WEICHAO ZHONG et al: SPECTRUM SENSING ALGORITHM TO DETECT SMALL-SCALE PRIMARY USERS …
Spectrum Sensing Algorithm to Detect Small-Scale Primary Users Based on
Maximum-Minimum Eigenvalue
Weichao ZHONG1 ,Pin WAN1,4,Yonghua WANG1,2,3, Ting LIANG 3, Yiquan ZHENG 1
1 School of Automation, Guangdong University of Technology, Guangzhou 510006, China
2 School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510641, China
3 China Electronics Technology Group Corporation No.7 Research Institute, Guangzhou 510310, China
4 Hubei Key Laboratory of Intelligent Wireless Communications, South-Central University for Nationalities, Wuhan 430074,
China
Abstract — In cognitive radio networks (CRNs), primary users can be divided into large-scale primary users and small-scale mobile
primary users (SSPU), such as wireless microphones. SSPU’s transmission power is weak, its signal is easily influenced by external
factors in the process of detection. The Maximum-Minimum Eigenvalue based algorithm (MME) with no prior knowledge about
the PU signal can still be effective under low SNR. So the MME is used to detect the SSPU signal in this paper, and its
performances are compared with the energy detection (ED). The detection performance of the traditional MME algorithm can still
be improved. Then the algorithm is improved by adding the weight coefficient, and we propose a new MME algorithm for SSPU
detection. This paper discusses the impact on detection performance of the number of SUs and the number of samples. The
simulation results show that the improved MME algorithm can effectively sense SSPU signal in low SNR environment, and achieve
the purpose of improving the detection probability.
Keywords - cognitive radio, spectrum sensing, small-scale mobile primary user, maximum-minimum eigenvalue, weight.
I. INTRODUCTION
Cognitive radio (CR) technology has great potential to
enhance spectrum efficiency by allowing secondary
(unlicensed) users/devices to utilize spectrum opportunities
temporarily unused by primary users (PUs).
Spectrum sensing technology is one of the key
technologies of cognitive radio. A lot of algorithms have
been proposed to detect the PU. Although many proposed
algorithms have good performance. Most of the methods
have generally focused on the various aspects of detecting
large-scale primary signals (e.g., TV signals). The spectrum
detection of small-scale primary users (SSPUs) such as
wireless microphones (WMs) and mobile devices is still an
open and challenging problem due to the characteristics of
SSPU. First, the weak transmit power of SSPUs (typically
10-50mW) makes the SU to perform spectrum sensing
under a low SNR, and the transmission range of a SSPU is
small, i.e., 100-150 m; Second, the spatial and temporal
variations of SSPUs are unpredictable, which brings
difficulties (such as time-varying channel and noise
uncertainty) to detect the SSPUs; Third, SSPU is always in a
mobile state [1].
Despite its practical importance, however, little has been
made for the research on small-scale primary signals. Based
on the correlation of temporal shadow fading of the energy
signal of the main user perceived by the cooperative nodes
due to mobility. [2] proposed a framework of robust
tracking of SSPU. Due to lack of energy detection accuracy,
it can not make sure about the performance of detecting PU.
In [3], by comparing and analyzing the energy detection and
DOI 10.5013/ IJSSST.a.17.44.39
the matched filter detection, the method of combining the
cooperative sensing and the matched filtering detection is
proposed. Combines the advantages of both, it optimized the
detection performance of SSPU. [4] adopts the double
threshold detection. It estimates the signal transmitting
power/position in the detection process repeatedly. Then the
cooperative sensing method is carried out, which improves
the detection performance of the PU signal to a certain
extent.
The spectrum sensing algorithm based on eigenvalue is
firstly introduced by S. Cardoso Leonardo (LSC method),
which is based on random matrix theory [5]. This algorithm
uses the Marchenko-Pastur law sensing system to give the
solution. However, its sample size not small, so it can not
satisfy certain conditions of the random matrix theory. Zeng
Yonghong proposed a method based on the maximum and
minimum eigenvalues (called MME method) [6]. In [7],
Kortun worked out the exact threshold value formula of
MME algorithm. The formula is closely related to the false
alarm probability. Then referring literature [8], Kortun
obtained a cooperative MME algorithm for sensing the radio,
which uses the distribution of the max eigenvalue to get the
detection threshold. According to the properties of Wishart
matrix, the ratio of the maximum eigenvalue and the
minimum eigenvalue is used as the statistical test. This
algorithm does not require the priori knowledge of PU
signal, which can have better detection performance in low
signal to noise ratio environment. Compared with other
methods, MME is wide applicability and with no obvious
disadvantages. However, the algorithm also has some
defects, such as the precise threshold is set too complicated,
39.1
ISSN: 1473-804x online, 1473-8031 print
WEICHAO ZHONG et al: SPECTRUM SENSING ALGORITHM TO DETECT SMALL-SCALE PRIMARY USERS …
and even it not has a concise form of expression. It makes
the theoretical derivation to estimate the performance of the
algorithm is not particularly good.
Considering the characteristics of SSPU, which can be
easily impacted on external shadowing and multipath fading
in the process of sensing, the signal-to-noise ratio of PU is
very low. In [9], it shows that the matrix of sampled signals
of MME algorithm has great randomness. The algorithm
makes full use of a random matrix of the asymptotic
spectrum distribution characteristics and values of
convergence to set the test statistic to improve perceived
performance. Therefore, MME algorithm is used to achieve
the SSPU sensing. In the experiment, the wireless
microphone signal is used as the research object, and the
signal is detected by MME algorithm and ED algorithm. In
addition to the detection performance of the two algorithms,
this paper has discussed the impact on detection
performance of the number of SUs and the number of
sample. Finally we improve this algorithm with adding the
concept of weight, which is according tothe user and the
primary user distance weighted sampling signal. The
improved MME algorithm can effectively detect SSPU
signal in low SNR environment and obviously achieve a
good performance.
H 0 and H1
of primary user respectively. Let xi ( k ) be the discrete
baseband sample at receiver
distributed white noise with zero mean and variance  .
hi (k ) denotes the channel response to receiver k, which is
assumed to be constant during the sensing time.
The spectrum sensing of cognitive radio networks can be
simplified as a hypothesis testing problem.
2
H0 ,T  
Decision 
 H1 , T  
Where T is test statistic,  is the threshold based on the
algorithm.
Generally, the spectrum sensing performance of
cognitive radio networks is described by false alarm
probability and detection probability. The false alarm
probability is defined as that the PU signal is detected when
PU is not present.
(3)
Pf  Prob(T   | H 0 )
Pd  Prob(T   | H1 )
 
T
x(k )  [ x1 (k ), , xM (k )]T
(6)
T
(7)
 (k )  [1 (k ),M (k )]
denotes transposed of the matrix,
k  1, 2, , N .
Where denotes yi (k ) be the discrete baseband sample at
receiver i (i  1, , M ) at time instant k ( k  1,  , N ) .
The received samples are stored by the detector or Fusion
center in the M  N matrix.
 8)
(1)
(4)
B. MME Algorithm
From type (1), the fusion center gets the combined
received signal matrix as
(5)
y (k )  [ y1 (k ), , yM (k )]T
 y1 (1)
 y (1)
Y  2
 

 yM (1)
In the fundamental transmitter detecting method, the
problem about PUs detection can be described as following
hypothesis
DOI 10.5013/ IJSSST.a.17.44.39
(2)
The detection probability is defined as
A. System Model
In this paper, we consider a cognitive radio network
framework with M SUs, such as Figure 1. The shadow part
is the signal coverage of SSPU (50-150m), and the sensing
target is the wireless microphone signal (WM). Assume the
following conditions:
 The M secondary users are located within the
primary user coverage area.
 The M secondary users are trying to sense the same
channel.
 The detection system has a priori knowledge about
the secondary users locations.
 Fusion center can be one of the secondary users.
 The distance between secondary users and primary
users is obtained according to the RSS algorithm.
H0
i (k ),
yi (k )  
hi (k ) xi (k )  i (k ), H 1
i (i  1, , M ) at time instant
k (k  1,  , N ) . i (k ) is the received normally
II. SSPU SENSING BASED on MME ALGORITHM
Figure 1. Cooperative spectrum sensing scenario ( M
are stand for no primary user and existing
y1 ( N ) 
y2 ( N ) 


 

yM (2)  yM ( N ) 
y1 (2) 
y2 (2) 
(8)
Here denotes the sample covariance matrix of the
received signal is:
R( N ) 
1
YY H
N
(9)
H
Matrix Y denotes transposed of the matrix Y .
Assuming the eigenvalues of the sample covariance
matrix are 1 , 2 , M . Where M is the number of SUs.
39.2
ISSN: 1473-804x online, 1473-8031 print
WEICHAO ZHONG et al: SPECTRUM SENSING ALGORITHM TO DETECT SMALL-SCALE PRIMARY USERS …
According to (9), the maximum and minimum eigenvalues
of the covariance matrix R ( N ) are obtained respectively
min  min[1 , 2 , M ]
max  max[1 , 2 , M ]
(WM). Most of the WM signals are transmitted using FM
mode. The signal model is as follows
t
(10)
x (t )  Ac cos[2 f c t  2 k f  m( ) d ]
(11)
Where Ac is carrier amplitude, f c is carrier frequency,
So the test statistic of MME algorithm is
k f is modulation sensitivity, m( ) is modulated signal.

T  max
min
(12)
C. Decision Threshold
The decision threshold of MME algorithm is obtained by
using the random matrix theory. Some knowledge exists
about noise usually the decision threshold is defined based
on the false alarm probability and probability density
function [10]. According to the above theory, literature [11]
derived the threshold of MME algorithm as
According to the difference of the modulation signal
frequency and the modulation sensitivity, the WM signal is
generally divided into three modes. Table 2 lists the
simulation parameters of three kinds of signal modes.
In this paper, the main research is focus on Silent mode.
TABLE II. THREE KINDS OF SIGNAL MODELS
Slient
Soft Speaker
Loud Speaker
( N  M )2

( N  M )2
m( )
[KHZ]
32
3.9
13.4
 ( N  M )  2 3 1

F1 (1  Pf )  (13)
1 
16
( NM )


1
Where F1 (t ) is the inverse Tracy-Widom cumulative
kf
[KHZ]
±5
±15
±32.6

distribution function. According to IEEE 802.22 WRAN
standards, Pf must be equal or less than 0.1( Pf  0.1 ).
Table 1 summarizes the average value of the threshold
from experiments [12]. Where F ( )  1  Pf .
TABLE I. RESULT OF EXPERIMENTS ANDTHEORY

-3.18
-2.78
-1.91
-1.27
-0.59
0.45
0.98
1  Pf
0.05
0.1
0.3
0.5
0.7
0.9
0.95
D. Sensing Algorithm Steps
The MME algorithm steps are as follows:

Step1.Sampling SSPU signal from each SU, and
format the sampling matrix Y from their signal.

Step2. Calculate the covariance matrix R( N ) .

Step3.Figure out the test statistic T .

Step4.Find out the data from Table 1 and
calculate the decision threshold  .

with  .
Step5. Consider the test statistic T and compare
H0 ,T  
Decision 
 H1 , T  
(15)
o
Then the algorithm is verified by MATLAB simulation.
Comparing with the performance of MME and ED in the
case of given false alarm probability. The distribution of
SUs is shown in Figure 1.
In consideration of the requirement of ED, the noise
power must be estimated accurately. However, the noise
power is often different from the actual value due to the
uncertainty of the noise. Here denotes the estimated noise
2
2
variance is ˆ   . The uncertainty of noise

B  max{10 lg  }(dB)
(16)
is the uncertain factor, which obeys the uniform
distribution in [ B, B] .
Fig. 2 and Fig.3 shows the performance comparison of
the MME and the ED under different SNR. Simulation
coefficient: the false alarm probability is 0.1, the numbers of
SUs were 7 and 8, the number of sample is 400, and the
number of Monte-Carlo simulations is 3000.
From the simulation results, we can see that the
detection performance of ED is best when the SNR is low.
When the SNR reaches -14dB, the performance of MME is
better than ED in noise determination. But for ED,
sometimes it is difficult to ensure the certainty of noise in
the actual situation. Once the noise is uncertain, the
detection performance will deteriorate sharply. The
detection probability of ED is close to 0, while the MME
algorithm can overcome the influence of noise uncertainty.
(14)
E. Simulation and Analysis
In this section, the MATLAB simulation of the MME is
presented, and the analysis target is wireless microphone
DOI 10.5013/ IJSSST.a.17.44.39
39.3
ISSN: 1473-804x online, 1473-8031 print
WEICHAO ZHONG et al: SPECTRUM SENSING ALGORITHM TO DETECT SMALL-SCALE PRIMARY USERS …
mi  1 
1
0.9
Probability of detection
0.8
0.5
between the SSPU and the i th SU.
So, we can get the diagonal modification matrix:
0.4
0.3
 m1  0 
W      
 0  mM 
(19)
1
1
R  WY (WY ) H = WYY H W H
N
N
(20)
0.2
MME
ED-0dB
ED-1dB
0.1
-18
-16
-14
-12
-10
-8
SNR(dB)
-6
-4
-2
0
Figure 2. Probability of detection in MME and ED when
M 7
Then the improved sample covariance matrix can be
expressed as:
1
0.9
0.8
Probability of detection
2   di
Where Rd is the reference radius, d i is the distance
0.6
C．Performance Analysis of Improved MME Algorithm
This paper proposes an improved MME algorithm with
the weight coefficient for SSPU detection. In Fig.4, the
radius of coverage area is 150m, Rd is 75m. Because the
position of SSPU is random, the distance between the PU
and the SUs is random when the WM signal appears, so the
distance d i is given randomly in the simulation.
0.7
0.6
0.5
0.4
0.3
0.2
MME
ED-0dB
ED-1dB
0.1
0
-20
(18)
M
i 1
0.7
0
-20
Rd  di
-18
-16
-14
-12
-10
-8
SNR(dB)
-6
-4
-2
0
Figure 3. Probability of detection in MME and ED when
M 8
III. MME ALGORITHM IMPROVEMENT
B．Weight Analysis
In most of the previous works the effect of different
distance on SNR of SUs from PU has not been taken into
account, especially for SSPU. In [13], the SSPU is very
difficult to detect accurately because of the influence of
channel fading and shadowing in the spectrum sensing
process. So this paper increases the signal weighting
coefficient about the distance between the SUs and the
SSPU.
In [14], the distance-weighted modification function has
been defined as:
(17)
mi  f ( Rd , di )
DOI 10.5013/ IJSSST.a.17.44.39
Figure 4. The improved MME sensing scenario ( M
 9)
We set M=9, N=400, false alarm probability Pf is 0.1,
the average SNR of the secondary users range from -20dB
to 0dB.
1
0.9
0.8
Probability of detection
A．The Shortage of the Traditional MME Algorithm
Although the traditional MME algorithm has a wide
applicability, it still has some problems in sensing SSPU
signal.
 According to the simulation results of Fig.2 and
Fig.3, the performance of traditional MME
algorithm is poor in low SNR. Beside the traditional
MME algorithm is complex.
 Because of its low signal power, SSPU signal is
sensitive to environmental factors. The influence of
distance between PU and SUs is ignored in the
traditional MME algorithm.
0.7
0.6
0.5
0.4
0.3
0.2
Traditional MME
Improved MME
ED-0dB
0.1
0
-20
-18
-16
-14
-12
-10
-8
SNR(dB)
-6
-4
-2
0
Figure 5. Probability of detection for three algorithms
Fig.5 shows the comparison of the improved MME
algorithm with the traditional MME algorithm and ED
39.4
ISSN: 1473-804x online, 1473-8031 print
WEICHAO ZHONG et al: SPECTRUM SENSING ALGORITHM TO DETECT SMALL-SCALE PRIMARY USERS …
algorithm. Under the different SNRs, we can find that the
performance of improved MME is better than the other
algorithms. The detection probability of the MME is very
low in the low SNR (-18dB or so). The detection
performance of improved MME is obvious, when the SNR
reaches -12dB, the spectrum detection probability can reach
more than 90%. In comparison of improved MME and ED,
the performance of the improved MME is better than that of
the ED, and it also shows good results in low SNR.
1
M=9
Probability of detection
0.5
0
-20
Maximum
Minimum
-15
-10
SNR(dB)
M=10
-5
0
1
Probability of detection
Probability of detection
Probability of detection
D．Effects of the Number of SUs
The spectrum sensing of SSPU and large-scale primary
user have a big difference. The number of SUs in the
cognitive network has a decisive effect on sensing SSPU
signal, so the first step is to consider the number of SUs.
Simulation parameters are set as follows: the number of SUs
is from 8 to 11, the average SNR of the secondary users
ranges from -20dB to 0dB, and the number of Monte-Carlo
simulations is 3000.
M=8
1
0.5
0
-20
Maximum
Minimum
-15
-10
SNR(dB)
-5
0
1
0.5
0
-20
Maximum
Minimum
-15
-10
SNR(dB)
M=11
-15
-10
SNR(dB)
-5
0
1
0.5
0
-20
Maximum
Minimum
-5
0
Figure 7. Effects of the number of SUs
E．Effects of the Number of Samples
Then the simulation is for sensing WM signal under the
different SNR (-9dB, -12dB, -15dB, and -18dB). Number of
samples in the range of 100 to 1000 and the number of
Monte-Carlo simulations is 3000.
0.9
1
0.9
0.7
0.8
0.6
Probability of detection
Probability of detection
0.8
0.5
0.4
0.3
M=8,N=400
M=9,N=400
M=10,N=400
M=11,N=400
0.2
0.1
-20
-18
-16
-14
-12
-10
-8
SNR(dB)
-6
-4
-2
0.5
SNR=-9dB
SNR=-12dB
SNR=-15dB
SNR=-18dB
0.4
0.3
0.1
0
100
Figure 6. Effects of the number of SUs
DOI 10.5013/ IJSSST.a.17.44.39
0.6
0.2
0
From the simulation results of Fig.6, it can be found that
the detection probability is very close in the low SNR
environment. With the increase of SNR, there is a certain
gap in the range of -15dB to -13 dB. The gap of the
detection probability becomes narrow in the -12dB, which
have reached more than 90%. At the same time, when the
SNR above -17dB, the probability of detection is
proportional to the number of SUs. From the Fig.6, the 4
curves can be found as the number of SUs increases, the
detection probability tends to be stable. Increase the number
of SUs will also increase the amount of calculation. So to
select that number is particularly important in sensing SSPU
signal.
From Fig. 7 simulation results showed that when the
number of users increased, the fluctuation range of detection
probability will be smaller. When the number of SUs is
M=8 and M=9, the fluctuation range of the detection
probability is relatively large. That range is up to 20%. This
greatly affected the accuracy of detection. With the increase
of the number of SUs will gradually narrow the range, and
ensure the accuracy of the algorithm.
0.7
200
300
400
500
600
700
Number of samples
800
900
1000
Figure 8. Effects on number of samples
Fig.8 shows that the probability of detection is increased
with the increase of the number of samples. At the same
time, the number of users has little effect on the probability
of detection under the low SNR. However, with the increase
of SNR, the effection on the number of samples is more and
more obvious. Although more samples will improve the
detection performance, but also will increase the amount of
calculation.
IV. CONCLUSIONS
In order to solve the problem of spectrum sensing in
SSPU, this paper studies the traditional MME algorithm,
and proposes an improved MME algorithm for spectrum
sensing. The simulation results show that the proposed
algorithm can overcome the influence of noise uncertainty
on the detection performance. It can also detect SSPU signal
effectively even in the low SNR environment. Increase the
number of SUs and the number of samples will also increase
the amount of calculation. It needs to be solved in later
studies.
39.5
ISSN: 1473-804x online, 1473-8031 print
WEICHAO ZHONG et al: SPECTRUM SENSING ALGORITHM TO DETECT SMALL-SCALE PRIMARY USERS …
ACKNOWLEDGEMENTS
This work was supported in part by the China
Postdoctoral Science Foundation (No.2014M552529,
No.2015T80920), the National Natural Science Foundation
of China (No.61471174),the Youth Foundation of
Guangdong University of Technology (No.13QNZD006),
the Higher Education Teaching Reform Project of
Guangdong Province (No.GDJG20142179), Innovation and
Entrepreneurship Training Programs for College Students
(No.201411845145) and Higher Education Quality Project
of Guangdong Province .
[6]
[7]
[8]
[9]
REFERENCES
[1]
[2]
[3]
[4]
[5]
Yuan Jing, Li Ma, Peng Li, Ji Ma and Bin Niu, "A novel spectrum
sensing algorithm for small-scale primary users detection," in
TENCON 2013 - 2013 IEEE Region 10 Conference (31194) , vol.,
no., pp.1-4, 22-25 Oct. 2013.
A.W.Min and K.G.Shin,"Robust Tracking of Small-Scale Mobile
Primary User in Cognitive Radio Networks," in Parallel and
Distributed Systems, IEEE Transactions on, vol.24, no.4, pp.778-788,
April, 2013.
K.Park and C.Kim, "Minimal sensor density for small-scale primary
detection in cognitive radio networks," in Information Networking
(ICOIN), 2011 International Conference on , vol., no., pp.457-462,
26-28 Jan. 2011.
A.W.Min, X.Zhang and K.G.Shin, "Detection of Small-Scale Primary
Users in Cognitive Radio Networks," in Selected Areas in
Communications, IEEE Journal on , vol.29, no.2, pp.349-361,
February,2011.
L.S.Cardoso, M.Debbah, P.Bianchi and J.Najim, "Cooperative
spectrum sensing using random matrix theory," in Wireless Pervasive
Computing, 2008. ISWPC 2008. 3rd International Symposium on ,
vol., no., pp.334-338, 7-9 May 2008.
DOI 10.5013/ IJSSST.a.17.44.39
[10]
[11]
[12]
[13]
[14]
39.6
Y.Zeng and Y.Liang, "Maximum-Minimum Eigenvalue Detection for
Cognitive Radio," in Personal, Indoor and Mobile Radio
Communications, 2007. PIMRC 2007. IEEE 18th International
Symposium on, vol., no., pp.1-5, 3-7 Sept. 2007.
A.Kortun, T.Ratnarajah, M.Sellathurai and C.Zhong, "On the
Performance of Eigenvalue-Based Spectrum Sensing for Cognitive
Radio," in New Frontiers in Dynamic Spectrum, 2010 IEEE
Symposium on , vol., no., pp.1-6, 6-9 April 2010.
W.Lei, “Cooperative Spectrum Sensing Based on Random Matrix
Theory,” in Journal of Electronics & Information Technology on, vol.
31, no. 8, pp. 1925-1929, 2009.
Y.Zeng and Y.Liang, "Covariance Based Signal Detections for
Cognitive Radio," in New Frontiers in Dynamic Spectrum Access
Networks, 2007. DySPAN 2007. 2nd IEEE International Symposium
on , vol., no., pp.202-207, 17-20 April 2007.
A.K.Kang and H.E.Bin, “A cooperative spectrum detection algorithm
based on maximum-minimum eigenvalue,” Journal of Changchun
University of Technology: Natural Science Edition, vol. 32, no. 3, pp.
214-217, 2011.
Y.Zeng and Y.Liang, "Eigenvalue-based spectrum sensing algorithms
for cognitive radio," in Communications, IEEE Transactions on ,
vol.57, no.6, pp.1784-1793, June 2009.
M.Chiani and A.Zanella, "Joint distribution of an arbitrary subset of
the ordered eigenvalues of Wishart matrices," in Personal, Indoor and
Mobile Radio Communications, 2008. PIMRC 2008. IEEE 19th
International Symposium on , vol., no., pp.1-6, 15-18 Sept. 2008.
W.Huang, P.Wan, Y.Wang, J.Huang, W.Jiang, et al, “Research on
perception and location of small-scale mobile primary users in
cognitive radio networks”. Mobile Communications, vol. 10, pp. 7984, 2014.
C.Liu and M.Yang, “A Distance-Weighed Algorithm Based on
Maximum-Minimum Eigenvalues for Cooperative Spectrum
Sensing,” in International Conference on Wireless Communications,
Networking & Mobile Computing. Wuhan, 2011: pp. 1-4.
ISSN: 1473-804x online, 1473-8031 print