [6] [7]. In order to minimize the required missed detection probability and false alarm probability, a number of optimal threshold setting algorithms have been proposed [8], [9]. In [8], the authors derived an optimal threshold setting algorithm by introducing a weighted factor principle to trade off the detection and false alarm probability. Instead of the weighted factor used in [8], a spectrum utilization factor
II. F IXED T HRESHOLD BASED W ELCH ’ S A LGORITHM The Welch’s algorithm is a modified periodogram. The principle of the Welch’s algorithm is to divide the data sequence
1
European Wireless 2013, 16 – 18 April, 2013, Guildford, UK
Filter and ADC
FFT squaring sevice
Average over M segments
Average over L samples
ISBN 978-3-8007-3498-6
Test against the adaptive threshold
be independent and identically distributed (iid) with zero mean and variance of σn2 . s(n) is the primary user’s signal also assumed to be iid random process with zero mean and variance of σs2 . h(n) is the channel gain. With the signal and noise variance, the signal to noise ratio can be defined as
Fig. 1: Block diagram of the Welch’s periodogram [13]
into segments in order to reduce the large fluctuations of the periodogram [13]. The block diagram of Welch’s periodogram is depicted in Fig. 1. The input data sequence is first filtered and A/D converted. The data sequence is then partitioned into M segments with length L. Furthermore, the FFT is performed for each segment and the samples of each segment are squared, and averaged over the M segments. This is followed by the averaging over L samples in the frequency domain. Finally, the output values in the band of interest are compared to a predefined threshold to decide whether the band is occupied or not. For instance, a signal s(n) is segmented into M segments in the time domain with length L for each segment. L is the number of frequency bins to be averaged around the zero frequency. Therefore, an input signal s(n) can be defined as a matrix with L × M length with elements s(m, l) = s(l + (m − 1) · (L − 1))
SN R =
M 1 2 [|F F T (s(m, l))|] M m=1
Pd = P (Y > λ |H1 ) = Q
L/2 1 P (l) ≷ λ L
(5)
(6)
(7)
It can be seen that both the detection and false alarm probability are mainly dependent on the threshold λ, if the signal variance σs2 and noise variance σn2 are known. Therefore, the threshold can be derived for a target detection or false alarm value. Under hypothesis H1 , the threshold λPd can be set for a constant detection rate (CDR) [15] as Q−1 (Pd ) 2 2 (8) λPd = (σn + σs ) 1 + N/2
(1)
(2)
Similarly, under hypothesis H0 , the threshold λPf can be set for a constant false alarm rate (CFAR) as Q−1 (Pf ) 2 (9) λ Pf = σ n 1 + N/2 It can be found that the threshold derivation results are similar for both CDR and CFAR. The threshold value based on CFAR is commonly applied in the conventional energy detection algorithm. However, the conventional threshold derivation process faces one problem that it only considers one aspect every time either in the favour of the primary users or the secondary users. If the CR network is designed to guarantee the spectrum efficiency of the secondary user spectrum, the CFAR method should be implemented and the target false alarm probability should be set as small as possible. The lower the false alarm probability, more chances a channel can be utilized by a secondary user. One the other hand, if the CR network is designed to guarantee primary user’s safety use of the spectrum, the CDR method should be used and the target detection probability can be set as high as possible. The higher the detection probability, the better the primary user can be protected. In order to maximize the benefit for both primary and secondary users, the optimal threshold should be set as a trade-off between Pd and Pf .
(3)
l=−L/2
This average energy Y is then compared with the pre-defined fixed threshold λ to determine whether the primary signal is present or not. The detail descriptions of λ will be shown in Section III. III. P ROPOSED O PTIMAL T HRESHOLD BASED W ELCH ’ S A LGORITHM In spectrum sensing field, the decision problem can be formulated into a binary hypothesis form H0 : y(n) = w(n) (signal absent) H1 : y(n) = h(n)s(n) + w(n) (signal present)
λ − (σn2 + σs2 ) (σn2 + σs2 )/ N/2
and the false alarm probability can be given as λ − σn2 Pf = P (Y > λ |H0 ) = Q σn2 / N/2
The average signal energy P (l) is averaged over L samples in the frequency domain. The average energy over the entire frequency band, Y, is obtained: Y =
σs2 σn2
The performance metric of spectrum sensing can be measured by the detection probability Pd and the false alarm probability Pf . When the sample points N is large enough, the detection probability Pd can be derived by [14]
where m = 1,...M and l = 1,...L. After partitioning the input signal s(n) into M segments, FFT is first applied to each segment, and averaging is then performed over the squared outputs of the FFT. At this point, the average signal energy of s(n) in the frequency domain can be presented by: P (l) =
© VDE VERLAG GMBH • Berlin • Offenbach, Germany
(4)
Where H0 and H1 denote the primary user absent or present respectively. y(n) is the received signal (n = 0,1,...,N-1). w(n) represents the additive white Gaussian noise and assumed to
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European Wireless 2013, 16 – 18 April, 2013, Guildford, UK
ISBN 978-3-8007-3498-6
In this paper, the optimization problem is formulated to an equivalent problem of minimizing the proposed error decision probability Pe in the function of the spectrum utilization α and threshold λ as
© VDE VERLAG GMBH • Berlin • Offenbach, Germany
TABLE I: Parameters for LTE downlink signals [16] Duplex
Frequency Division Duplex (FDD)
LTE channel
4.5
Number of LTE channels
16
Subcarrier spacing
15 KHz
(10)
Number of useful carriers
300
where (1 − Pd ) represents the probability that Welch’s energy detection algorithm indicates the primary user is absent while actually present. α(1 − Pd ) indicates the error decision probability for primary user being present with spectrum utilization α. Similarly, (1 − α)Pf is the error decision probability for primary user being absent. Therefore, our goal is try to minimize the total error decision probability as much as possible. Substitute Pd in equation (6) and Pf in equation (7) into equation (10)
Number of resource blocks
25
· (σn2 + σs2 N
σs2 )
ln
(1 −
α)(σn2 ασn2
+
σs2 )
λ1 =
λ2 =
2 +σ 2 ) 4(2σn s N σs2
· ln
2) (1−α)(σs2 +σn 2 ασn
1− 1+
2 +σ 2 ) 4(2σn s N σs2
· ln
2) (1−α)(σs2 +σn 2 ασn
λ∗ =
1+
1+
2 +σ 2 ) 4(2σn s N σs2
· ln
2 +σ 2 ) (2σn s 2 (σ 2 +σ 2 ) σn n s
2) (1−α)(σs2 +σn 2 ασn
Channel 3,7,11,15
Channel 3
Channel 15
Channel 11
Channel 7
1.4 1.2 1 0.8 0.6 0.4
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Frequency (Hz)
5.5
6
6.5
7
7.5 8 7 x 10
Fig. 2: PSD for 16 LTE channels where channel 3,7,11 and 15 are occupied (SNR=10dB).
=0
(12)
perform spectrum sensing. The effect of spectrum utilization α on the performance of the spectrum sensing will also be analyzed in this paper.
IV. T RANSMISSION PARAMETERS OF OFDM S IGNALS The LTE physical layer uses orthogonal frequency division multiple access (OFDMA) in the downlink and single carrier frequency division multiple access (SC-FDMA) in the uplink [16]. In this paper, we take the LTE downlink signals as the study of OFDM signals. The downlink LTE signals used in this paper are generated with the LTE transmission parameters shown in Table I. An example of power spectral density (PSD) for 4 out of 16 LTE channels occupied at SNR = 10dB is shown in Fig. 2. LTE supports channel bandwidth ranging from 1.4MHz to 20MHz. In this paper, it is assumed that there are 16 LTE channels for a spectrum of interest span from 0MHz to 80MHz with each channel occupied 4.5 MHz. Channel 3 (10MHz - 14.5MHz), Channel 7 (30MHz - 34.5MHz), Channel 11 (50MHz - 54.5MHz), Channel 15 (70MHz - 74.5MHz) are assumed to be occupied by four primary users. The remaining 12 channels are empty, but with the additive white Gaussian noise.
(14)
Since the decision threshold should be real and positive. The optimal threshold that can minimize the error decision probability is
80 MHz
Primary users
0 0
(13)
2 +σ 2 ) (2σn s 2 (σ 2 +σ 2 ) σn n s
Sampling frequency
0.2
2 +σ 2 ) (2σn s 2 (σ 2 +σ 2 ) σn n s
2048
1.6
The solutions are 1+ 1+
12
FFT size
1.8
Pe (λ) = (1 − α)Pf + α(1 − Pd ) 2 2 λ−σn λ−(σn +σs2 ) √ √ + α 1 − Q = (1 − α)Q 2 +σ 2 )/ σ 2 / N/2 (σn N/2 s
∞ −z2n
∞ −z2 1−α α = √π √a e dz − √π √b e dz + α 2 2 (11) 2 2 (λ−σ ) λ−(σn +σs2 ) · N/2. If where a = σ2 n · N/2 and b = σ2 +σ 2 n n s a specific spectrum utilization value α is known in advance, the probability of error decision Pe (λ) will become a convex e (λ) function changing with varying threshold λ. Then ∂P∂λ =0 2σn2 (2σn2 + σs2 ) · λ2 −λ− 2σn2 (σn2 + σs2 )
Number of carriers per RB
Power/Frequency (dB/Hz)
min(Pe ) = min{(1 − α)Pf + α(1 − Pd )}
(15)
According to the above derivation, the optimal threshold of a given spectrum utilization value α can be obtained with the knowledge of the signal and noise variance or the SNR ratio and the number of sample points. This optimal threshold is then implemented with Welch’s algorithm to
3
European Wireless 2013, 16 – 18 April, 2013, Guildford, UK
ISBN 978-3-8007-3498-6
0.4
1 P of Optimal Threshold
0.35
0.9
e
0.3
P of Optimal Threshold d
Pe of Fixed Threshold Probability of detection
Probability of error decision
© VDE VERLAG GMBH • Berlin • Offenbach, Germany
0.25 0.2 0.15 0.1 0.05
Pd of Fixed Threshold
0.8 0.7 0.6 0.5 0.4 0.3
0 −20
−18
−16 −14 −12 Signal to noise ratio (SNR)(dB)
0.2 −20
−10
Fig. 3: Comparison of Pe between the fixed and optimal threshold Welch’s methods for 50% spectrum utilization.
−18
−16 −14 −12 Signal to noise ratio (SNR) (dB)
−10
Fig. 4: Comparison of Pd between the fixed and optimal threshold Welch’s methods for 50% spectrum utilization.
V. S IMULATION R ESULTS A ND A NALYSIS
0.35
Based on the signal parameters described in Table I, the performance of the proposed optimal threshold based Welch’s algorithm is analyzed. In the simulation, the number of sample points is defined as N = 16385. The desired probability of false alarm for the fixed threshold is set as Pf = 0.1. The primary users’ initial spectrum utilization is set to α = 0.5 and a range of varying values will be investigated later. Fig. 3 shows a comparison of error decision probability Pe between traditional fixed and proposed optimal threshold based Welch’s algorithm for 50% spectrum utilization at the SNR ranging from -20dB to -10dB. It can be seen that the Welch’s method with the proposed optimal threshold can always obtain a lower error decision probability compared to the traditional fixed threshold. This is because the optimal solution obtained from equation (15) could always result in a minimum error decision probability. In addition, it can be seen that the error decision probability Pe of both algorithms decreases as the SNR value increases. This is because the higher the SNR value, the easier the primary user can be differentiated from the noise, which leads to more protection to the primary user and more spectrum access opportunities for the secondary users. With the same simulation settings, Pd and Pf for the fixed threshold algorithm is compared with the proposed optimal threshold algorithm, as shown in Fig. 4 and Fig. 5, respectively. Fig. 4 shows a higher detection probability for the proposed optimal threshold based Welch’s algorithm, especially when SNR is lower than -15dB. The false alarm probability of the proposed algorithm drops quickly compared to the conventional fixed one after SNR = -15dB. This is due to the optimal threshold is an increasing function with the increase of SNR values. The optimal threshold is equal to the fixed one at SNR = -15dB and further increases for the 50% spectrum utilization. The proposed optimal threshold performs better in terms of the
Pf of Fixed Threshold
Probability of false alarm
0.3
Pf of Optimal Threshold 0.25 0.2 0.15 0.1 0.05 0 −20
−18
−16 −14 −12 Signal to noise ratio (SNR)(dB)
−10
Fig. 5: Comparison of Pf between fixed and optimal threshold Welch’s methods for 50% spectrum utilization.
detection probability when the SNR value is lower than -15dB and a better false alarm performance when the SNR is greater than -15dB. However, the overall performance of the optimal threshold outperforms the fixed threshold in terms of the error decision probability for SNR ranging from -20dB to -10dB as shown Fig. 3. Fig. 6 depicts the effect of spectrum utilization α on the probability of error decision Pe . The spectrum utilization varies from 25% to 75%. It is obvious to find that the highest total error decision probability Pe can be achieved at α = 50% for the proposed optimal threshold Welch’s method. This indicates that the total spectrum utilization ratio is at the lowest point for both primary and secondary users. No matter α decreases or increases, the error decision probability Pe always decreases. For spectrum utilization α of both 25% and 75%,
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European Wireless 2013, 16 – 18 April, 2013, Guildford, UK
ISBN 978-3-8007-3498-6
[6] T. Yucek and H. Arslan, “A survey of spectrum sensing algorithms for cognitive radio applications,” Communications Surveys Tutorials, IEEE, vol. 11, no. 1, pp. 116–130, Quarter. [7] E. Axell, G. Leus, E. Larsson, and H. Poor, “Spectrum sensing for cognitive radio : State-of-the-art and recent advances,” Signal Processing Magazine, IEEE, vol. 29, no. 3, pp. 101–116, May. [8] S. Zhang and Z. Bao, “An adaptive spectrum sensing algorithm under noise uncertainty,” in Communications (ICC), 2011 IEEE International Conference on, June, pp. 1–5. [9] A. Kozal, M. Merabti, and F. Bouhafs, “An improved energy detection scheme for cognitive radio networks in low snr region,” in Computers and Communications (ISCC), 2012 IEEE Symposium on, July, pp. 000 684–000 689. [10] J. Lotze, S. A. Fahmy, J. Noguera, B. Ozgul, and L. E. Doyle, “Spectrum sensing on lte femtocells for gsm spectrum refarming using xilinx fpgas,” in Software-Defined Radio Forum Technical Conference (SDR Forum), Washington DC, USA, Dec 2009. [11] M. Kim, P. Kimtho, and J.-i. Takada, “Performance enhancement of cyclostationarity detector by utilizing multiple cyclic frequencies of ofdm signals,” in New Frontiers in Dynamic Spectrum, 2010 IEEE Symposium on, April, pp. 1–8. [12] Y. Zeng and Y.-C. Liang, “Maximum-minimum eigenvalue detection for cognitive radio,” in Personal, Indoor and Mobile Radio Communications, 2007. PIMRC 2007. IEEE 18th International Symposium on, Sept., pp. 1–5. [13] P. Stoica and R. L. Moses, Introduction to spectral analysis. Upper Saddle River, N.J. Prentice Hall, 1997. [Online]. Available: http://opac.inria.fr/record=b1092427 [14] Z. Ye, G. Memik, and J. Grosspietsch, “Energy detection using estimated noise variance for spectrum sensing in cognitive radio networks,” in Wireless Communications and Networking Conference, 2008. WCNC 2008. IEEE, 31 2008-April 3, pp. 711–716. [15] E. Peh and Y.-C. Liang, “Optimization for cooperative sensing in cognitive radio networks,” in Wireless Communications and Networking Conference, 2007.WCNC 2007. IEEE, March, pp. 27–32. [16] 3GPP, “Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation,” 3rd Generation Partnership Project (3GPP), TS 36.211, Sep. 2008. [Online]. Available: http: //www.3gpp.org/ftp/Specs/html-info/36211.htm
0.45
Probability of error decision
0.4 0.35
α=25% Optimal Threshold α=50% Optimal Threshold α=75% Optimal Threshold
0.3 0.25 0.2 0.15 0.1 0.05 0 −25
−20 −15 Signal to noise ratio (SNR)(dB)
© VDE VERLAG GMBH • Berlin • Offenbach, Germany
−10
Fig. 6: Comparison of Pe for optimal Welch with different α.
two very close results are obtained.
VI. C ONCLUSION In this paper, an optimal threshold algorithm based on the conventional Welch’s energy detection algorithm has been proposed to minimize the total error decision probability for OFDM sensing signals. A closed-form expression to the optimal threshold has been derived. The simulation results have shown that a lower error decision probability can be obtained for the proposed optimal threshold based Welch’s method compared to the conventional fixed one. The proposed algorithm also showed a higher detection probability and a quick drop in terms of the false alarm probability. The effect of spectrum utilization on the performance of spectrum sensing has also been analyzed. The simulation results have shown that the highest total error decision probability can be obtained when the spectrum utilization is about 50%. R EFERENCES [1] J. Mitola and J. Maguire, G.Q., “Cognitive radio: making software radios more personal,” Personal Communications, IEEE, vol. 6, no. 4, pp. 13– 18, Aug. [2] S. Haykin, “Cognitive radio: brain-empowered wireless communications,” Selected Areas in Communications, IEEE Journal on, vol. 23, no. 2, pp. 201–220, Feb. [3] M. Nekovee, “Impact of cognitive radio on future management of spectrum,” in Cognitive Radio Oriented Wireless Networks and Communications, 2008. CrownCom 2008. 3rd International Conference on, May, pp. 1–6. [4] P. Van Wesemael, S. Pollin, E. Lopez, and A. Dejonghe, “Performance evaluation of sensing solutions for lte and dvb-t,” in New Frontiers in Dynamic Spectrum Access Networks (DySPAN), 2011 IEEE Symposium on, May, pp. 531–537. [5] D. Cabric, A. Tkachenko, and R. W. Brodersen, “Experimental study of spectrum sensing based on energy detection and network cooperation,” in Proceedings of the first international workshop on Technology and policy for accessing spectrum, ser. TAPAS ’06. New York, NY, USA: ACM, 2006. [Online]. Available: http://doi.acm.org/10.1145/1234388.1234400
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ISBN 978-3-8007-3498-6
© VDE VERLAG GMBH • Berlin • Offenbach, Germany
Optimal Threshold of Welch’s Periodogram for Sensing OFDM Signals at Low SNR Levels Nan Wang, Yue Gao School of Electronic Engineering and Computer Science Queen Mary University of London, London E1 4NS, UK Email: [email protected] Abstract—Spectrum sensing is one of the key technologies to realize dynamic spectrum access in cognitive radio systems, especially being able to reliably detect primary user signal in low signal-to-noise ratio (SNR) levels. In this paper, a new optimal threshold setting algorithm based on the conventional Welch’s energy detection algorithm is proposed to achieve an efficient trade-off between the detection probability and false alarm probability for OFDM signals at the low SNR levels. The proposed optimal threshold algorithm in the Welch’s method demonstrates a better spectrum sensing performance at the low SNR levels. The relationship between the spectrum utilization and optimal threshold is derived. The effect of spectrum utilization on the performance of spectrum sensing is also analyzed.
was considered in [9] to minimize the total error sensing probability. All these work has assumed that the impact factor (weighted factor or spectrum utilization) is a constant value in their derivation or simulations, e.g. 50%. However, the effect of varying impact factors on the performance of spectrum sensing should be considered. In addition to the requirements of the detection probability and false alarm probability, another major challenge for the spectrum sensing is the ability of detecting signal at low SNR levels. However, due to the noise uncertainty, the sensing performance at low SNR levels deteriorates rapidly for the conventional spectrum sensing techniques such as matched filters, energy detectors and even cyclostationary detectors. The sensing performance of Welch’s energy detector was studied for detecting the OFDM signals used in LTE femtocell scenarios at SNR = -11dB in [10]. In [11], spectrum sensing using cyclostationaryity detector was studied for OFDM signals used in DVB-T signals. The minimum sensing level achieved in [11] was -14dB, which still has a big gap compared to the sensing requirement of DTV signals, e.g. -18dB [12]. Therefore, a very challenging task associated with each sensing technique is to detect signals at low SNR levels while optimize the trade-off between the detection and false alarm probability. In this paper, an optimal threshold setting algorithm is proposed to minimize the error decision probability at low SNR levels for different spectrum utilizations. The proposed optimal threshold is also implemented with Welch’s algorithm for the sensing of OFDM signals at the SNR ranging from 20dB to -10dB. Furthermore,variable spectrum utilizations are analyzed with regard to the performance of spectrum sensing. The remainder of this paper is organized as follows: The principle of conventional fixed threshold based Welch’s algorithm is described in Section II. The proposed optimal threshold determination algorithm is described in Section III. The downlink LTE signals used for testing our proposed sensing algorithm are presented in Section IV. In section V, simulations of both proposed and conventional algorithm to detect OFDM signals are compared and analyzed. The conclusions are drawn in Section VI.
I. I NTRODUCTION Cognitive Radio (CR) is being viewed as a new intelligent wireless communication technology to solve the inefficiency of the fixed spectrum assignment policy [1], [2]. The spectrum sensing is one of the most challenging tasks in CR systems as it requires precise accuracy and low complexity for dynamic spectrum access [3]. In the field of spectrum sensing, the performance metric is usually measured as a trade-off between selectivity and sensitivity, and can be specified by the levels of detection probability and false alarm probability. The higher the detection probability, the better the primary user can be protected. The lower the false alarm probability, the more chances a channel can be utilized by a secondary user. A detection probability of 90% and a false alarm probability of 10% have been regarded as the target requirements for all the sensing algorithms [4]. Generally, the performance of spectrum sensing depends greatly on the setting of detection threshold. Most conventional spectrum sensing methods adopt a fixed threshold to distinguish the primary user from noise. For example, an experimental value is set in [5] by the measurements of the noise power. However, it is difficult to guarantee the detection probability and false alarm probability with the fixed threshold setting method, especially when the noise power fluctuates [6] [7]. In order to minimize the required missed detection probability and false alarm probability, a number of optimal threshold setting algorithms have been proposed [8], [9]. In [8], the authors derived an optimal threshold setting algorithm by introducing a weighted factor principle to trade off the detection and false alarm probability. Instead of the weighted factor used in [8], a spectrum utilization factor
II. F IXED T HRESHOLD BASED W ELCH ’ S A LGORITHM The Welch’s algorithm is a modified periodogram. The principle of the Welch’s algorithm is to divide the data sequence
1
European Wireless 2013, 16 – 18 April, 2013, Guildford, UK
Filter and ADC
FFT squaring sevice
Average over M segments
Average over L samples
ISBN 978-3-8007-3498-6
Test against the adaptive threshold
be independent and identically distributed (iid) with zero mean and variance of σn2 . s(n) is the primary user’s signal also assumed to be iid random process with zero mean and variance of σs2 . h(n) is the channel gain. With the signal and noise variance, the signal to noise ratio can be defined as
Fig. 1: Block diagram of the Welch’s periodogram [13]
into segments in order to reduce the large fluctuations of the periodogram [13]. The block diagram of Welch’s periodogram is depicted in Fig. 1. The input data sequence is first filtered and A/D converted. The data sequence is then partitioned into M segments with length L. Furthermore, the FFT is performed for each segment and the samples of each segment are squared, and averaged over the M segments. This is followed by the averaging over L samples in the frequency domain. Finally, the output values in the band of interest are compared to a predefined threshold to decide whether the band is occupied or not. For instance, a signal s(n) is segmented into M segments in the time domain with length L for each segment. L is the number of frequency bins to be averaged around the zero frequency. Therefore, an input signal s(n) can be defined as a matrix with L × M length with elements s(m, l) = s(l + (m − 1) · (L − 1))
SN R =
M 1 2 [|F F T (s(m, l))|] M m=1
Pd = P (Y > λ |H1 ) = Q
L/2 1 P (l) ≷ λ L
(5)
(6)
(7)
It can be seen that both the detection and false alarm probability are mainly dependent on the threshold λ, if the signal variance σs2 and noise variance σn2 are known. Therefore, the threshold can be derived for a target detection or false alarm value. Under hypothesis H1 , the threshold λPd can be set for a constant detection rate (CDR) [15] as Q−1 (Pd ) 2 2 (8) λPd = (σn + σs ) 1 + N/2
(1)
(2)
Similarly, under hypothesis H0 , the threshold λPf can be set for a constant false alarm rate (CFAR) as Q−1 (Pf ) 2 (9) λ Pf = σ n 1 + N/2 It can be found that the threshold derivation results are similar for both CDR and CFAR. The threshold value based on CFAR is commonly applied in the conventional energy detection algorithm. However, the conventional threshold derivation process faces one problem that it only considers one aspect every time either in the favour of the primary users or the secondary users. If the CR network is designed to guarantee the spectrum efficiency of the secondary user spectrum, the CFAR method should be implemented and the target false alarm probability should be set as small as possible. The lower the false alarm probability, more chances a channel can be utilized by a secondary user. One the other hand, if the CR network is designed to guarantee primary user’s safety use of the spectrum, the CDR method should be used and the target detection probability can be set as high as possible. The higher the detection probability, the better the primary user can be protected. In order to maximize the benefit for both primary and secondary users, the optimal threshold should be set as a trade-off between Pd and Pf .
(3)
l=−L/2
This average energy Y is then compared with the pre-defined fixed threshold λ to determine whether the primary signal is present or not. The detail descriptions of λ will be shown in Section III. III. P ROPOSED O PTIMAL T HRESHOLD BASED W ELCH ’ S A LGORITHM In spectrum sensing field, the decision problem can be formulated into a binary hypothesis form H0 : y(n) = w(n) (signal absent) H1 : y(n) = h(n)s(n) + w(n) (signal present)
λ − (σn2 + σs2 ) (σn2 + σs2 )/ N/2
and the false alarm probability can be given as λ − σn2 Pf = P (Y > λ |H0 ) = Q σn2 / N/2
The average signal energy P (l) is averaged over L samples in the frequency domain. The average energy over the entire frequency band, Y, is obtained: Y =
σs2 σn2
The performance metric of spectrum sensing can be measured by the detection probability Pd and the false alarm probability Pf . When the sample points N is large enough, the detection probability Pd can be derived by [14]
where m = 1,...M and l = 1,...L. After partitioning the input signal s(n) into M segments, FFT is first applied to each segment, and averaging is then performed over the squared outputs of the FFT. At this point, the average signal energy of s(n) in the frequency domain can be presented by: P (l) =
© VDE VERLAG GMBH • Berlin • Offenbach, Germany
(4)
Where H0 and H1 denote the primary user absent or present respectively. y(n) is the received signal (n = 0,1,...,N-1). w(n) represents the additive white Gaussian noise and assumed to
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European Wireless 2013, 16 – 18 April, 2013, Guildford, UK
ISBN 978-3-8007-3498-6
In this paper, the optimization problem is formulated to an equivalent problem of minimizing the proposed error decision probability Pe in the function of the spectrum utilization α and threshold λ as
© VDE VERLAG GMBH • Berlin • Offenbach, Germany
TABLE I: Parameters for LTE downlink signals [16] Duplex
Frequency Division Duplex (FDD)
LTE channel
4.5
Number of LTE channels
16
Subcarrier spacing
15 KHz
(10)
Number of useful carriers
300
where (1 − Pd ) represents the probability that Welch’s energy detection algorithm indicates the primary user is absent while actually present. α(1 − Pd ) indicates the error decision probability for primary user being present with spectrum utilization α. Similarly, (1 − α)Pf is the error decision probability for primary user being absent. Therefore, our goal is try to minimize the total error decision probability as much as possible. Substitute Pd in equation (6) and Pf in equation (7) into equation (10)
Number of resource blocks
25
· (σn2 + σs2 N
σs2 )
ln
(1 −
α)(σn2 ασn2
+
σs2 )
λ1 =
λ2 =
2 +σ 2 ) 4(2σn s N σs2
· ln
2) (1−α)(σs2 +σn 2 ασn
1− 1+
2 +σ 2 ) 4(2σn s N σs2
· ln
2) (1−α)(σs2 +σn 2 ασn
λ∗ =
1+
1+
2 +σ 2 ) 4(2σn s N σs2
· ln
2 +σ 2 ) (2σn s 2 (σ 2 +σ 2 ) σn n s
2) (1−α)(σs2 +σn 2 ασn
Channel 3,7,11,15
Channel 3
Channel 15
Channel 11
Channel 7
1.4 1.2 1 0.8 0.6 0.4
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Frequency (Hz)
5.5
6
6.5
7
7.5 8 7 x 10
Fig. 2: PSD for 16 LTE channels where channel 3,7,11 and 15 are occupied (SNR=10dB).
=0
(12)
perform spectrum sensing. The effect of spectrum utilization α on the performance of the spectrum sensing will also be analyzed in this paper.
IV. T RANSMISSION PARAMETERS OF OFDM S IGNALS The LTE physical layer uses orthogonal frequency division multiple access (OFDMA) in the downlink and single carrier frequency division multiple access (SC-FDMA) in the uplink [16]. In this paper, we take the LTE downlink signals as the study of OFDM signals. The downlink LTE signals used in this paper are generated with the LTE transmission parameters shown in Table I. An example of power spectral density (PSD) for 4 out of 16 LTE channels occupied at SNR = 10dB is shown in Fig. 2. LTE supports channel bandwidth ranging from 1.4MHz to 20MHz. In this paper, it is assumed that there are 16 LTE channels for a spectrum of interest span from 0MHz to 80MHz with each channel occupied 4.5 MHz. Channel 3 (10MHz - 14.5MHz), Channel 7 (30MHz - 34.5MHz), Channel 11 (50MHz - 54.5MHz), Channel 15 (70MHz - 74.5MHz) are assumed to be occupied by four primary users. The remaining 12 channels are empty, but with the additive white Gaussian noise.
(14)
Since the decision threshold should be real and positive. The optimal threshold that can minimize the error decision probability is
80 MHz
Primary users
0 0
(13)
2 +σ 2 ) (2σn s 2 (σ 2 +σ 2 ) σn n s
Sampling frequency
0.2
2 +σ 2 ) (2σn s 2 (σ 2 +σ 2 ) σn n s
2048
1.6
The solutions are 1+ 1+
12
FFT size
1.8
Pe (λ) = (1 − α)Pf + α(1 − Pd ) 2 2 λ−σn λ−(σn +σs2 ) √ √ + α 1 − Q = (1 − α)Q 2 +σ 2 )/ σ 2 / N/2 (σn N/2 s
∞ −z2n
∞ −z2 1−α α = √π √a e dz − √π √b e dz + α 2 2 (11) 2 2 (λ−σ ) λ−(σn +σs2 ) · N/2. If where a = σ2 n · N/2 and b = σ2 +σ 2 n n s a specific spectrum utilization value α is known in advance, the probability of error decision Pe (λ) will become a convex e (λ) function changing with varying threshold λ. Then ∂P∂λ =0 2σn2 (2σn2 + σs2 ) · λ2 −λ− 2σn2 (σn2 + σs2 )
Number of carriers per RB
Power/Frequency (dB/Hz)
min(Pe ) = min{(1 − α)Pf + α(1 − Pd )}
(15)
According to the above derivation, the optimal threshold of a given spectrum utilization value α can be obtained with the knowledge of the signal and noise variance or the SNR ratio and the number of sample points. This optimal threshold is then implemented with Welch’s algorithm to
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European Wireless 2013, 16 – 18 April, 2013, Guildford, UK
ISBN 978-3-8007-3498-6
0.4
1 P of Optimal Threshold
0.35
0.9
e
0.3
P of Optimal Threshold d
Pe of Fixed Threshold Probability of detection
Probability of error decision
© VDE VERLAG GMBH • Berlin • Offenbach, Germany
0.25 0.2 0.15 0.1 0.05
Pd of Fixed Threshold
0.8 0.7 0.6 0.5 0.4 0.3
0 −20
−18
−16 −14 −12 Signal to noise ratio (SNR)(dB)
0.2 −20
−10
Fig. 3: Comparison of Pe between the fixed and optimal threshold Welch’s methods for 50% spectrum utilization.
−18
−16 −14 −12 Signal to noise ratio (SNR) (dB)
−10
Fig. 4: Comparison of Pd between the fixed and optimal threshold Welch’s methods for 50% spectrum utilization.
V. S IMULATION R ESULTS A ND A NALYSIS
0.35
Based on the signal parameters described in Table I, the performance of the proposed optimal threshold based Welch’s algorithm is analyzed. In the simulation, the number of sample points is defined as N = 16385. The desired probability of false alarm for the fixed threshold is set as Pf = 0.1. The primary users’ initial spectrum utilization is set to α = 0.5 and a range of varying values will be investigated later. Fig. 3 shows a comparison of error decision probability Pe between traditional fixed and proposed optimal threshold based Welch’s algorithm for 50% spectrum utilization at the SNR ranging from -20dB to -10dB. It can be seen that the Welch’s method with the proposed optimal threshold can always obtain a lower error decision probability compared to the traditional fixed threshold. This is because the optimal solution obtained from equation (15) could always result in a minimum error decision probability. In addition, it can be seen that the error decision probability Pe of both algorithms decreases as the SNR value increases. This is because the higher the SNR value, the easier the primary user can be differentiated from the noise, which leads to more protection to the primary user and more spectrum access opportunities for the secondary users. With the same simulation settings, Pd and Pf for the fixed threshold algorithm is compared with the proposed optimal threshold algorithm, as shown in Fig. 4 and Fig. 5, respectively. Fig. 4 shows a higher detection probability for the proposed optimal threshold based Welch’s algorithm, especially when SNR is lower than -15dB. The false alarm probability of the proposed algorithm drops quickly compared to the conventional fixed one after SNR = -15dB. This is due to the optimal threshold is an increasing function with the increase of SNR values. The optimal threshold is equal to the fixed one at SNR = -15dB and further increases for the 50% spectrum utilization. The proposed optimal threshold performs better in terms of the
Pf of Fixed Threshold
Probability of false alarm
0.3
Pf of Optimal Threshold 0.25 0.2 0.15 0.1 0.05 0 −20
−18
−16 −14 −12 Signal to noise ratio (SNR)(dB)
−10
Fig. 5: Comparison of Pf between fixed and optimal threshold Welch’s methods for 50% spectrum utilization.
detection probability when the SNR value is lower than -15dB and a better false alarm performance when the SNR is greater than -15dB. However, the overall performance of the optimal threshold outperforms the fixed threshold in terms of the error decision probability for SNR ranging from -20dB to -10dB as shown Fig. 3. Fig. 6 depicts the effect of spectrum utilization α on the probability of error decision Pe . The spectrum utilization varies from 25% to 75%. It is obvious to find that the highest total error decision probability Pe can be achieved at α = 50% for the proposed optimal threshold Welch’s method. This indicates that the total spectrum utilization ratio is at the lowest point for both primary and secondary users. No matter α decreases or increases, the error decision probability Pe always decreases. For spectrum utilization α of both 25% and 75%,
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European Wireless 2013, 16 – 18 April, 2013, Guildford, UK
ISBN 978-3-8007-3498-6
[6] T. Yucek and H. Arslan, “A survey of spectrum sensing algorithms for cognitive radio applications,” Communications Surveys Tutorials, IEEE, vol. 11, no. 1, pp. 116–130, Quarter. [7] E. Axell, G. Leus, E. Larsson, and H. Poor, “Spectrum sensing for cognitive radio : State-of-the-art and recent advances,” Signal Processing Magazine, IEEE, vol. 29, no. 3, pp. 101–116, May. [8] S. Zhang and Z. Bao, “An adaptive spectrum sensing algorithm under noise uncertainty,” in Communications (ICC), 2011 IEEE International Conference on, June, pp. 1–5. [9] A. Kozal, M. Merabti, and F. Bouhafs, “An improved energy detection scheme for cognitive radio networks in low snr region,” in Computers and Communications (ISCC), 2012 IEEE Symposium on, July, pp. 000 684–000 689. [10] J. Lotze, S. A. Fahmy, J. Noguera, B. Ozgul, and L. E. Doyle, “Spectrum sensing on lte femtocells for gsm spectrum refarming using xilinx fpgas,” in Software-Defined Radio Forum Technical Conference (SDR Forum), Washington DC, USA, Dec 2009. [11] M. Kim, P. Kimtho, and J.-i. Takada, “Performance enhancement of cyclostationarity detector by utilizing multiple cyclic frequencies of ofdm signals,” in New Frontiers in Dynamic Spectrum, 2010 IEEE Symposium on, April, pp. 1–8. [12] Y. Zeng and Y.-C. Liang, “Maximum-minimum eigenvalue detection for cognitive radio,” in Personal, Indoor and Mobile Radio Communications, 2007. PIMRC 2007. IEEE 18th International Symposium on, Sept., pp. 1–5. [13] P. Stoica and R. L. Moses, Introduction to spectral analysis. Upper Saddle River, N.J. Prentice Hall, 1997. [Online]. Available: http://opac.inria.fr/record=b1092427 [14] Z. Ye, G. Memik, and J. Grosspietsch, “Energy detection using estimated noise variance for spectrum sensing in cognitive radio networks,” in Wireless Communications and Networking Conference, 2008. WCNC 2008. IEEE, 31 2008-April 3, pp. 711–716. [15] E. Peh and Y.-C. Liang, “Optimization for cooperative sensing in cognitive radio networks,” in Wireless Communications and Networking Conference, 2007.WCNC 2007. IEEE, March, pp. 27–32. [16] 3GPP, “Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation,” 3rd Generation Partnership Project (3GPP), TS 36.211, Sep. 2008. [Online]. Available: http: //www.3gpp.org/ftp/Specs/html-info/36211.htm
0.45
Probability of error decision
0.4 0.35
α=25% Optimal Threshold α=50% Optimal Threshold α=75% Optimal Threshold
0.3 0.25 0.2 0.15 0.1 0.05 0 −25
−20 −15 Signal to noise ratio (SNR)(dB)
© VDE VERLAG GMBH • Berlin • Offenbach, Germany
−10
Fig. 6: Comparison of Pe for optimal Welch with different α.
two very close results are obtained.
VI. C ONCLUSION In this paper, an optimal threshold algorithm based on the conventional Welch’s energy detection algorithm has been proposed to minimize the total error decision probability for OFDM sensing signals. A closed-form expression to the optimal threshold has been derived. The simulation results have shown that a lower error decision probability can be obtained for the proposed optimal threshold based Welch’s method compared to the conventional fixed one. The proposed algorithm also showed a higher detection probability and a quick drop in terms of the false alarm probability. The effect of spectrum utilization on the performance of spectrum sensing has also been analyzed. The simulation results have shown that the highest total error decision probability can be obtained when the spectrum utilization is about 50%. R EFERENCES [1] J. Mitola and J. Maguire, G.Q., “Cognitive radio: making software radios more personal,” Personal Communications, IEEE, vol. 6, no. 4, pp. 13– 18, Aug. [2] S. Haykin, “Cognitive radio: brain-empowered wireless communications,” Selected Areas in Communications, IEEE Journal on, vol. 23, no. 2, pp. 201–220, Feb. [3] M. Nekovee, “Impact of cognitive radio on future management of spectrum,” in Cognitive Radio Oriented Wireless Networks and Communications, 2008. CrownCom 2008. 3rd International Conference on, May, pp. 1–6. [4] P. Van Wesemael, S. Pollin, E. Lopez, and A. Dejonghe, “Performance evaluation of sensing solutions for lte and dvb-t,” in New Frontiers in Dynamic Spectrum Access Networks (DySPAN), 2011 IEEE Symposium on, May, pp. 531–537. [5] D. Cabric, A. Tkachenko, and R. W. Brodersen, “Experimental study of spectrum sensing based on energy detection and network cooperation,” in Proceedings of the first international workshop on Technology and policy for accessing spectrum, ser. TAPAS ’06. New York, NY, USA: ACM, 2006. [Online]. Available: http://doi.acm.org/10.1145/1234388.1234400
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