Analysis of Effect of Primary User Traffic on
Spectrum Sensing Performance
Tinghuai Wang, Yunfei Chen, Evor L. Hines and Bo Zhao
School of Engineering
University of Warwick
Coventry, U.K. CV4 7AL
Email: Tinghuai.Wang, Yunfei.Chen, E.L.Hines, [email protected]
Abstract—The effect of the primary user traffic on the performance of spectrum sensing is investigated. The investigation
considers both local and collaborative spectrum sensing. Numerical results show that the performance of spectrum sensing can be
significantly degraded if the primary user channel state changes
frequently, and that collaborative spectrum sensing is effective
in alleviating the deleterious effect caused by the primary user
traffic.
I. I NTRODUCTION
Cognitive radio (CR) [1] [2] has been proposed to provide
opportunistic access to the licensed spectrum by detecting
the radio environment. Spectrum sensing is an important
requirement in the realization of cognitive radios. Spectrum
sensing enables unlicensed users, referred to as CR users,
to adapt to the radio environment by detecting the spectrum
holes in the absence of cooperation between the licensed
primary users and the CR users, to avoid interferences to the
primary users. In this case, a CR user senses and monitors a
licensed frequency band and opportunistically accesses it if no
primary users are detected. Thus, efficiency and accuracy are
the two most important factors that determine the performance
of spectrum sensing.
Many works have been conducted on spectrum sensing [3]
- [9]. In [3], three different detection methods of spectrum
sensing were investigated as matched filter detector, energy detector, and cyclostationary feature detector. While the matched
filter detector is capable of conducting coherent detection to
maximize the received signal-to-noise ratio, it requires a priori
knowledge of the primary user signal. The energy detector
simplifies the matched filter approach by performing noncoherent detection [4]. However, the energy detector cannot
differentiate between modulated signals, noise and interference
when the signal-to-noise ratio is low. Cyclostationary feature
detector can perform parameter estimation based on the inherent cyclostationary characteristics of modulated signals, and
is able to detect a random signal with a particular modulation
type buried in noise and interference. However, it is difficult to
distinguish interference from the licensed signal. To mitigate
the uncertainties caused by multi-path fading and shadowing,
collaboration among secondary users has been introduced by
several authors [5], [6].
Most of these previous works assume that the primary user
is either absent or present during the whole sensing period.
However, in practice, the primary user may arrive or leave
during the sensing period, especially when a long sensing
period is used to achieve good sensing performance, or when
spectrum sensing is performed for a network with high traffic
load. Thus, the primary user traffic will affect the sensing
performance. Reference [7] applied a traffic model of the
primary user to the optimization of the sensing period, while
the primary user is still either absent or present during the
optimized sensing period. Reference [8] presented a maximum
a posteriori (MAP) energy detection for spectrum sensing,
as well as an analytical model for interference. Although
they recognized the fact that the primary user traffic might
affect the sensing performance, they included this effect in
the interference model rather than in the sensing model.
In this paper, the effect of the primary user traffic on
the performance of spectrum sensing is evaluated. Both local spectrum sensing and collaborative spectrum sensing are
conducted. Numerical results show that the performance of
spectrum sensing is significantly degraded if the primary user
channel state changes frequently between busy and idle, and
that collaborative spectrum sensing is a promising method of
alleviating the deleterious effect caused by the primary user
traffic.
II. S YSTEM M ODEL
Consider two types of users for the interested frequency
band: the primary users and the CR users. The primary users
are licensed to access the frequency band at any time, while the
CR users are only allowed to access the frequency band when
there are no primary users present. The primary users need to
be protected against harmful interferences caused by the CR
users. The energy detector is often used for the detection of
unknown signals in noise. In the energy detection, the output
signal of a band-pass filter with bandwidth W is squared and
integrated over the observation interval, T . The normalized
output of the integrator is compared with a threshold to decide
whether the primary user is present. Let the time-bandwidth
product T W = m, and assume that m is an integer.
In the previous works, spectrum sensing is formulated as
the following binary hypothesis testing problem [10]
P2m
(Sn + Zn )2 , H1 (licensed channel busy)
Pn=1
Y=
2m
2
H0 (licensed channel idle)
n=1 Zn ,
(1)
distribution, can be examined in a similar way. The “1” and
“0” states represent the busy and idle periods of the licensed
channel, respectively. At any time instant, the licensed channel
µ
, and idle with probability
is busy with probability pb = µ+λ
pi = 1 − pb .
We begin with the conventional model in (1). The detection
and false-alarm probabilities can be derived as [10]
Fig. 1.
Primary user traffic patterns during the CR sensing
period
where Y is the normalized output of the integrator, Sn are the
samples of the signal from the primary users, and Zn are the
samples of the additive white Gaussian noise (AWGN). The
model in (1) assumes that the primary user is either present or
absent during the whole sensing period. However, in practice,
the primary user may arrive or leave during the sensing period,
especially when a long sensing period is used to achieve
good sensing performance, or when sensing is performed for a
network with high traffic. This affects the sensing performance
as well. In this paper, the effect of the primary user traffic
on the spectrum sensing performance is evaluated. We begin
with an introduction of the primary user traffic model. Assume
that the lengths of the busy and idle periods of the licensed
channel are comparable with the length of the sensing period.
Further, assume that the state of the licensed channel changes
at most once during the whole sensing period. Based on
these assumptions, the hypothesis test in (1) can be further
decomposed into four cases as shown in Fig. 1. In H0 , the
licensed channel is either idle all over the sensing period
(H0,1 ), or is busy then idle by the end of the sensing period
(H0,2 ). In H1 , the licensed channel is either busy during the
whole sensing period (H1,1 ), or is idle then busy by the end
of the sensing period (H1,2 ). From Fig. 1, if the primary user
traffic is taken into account, the hypothesis testing problem for
spectrum sensing can be formulated as
 P2m
2

H1,1

n=1 (Sn + Zn ) ,

 Pk1 Z 2 + P2m
2
(S
+
Z
)
,
H1,2
n
n
n
n=k1 +1
Pn=1
(2)
Y=
2m
2

Z
,
H
0,1

n
 Pkn=1
P
2m

2
2
2
n=1 (Sn + Zn ) +
n=k2 +1 Zn , H0,2
where k1 represents the number of signal samples that the
licensed channel is idle before it becomes occupied in H1,2 ,
and k2 represents the number of signal samples that the
licensed channel is busy before it becomes vacant in H0,2 . One
sees that the conventional sensing model in (1) corresponds to
the hypotheses of H0,1 and H1,1 in (2).
In this paper, the primary user traffic is modeled as an
independent and identically distributed (i.i.d.) two-state (1/0)
random process with exponential holding time, and mean
parameters λ and µ, similar to [11], [12]. Other distributions,
such as Gamma distribution, lognormal distribution and Erlang
p
√
P (H1 |H1 ) = P {Y > η|H1 } = Qm ( 2mγ, η) (3)
Γ(m, η/2)
(4)
P (H1 |H0 ) = P {Y > η|H0 } = 1 −
Γ(m)
where γ is the average signal-to-noise ratio
of the
R ∞ (SNR)
z−1 −t
primary signal
at
the
CR
users,
Γ(z)
=
t
e
dt
and
0
R x z−1 −t
Γ(z, x) = 0 t e dt are the complete and lower incomplete gamma functions, respectively [13], and Qm (·, ·) is the
generalized Marcum Q-function [14], defined as Qm (a, b) =
R ∞ xm − x2 +a2
2
e
Im−1 (ax)dx, with Im−1(·) being the modb am−1
ified Bessel function of the (m − 1)th order, and η is the
detection threshold.
Note that P (H1 |H1 ) and P (H1 |H0 ) in (3) and (4) equal to
the P (H1 |H1,1 ) and P (H1 |H0,1 ), respectively, in (2). Thus,
p
one has
√
P (H1 |H1,1 ) = Qm ( 2mγ, η)
(5)
Γ(m, η/2)
.
(6)
P (H1 |H0,1 ) = 1 −
Γ(m)
Similarly, one has
P (H1 |H1,2 , k1 )
P (H1 |H0,2 , k2 )
= P {Y > η|H1,2 , k1 }
p
√
= Qm ( (2m − k1 )γ, η)
= P {Y > η|H0,2 , k2 }
p
√
= Qm ( k2 γ, η)
(7)
(8)
where the symbols are defined as before. Note that k1 = 0
in (7) corresponds to (5), while k2 = 0 in (8) corresponds to
(6). The probabilities of detection and false-alarm in (7) and
(8) are conditioned on the parameters of k1 and k2 , which
are determined by the primary user traffic. The unconditional
probabilities of detection and false-alarm can be derived by
averaging (7) and (8) over the probabilities of k1 and k2 based
on the traffic model.
As shown in Fig. 1, we assume that there is at most one
transition in the primary user channel state, and that the
state transition happens in one sample interval. Denote the
probabilities that the licensed channel is either busy during
the whole sensing period or idle for k1 samples then busy as
P (H1,1 ) and P (H1,2 , k1 ), respectively. It can be derived that
P (H1,1 ) = pb · (p11 (Ts ))2m
P (H1,2 , k1 ) = pi · ((p00 (Ts ))k1 · p01 (Ts )
·(p11 (Ts ))2m−k1 −1 .
(9)
(10)
Similarly, denote probabilities that the licensed channel is
either idle during the whole sensing period or busy for k2
samples then idle as P (H0,1 ) and P (H0,2 , k2 ), respectively.
One has
P (H0,1 ) = pi · (p00 (Ts ))2m
P (H0,2 , k2 ) = pb · ((p11 (Ts ))k2 · p10 (Ts )
·(p00 (Ts ))2m−k2 −1 .
(11)
(12)
Note that the above probabilities depend on the parameters of
the primary user traffic model. In some applications, such as
the TV licensed spectrum, the state of the licensed channel
changes slowly, corresponding to small values of λ and µ.
In this case, the conventional model without considering the
primary user traffic may give good approximation to the
sensing performance. In other applications, such as the public
safety spectrum, the state of the licensed channel changes more
frequently, corresponding to large values of λ and µ. In this
case, P (H1,2 , k1 ) and P (H0,2 , k2 ) are not negligible, and the
conventional model may give a less accurate prediction of
the sensing performance. The probabilities in (9) - (12) take
all these cases into account. By combining the conditional
probabilities of detection, false-alarm and the transition probabilities of the licensed channel state, the overall probabilities
of detection and false-alarm for the new sensing model can be
derived as
Pd
Pf
= P (H1 |H1 )
P (H1,1 ) · P (H1 |H1,1 )
=
P2m−1
P (H1,1 ) + k1 =1 P (H1,2 , k1 )
P2m−1
k1 =1 (P (H1,2 , k1 ) · P (H1 |H1,2 , k1 ))
(13)
+
P2m−1
P (H1,1 ) + k1 =1 P (H1,2 , k1 )
= P (H1 |H0 )
P2m−1
k2 =1 (P (H0,2 , k2 ) · P (H1 |H0,2 , k2 ))
=
P2m−1
P (H0,1 ) + k2 =1 P (H0,2 , k2 )
P2m−1
k2 =1 (P (H0,2 , k2 ) · P (H1 |H0,2 , k2 ))
+
. (14)
P2m−1
P (H0,1 ) + k2 =1 P (H0,2 , k2 )
The above derivation is based on the chi-square distribution,
which involves complicated functions, such as the Marcum Qfunction. Thus, it is difficult to determine η. In the previous
works [7] - [9], the Gaussian distribution is often used to
approximate the sample distribution. If the time-bandwidth
product m is relatively large, the central limit theorem applies.
Then, the conditional probabilities of detection and false-alarm
in H1,1 and H0,1 are given by
P (H1 |H1,1 )
P (H1 |H0,1 )
= P {Y > η|H1,1 }
1
1 η − 2m(γ + 1)
)
erf c( √ p
≈
2
2 4m(2γ + 1)
= P {Y > η|H0,1 }
1
1 η − 2m
≈
).
erf c( √ √
2
2
4m
(15)
(16)
Similarly, the conditional probabilities of detection and false-
alarm in H1,2 and H0,2 are given by
P (H1 |H1,2 , k1 ) = P {Y > η|H1,2 , k1 }
(17)
1 η − 2m(γ + 1) + k1 γ
1
Erf c( √ p
)
≈
2
2 4m(2γ + 1) − 4k1 γ
P (H1 |H0,2 , k2 ) = P {Y > η|H0,2 , k2 }
1
1 η − 2m − k2 γ
≈
Erf c( √ p
).
(18)
2
2 4(k2 γ + m)
Note that k1 = 0 in (17) corresponds to (15), while k2 = 0 in
(18) corresponds to (16). The overall probabilities of detection
and false-alarm using the Gaussian approximation can be
derived by using (15) (16) (17) and (18) in (13) and (14).
All the above results are for local spectrum sensing. In order
to alleviate the effects of multi-path fading and shadowing in
the wireless channels, collaborative spectrum sensing is often
used. We will derive the probabilities of detection and falsealarm for collaborative spectrum sensing.
For simplicity, consider the hard decision rule where the
CR users send their 1-bit hard decisions to the fusion centre.
Without loss of generality, assume that all CR users experience
independent and identically distributed (i.i.d) fading. The
fusion centre employs the 1-out-of-n fusion rule [17] [18].
The probabilities of detection and false-alarm for collaborative
spectrum sensing can be derived, respectively, as [18]
Qd = 1 − (1 − Pd )n
Qf = 1 − (1 − Pf )n
(19)
(20)
where Pd and Pf are probabilities of detection and false-alarm,
respectively, in local spectrum sensing given by (13), (14).
Although reference [18] has analyzed the effect of cooperation,
it is the first time that this effect is studied by considering the
primary user traffic.
III. R ESULTS AND D ISCUSSION
In this section, the performance of spectrum sensing based
on the primary user traffic is investigated. Two criteria,
Neyman-Pearson (NP) [15] and minimum error-probability
(ME) [16] are applied to calculate the detection threshold η.
Fig. 2 compares the analytical results in (7) and (17)
with the corresponding simulated results. In the comparison,
m = 50 and γ = −10 dB. In the NP criteria, the target
probability of false alarm is set to 0.01. From Fig. 2, it
can be observed that the conditional probability of detection
decreases as k1 increases. This is due to the fact that the energy
of the primary user signal in the sensing period decreases
as k1 increases, making its detection more difficult. One
also sees that the chi-square method matches well with the
simulation result, while the Gaussian approximation has large
approximation errors in the NP criteria. Similar observations
can be made for the conditional probability of false-alarm,
which is not shown here due to the length restriction. Since
the chi-square method gives results closer to the simulation
result than the Gaussian approximation, it will be used in the
following.
0
−1
−1
10
e
10
Error Probability P
Conditional Probability of Detection, Pd
10
The Gaussian approximation with NP
−2
10
2
χ with NP
Simulation with NP
The Gaussian approximation with ME
λ=µ=0.5
2
χ with ME
λ=µ=1
Simulation with ME
λ=µ=2
−3
10
0
10
20
30
40
50
k
60
70
80
90
λ=µ=4
100
−2
10
1
10
20
30
40
50
60
70
80
90
100
m
Conditional probability of detection vs. k1 when γ =
−5 dB, m = 50.
Fig. 2.
Error probability Pe vs. time-bandwidth product m
based on ME criteria.
Fig. 5.
0
10
0
d
Probability of Detection Q
Probability of Detection Pd
10
−1
10
λ=µ=0.5
−1
10
n=1
n=2
λ=µ=1
n=3
λ=µ=2
n=4
λ=µ=4
n=5
−2
10
−3
−2
10
−1
0
10
10
Probability of False−alarm Pf
−2
10
10
−3
−2
10
−1
0
10
10
Probability of False−alarm Q
10
f
The ROC for local spectrum sensing performance based
on NP criteria (m = 50).
Fig. 3.
The ROC for collaborative spectrum sensing performance based on NP criteria (m = 50).
Fig. 6.
0
10
0
10
n=1
n=2
n=4
e
n=5
Error Probability Q
Probability of Detection Pd
n=3
−1
10
−1
10
λ=µ=0.5
λ=µ=1
λ=µ=2
λ=µ=4
−2
10
10
−2
20
30
40
50
60
70
80
90
100
m
The probability of detection vs. m for local spectrum
sensing performance based on NP criteria.
Fig. 4.
10
10
20
30
40
50
60
70
80
90
100
m
Fig. 7. Error probability Qe vs. time-bandwidth product m
based on ME criteria.
when m = 100, Qe ≈ 0.165 for n = 1 and Qe ≈ 0.058 for
n = 5. Another observation is that when n = 1, Qe increases
slightly with increasing m. The effect of n on Qe can be seen
more clearly in Fig. 8. Our analysis is based on a general
system model where different values of λ and µ can be adopted
to represent different application environments. For example,
for the TV spectrum that the 802.22 standard aims to reuse,
small values of λ and µ can be used to indicate the band
characteristics. For other practical cognitive systems, similar
methods can be used.
0
10
Error Probability Pe
m=20
m=40
m=60
m=80
m=100
−1
10
R EFERENCES
−2
10
Fig. 8.
1
2
3
4
5
6
7
8
Number of cooperating secondary users, n
9
10
The error probability Qe vs. n based on ME criteria.
Fig. 3 shows the receiver operating characteristic (ROC)
curve of spectrum sensing for different values of the parameters of the primary user traffic model using the NP criteria
in local spectrum sensing. In the calculation, the detection
threshold η is derived from (13) and (14) numerically, by
varying Pf from 10−3 to 1. Without loss of generality, assume
λ = µ. The average busy and idle time of the licensed
channel are set to 0.25, 0.5, 1 and 2 seconds, corresponding
to λ = µ = 4, 2, 1, 0.5, respectively, while the sensing period
is set to 0.05 second. Also, m = 50 and γ = 5 dB. Larger
values of λ and µ result in more frequent state transition in
the primary user channel. One observes that frequent state
transition in the primary user traffic degrades the sensing
performance significantly. For example, to achieve a Pf of
10−2 , one has a probability of detection of Pd ≈ 0.52 when
λ = µ = 4, while a probability of detection of Pd ≈ 0.98
when λ = µ = 0.5. Fig. 4 shows the probability of detection
vs. m. One observes that Pd increases as m increases, as
expected. Fig. 5 shows the error probability Pe for different
values of m, when the ME criteria is used in local spectrum
sensing. It can be observed that Pe is not sensitive to m, while
it is to λ and µ. One sees from Fig. 5 that frequent state
transitions lead to higher error probability.
Fig. 6 shows the ROC curve for different numbers of
collaborating CR users when the NP criterion is used in
collaborative spectrum sensing. In this case, λ = µ = 4. Also,
m = 50 and γ = 5 dB. The detection threshold η is derived
by varying Qf from 10−3 to 1. The curve of n = 1 represents
local spectrum sensing. Comparing the curve of n = 1 with
other curves, one sees that the deleterious effect of frequent
state transitions in the primary user traffic is mitigated by using
multiple users in sensing. For example, to achieve a Qf of
10−2 , one has a probability of detection of Qd ≈ 0.6 when
n = 5 in Fig. 6, while a probability of detection of Pd ≈ 0.52
in Fig. 3.
Fig. 7 shows the error probability for different numbers
of collaborating CR users when the ME criterion is used in
collaborative spectrum sensing. One sees that Qe decreases
with increasing m in this case as n increases. For example,
[1] J. Mitola and G. Q. Maguire, “Cognitive radios: Making software radios
more personal,” IEEE Pers. Commun., vol. 6, pp. 13-18, Aug. 1999.
[2] J. Mitola, “Cognitive radio: An integrated agent architecture for software
defined radio,” PhD. diss., Royal Inst. Technol. (KTH), Stockholm,
Sweden, 2000.
[3] D. Cabric, S. M. Mishra, R. W. Brodersen, “Implementation issues in
spectrum sensing for cognitive radios,” in Proc. IEEE Asilomar Conference on Signals, Systems and Computers 2004, pp. 772-776, Pacific
Grove, CA, USA, Nov. 2004.
[4] H. Urkowitz, “Energy detection of unknown deterministic signals,” in
Proceedings of IEEE, pp. 523-531, Apr. 1967.
[5] E. Visotsky, S. Kuffner, R. Peterson, “On collaborative detection of TV
transmissions in support of dynamic spectrum sharing,” in Proc. IEEE 1st
Symposium on Dynamic Spectrum Access Networks (DySPAN’05), pp.
338-345, Baltimore, MD, USA, Nov. 2005.
[6] S. M. Mishra, A. Sahai, R. W.Brodersen, “Cooperative Sensing among
Cognitive Radios,” in Proc. of International Conference on Communications (ICC’06), pp. 1658-1663, Istanbul, Turkey, Jun. 2006.
[7] A. Ghasemi and E. S. Sousa, “Optimization of spectrum sensing for
opportunistic spectrum access in cognitive radio networks,” in Proc. 4th
IEEE Consumer Commun. Networking Conf. (CCNC), pp. 1022-1026,
Las Vegas, NV, USA, Jan. 2007.
[8] W. Lee and I. F. Akyildiz, “Optimal spectrum sensing framework for
cognitive radio networks,” IEEE Trans. Wireless Communications, vol 7,
pp. 3845-3857, Oct. 2008.
[9] Y. C. Liang, Y. Zeng, E. C. Y. Peh, and A. T. Hoang, “Sensingthroughput tradeoff for cognitive radio networks,” IEEE Trans. Wireless
Communications, vol. 7, pp. 1326-1337, Apr. 2008.
[10] F. F. Digham, MS. Alouini , MK. Simon “On the energy detection
of unknown signals over fading channels,” in Proceedings of the IEEE
International Conference on Communications (ICC’03), pp. 3575-3579,
Anchorage, Alaska, USA, May. 2003.
[11] L. Yang, L. Cao, and H.-T. Zheng, ” Proactive channel access in dynamic
spectrum network”’, Elsevier Physical Communication, Vol. 1, pp. 103111, June 2008.
[12] M. Hoyhtya, S. Pollin, and A. Mammela, ”Performance improvement
with predictive channel selection for cognitive radios,” in Cognitive Radio
and Advanced Spectrum Management, pp. 1-5, Aalborg, Denmark, Feb.
2008.
[13] I. S. Gradshteyn , IM. Ryzhik, Table of Integrals, Series, and Products,
5th ed., San Diego, CA: Academic Press, 1994.
[14] A. H. Nuttall, “Some integrals involving the QM function,” IEEE Trans.
Information Theory, vol. 21, pp. 95-96, 1975.
[15] J. Hillenbrand, T. A. Weiss, and F. K. Jondral, “Calculation of detection and false-alarm probabilities in spectrum pooling systems,” IEEE
Communications Letters, pp. 349-351, vol. 9, Apr. 2005.
[16] M. Barkat, Signal Detection and Estimation, 2nd ed., Boston, MA:
Artech, 2005.
[17] P. K. Varshney, Distributed Detection and Data Fusion, New York:
Springer-Verlag, 1997.
[18] A. Ghasemi and E. S. Sousa,“Spectrum sensing in cognitive radio
networks: the cooperation-processing tradeoff,” Wireless Communications
and Mobile Computing-Whiley, pp. 1049-1060, 2007.