Chinese Journal of Electronics
Vol.25, No.5, Sept. 2016
Optimal Sensing Time Strategy Under Primary
Outage Constraint in Cognitive Radio Networks∗
LIU Xinyi1,2 , LI Jiandong2 and JIANG Jian2,3
(1. School of Information Engineering, Chaug’an University, Xi’an 710071, China)
(2. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an 710071, China)
(3. China Academy of Telecommunication Research of MIIT, Beijing 100191, China)
Abstract — With the underlay approach, Secondary
users (SUs) can utilize the same frequency bands simultaneously with Primary users (PUs) in Cognitive radio
networks (CRNs). How to choose the appropriate transmission power of SUs under the influence caused by other
cells is a problem. To solve this problem, spectrum sensing
is introduced to identify the existence of interference which
using pilot signal to perform coherent processing. Consider
the probability of detection of SUs, there exists a trade-off
between the sensing time and the achievable throughput
of CRNs. When the prior probability of other cells’ activity is unknown to SUs, throughput of the CRNs can be
viewed as a concave function. According to solving the optimization problem, the optimal sensing time is obtained.
Simulation results show the feasibility and correctness.
Key words — CRNs, Underlay approach, Inter-cell interference, Sensing-throughput tradeoff.
I. Introduction
Cognitive radio attracts much attention due to the advantage in improving the spectrum usage efficiency[1−3] .
To ensure the Quality of service (QoS) of PUs, interference received at PUs must be controlled with certain qualifications. In CRNs, diminishing the interference introduced by spectrum sensing is a hot topic which is very important. Critical interference is caused by the poor sensing
performance.
SUs need to scan and detect the usage condition of
spectrum periodically. There are many spectrum sensing
methods, such as energy detection, matched filter, cyclostationary feature detection, etc. Energy detection is easy
to implement and has been commonly used[4] . But sensing
with energy detection does not work well when the Signalto-interference-plus-noise ratio (SINR) of received signal
is very low. Similarly, energy detection cannot be used
to distinguish the specific signal from the complex environment. If the prior information of the objective signal
is known, the pilot sensing will have better performance
which is referred to Refs.[5,6].
The interference should be limited under a threshold
to guarantee the PUs’ performance. Ref.[7] represents the
interference problem through controlling the miss detection probability in the overlay model. The probability of
the false decision when PUs are using the spectrum will
generate extra collision to effect the PUs’ transmission.
Underlay technique is also used widely in CRNs. The authors of Ref.[8] proposed the outage constraint model to
maximize the throughput of SUs with underlay approach
in the CRNs. In Ref.[9], the authors proposed an auctionbased power allocation framework for spread spectrum
users to share spectrum with an interference temperature sensed at a measurement point, whereas a central
manager needs to collect bids from distributed users. The
authors of Ref.[10], formulated a power allocation game
considering both the interference temperature constraint
at the PUs and the QoS requirement at the SUs. These
previous works do not focus on the transmission of SUs
when there exists other interference source with underlay
approach. To justify the transmission power, SUs have to
acquire the interference information through sensing.
In this paper we focus on the scheme that SUs and
interference source effect the PUs commonly. SUs need to
sense the activity of interference source to change their
transmission power.
II. System Model and Pilot-Energy
Sensing
∗ Manuscript Received July 4, 2014; Accepted Oct. 30, 2014. This work is supported by the Fundamental Research Funds for the
Central Universities (No.310824161008), the National Natural Science Foundation of China (No.61231008, No.61101143), the Program for
Changjiang Scholars and Innovative Research Team in University (No.IRT0852), and the 111 Project (No.B08038).
c 2016 Chinese Institute of Electronics. DOI:10.1049/cje.2016.08.023
908
Chinese Journal of Electronics
We consider that the primary network is a macro-cell
which consist of a Primary transmitter (PU-T) and a Primary receiver (PU-R), as shown in Fig.1. In the CRN,
secondary users’ Transmitters (SU-Ts) send data packet
to secondary users’ Receivers (SU-Rs) using underlay approach which allows SUs occupy the same spectrum with
PUs. SU-Ts will cause interference to primary network by
this approach. Users in other cells will also causes interference by occupying the same spectrum with probability. In
order to ensure the transmission of PUs, the interference
received at PU-R must be controlled under a threshold.
Consider the simplest sense, we set only one active SU
pair and one interference source transmitter (I-T). We
also assume that the information about the pilot signal of
I-T is known at SU-T.
Fig. 1. The system model of the CRN with interference source
To maximize throughput of the CRN, SU-T must adjust the transmit power according the activity of I-T. SUs
should sense whether I-T is using the spectrum. If SUs
have no data to broadcast sometimes, they can be used
to sense spectrum without causing interference. The SUs
at this state are called inactive SUs[11] . We set N SUs to
sense cooperatively, which consist of one active SU pair
and N − 1 inactive SU pairs. The signal received at SU-Ts
contain the primary signal and the interference signal. So
the energy detection is not applicable at this case. The
signal of I-T should be isolated that we need to use pilot
signal to perform coherent processing[12]. Consider the M
as the number of samples at each SU-T, which equals the
product of the sensing time τ and the sampling frequency
f.
Let Yn = [[Yn [0], Yn [1], · · · , Yn [M − 1]]T . The two hypothesis results of n-th SU-T can be represented by:
H0 :Yn [m] = Zn [m],
m = 0, 1, 2, · · · , M − 1
H1 :Yn [m] = gn Xnp [m] + Zn [m], m = 0, 1, 2, · · · , M − 1
(1)
where Xnp [m] denotes the known pilot data with variance
σx2 which modulated by complex PSK, Zn [m] is circularly
symmetric complex Gaussian noise with mean 0 and variance σ 2 , gn means the uncorrelated circularly symmetric complex Gaussian gain coefficient with zero-mean and
unit variance. After processed the pilot signal by using
the energy detector, each SU-T sums the sensing results
2016
M−1
which equal Xn (Yn ) = (1/M ) m=0 |Yn [m]|2 . In the reporting phase, each SU sends the data to the fusion center through control channel. In a time slot only one SU-T
should send its local decision. Since the number of the cooperative SUs is not great, the reporting phase is far less
than the sensing period. The report overhead and interference of adjacent-channel signals can be ignored. After all
the test statistics are collected, the fusion center makes
the final decision by comparing the global test statistic
N −1
X = (1/N ) n=0 |Xn (Yn )|2 to the global threshold φs .
If X < φs , H0 is considered as true; otherwise, we think
the interference signal exists.
Since the number of sensing samples is enormous
enough to fit the central limit theorem, we can obtain
the probability of false alarmPF and the probability of
detectionPD , respectively.
φs
−
1
N
τ
f
(2)
PF (τ ) = Q
σ2
γs
φs
Nτf
−1
(3)
−
PD (τ ) = Q
σ2
N
1 + (2γs /N )
N −1
where γs = n=0 |gn |2 σx2 /σ 2 denotes the average SINR.
Q(·) denotes the right tail probability of the normalised
Gaussian distribution. After substituting Eq.(2) into
Eq.(3), the probability of detection is obtained with the
given probability of false alarm PF :
τf
1
Q−1 (PF ) − γs
(4)
PD (τ ) = Q N
1 + 2γs /N
III. Outage Constraint with Unknown
Prior Probability
It will arouse additional interference to the PU when
the active SU-T sends package with underlay approach.
Consider the influence caused by other cells, and the interference received at primary receivers, which consisting of
the cognitive interference and the inter-cell interference,
should be limited under the primary outage constraint.
To ensure a normal operation of the transmission of the
PU, the influence caused by interference should be controlled under the special level. We need to constraint the
probability that the SINR received at PU-R, represented
by γr , is lower than its desired SINR γth . It should stay
below a certain threshold φ, which can be represented by:
Pro (γr < γth ) ≤ φ
(5)
Pro(·) means the probability of a random event. Consider the channel between PU-R and other devices is frequency selective channel, which gain can be denoted by
G = αd−β , with d is the distance, β is the loss exponent, α denotes the Rayleigh distributed fading ampli-
Optimal Sensing Time Strategy Under Primary Outage Constraint in Cognitive Radio Networks
tude which follows the independent exponential distribution with mean of 1. Then Eq.(5) becomes:
Pp Gp
Pro
< γth ≤ φ
(6)
N0 + PI GI + Pc Gc
where Pp ,PI ,Pc denote the transmit powers of PU-T, I-T
and SU-T, Gp ,GI ,Gc express the channel gains from PU-R
to PU-T, I-T and SU-T, N0 is the white Gaussian noise
power received at PU-R. As mentioned in Ref.[13], the
outage probability of PU-R can be denoted by:
Pro [γ < γth ] = 1 − b0 [(1 + bc Pc )−1 (1 + bi Pi )−1 ] ≤ φ
Gc γth
Gi γth
γth N0
(7)
, bi =
, b0 = exp(
)
bc =
Pp Gp
Pp Gp
Pp Gp
The PU-R has different outage probabilities based on
the activity of I-T when SU-T transmits with a constant
power. When the transmit power of SU-T makes the outage probability of PU satisfy the limit with the active I-T,
it will have comfortable margin to the outage probability
limit with the inactive I-T. It is necessary to spend time
on sensing the activity of I-T for effectiveness. Using Pc0
and Pc1 to describe the transmit powers of SU-T when I-T
are active and inactive, respectively. Obviously, Pc0 > Pc1 .
After taking the prior probability of I-T’s activity and the
sensing performance into account, Eq.(7) can be changed
to Eq.(8).
b0
)
(1 + bi Pi )(1 + bc Pc1 )
b0
)]
+Pro(H0 |H1 )(1 −
(1 + bi Pi )(1 + bc Pc0 )
b0
)
+Pro(H0 )[Pro(H0 |H0 )(1 −
(1 + bc Pc0 )
b0
+Pro(H1 |H0 )(1 −
)] ≤ φ
(1 + bc Pc1 )
Pro(H1 )[Pro(H1 |H1 )(1 −
(8)
Pro(H1 ) and Pro(H0 ) denote the prior probability of
active I-T and inactive I-T, respectively. Since the prior
probability changes over time, it is unknown to the SUs.
To maintain the QoS of the PU, the transmit power of
SU-T must fit PU’s outage probability goal prior whatever prior probability is known to the SUs. The restraint
condition Eq.(8) can be split into two after removing the
element of prior probability:
b0
Pro(H0 |H0 ) 1 −
(1 + bc Pc0 )
b0
≤φ
(9)
+Pro(H1 |H0 ) 1 −
(1 + bc Pc1 )
Pro(H1 |H1 ) 1 −
b0
(1 + bi Pi )(1 + bc Pc1 )
b0
≤ φ (10)
+Pro(H0 |H1 ) 1 −
(1 + bi Pi )(1 + bc Pc0 )
909
It is easy to find the suited Pc0 and Pc1 with perfect
sensing results: Pro(H1 |H0 ) = 0, Pro(H0 |H1 ) = 0. Because the active SU-T has to control the transmit power
due to its interference, the accuracy of sensing affects
the transmitting rate of the SU-T. Eq.(9) shows affection
of the probability of false alarm to the outage probability. When false alarm happens, the SU-T makes a wrong
judgement that I-T is sending data. So it transmits with
power Pc1 which is lower than Pc0 . In this case, the inaccuracy of sensing leads a decreased performance, but not
extra interference for the PU. Pc0 can be set as a fixed
value which not only fit the Eq.(8) at any time but also
achieve a high transmitting rate. Apparently, we get
Pc0 =
b0 /(1 − φ) − 1
bc
(11)
Eq.(10) shows the restraint condition under the influence of probability of miss detection. SU-T will transmit
with power Pc0 based on the incorrect sensing result when
I-T is sending data. PU’s outage probability may exceed
the limit because of the extra interference. SU-T need
to decrease the transmit power to fit the requirement of
CRN. Since the length of time slot T is fixed, the longer
sensing time means the transmission period will be deduced. To maximize the throughput of SU, the optimisation problem can be expressed as:
T −τ
log(1+ν ∗ Pc1 )
C(τ, Pc1 ) = Tt (τ )R(Pc1 ) =
max
1
τ,Pc
T
b0
s.t. Pro(H1 |H1 ) 1 −
1
(12)
(1+bi Pi )(1+bc Pc ) b0
+ Pro(H0 |H1 ) 1 −
≤ φ,
(1+bi Pi )(1+bc Pc0 )
0≤τ ≤T
ν denotes the SINR of received useful signal at SU-R when
SU-T transmits with unit power. The sensing performance
can be enhanced by increasing the sensing time. As sensing time increase, we can choose a higher Pc1 which satisfies the Eq.(10). There exists a sensing-throughput tradeoff problem which needs to balance the transmission period and transmission power. Obviously, the outage probability increases when Pc1 is selected as a higher value.
While the outage probability equals φ, Pc1 achieves the
maximum value. Using the Eq.(10) and Eq.(11), we can
see that the throughput of the SU pair is a function of
sensing time τ :
max C(τ ) = T (τ )R(τ ) =
τ
T −τ
log(1 + ν ∗ Pc1 )
T
s.t. Pc1 (τ )
(13)
0
1 + b c pc
=
− 1 /bc ,
(1 + bc Pc0 )(1 + bi Pi )(1 − φ) − b0
b0 Pd (τ ) + 1
0≤τ ≤T
Chinese Journal of Electronics
910
To ensure the system is working successfully, the detection probability is set to a value which is larger than
0.5 in practice. We will show the probability is concave
at this case.
Theorem 1 Based on the assumptions of system
model, PD (τ ) is increasing and convex for the range of τ
at PD (τ ) > 0.5.
Proof Since the probability of detection is a Q function and Q(x) = 1 − Q(−x), we have:
τf
1
−1 PD (τ ) = 1 − Q − Q (PF )
γs
N
1 + 2γs /N
(14)
It is increasing when PD (τ ) > 0.5, obviously. According to Eq.(4), differentiating PD (τ ) to τ :
γs f /N −1/2
1
√
PD (τ ) =
τ
exp − 2 2π
1 + 2γs /N
2
τf
−1 − Q (PF )
· γs
2
(15)
N
2016
In this section, we present the simulation results about
the performance of sensing-throughput tradeoff problem
with MATLAB software system. We set the system with
multiple SU pairs, one interference source and one PU
pair with their locations are shown in Fig.2. The desired
probability of false alarm was set to 0.05. The power of the
pilot accounts for 10 percent in transmission power. We
set T = 10ms. The bandwidth of SU is 20MHz. Following
the setting in Ref.[8], φ = 0.1 and γth = 6.
Fig. 2. Interference source and users locations
It implies PD (τ ) is monotonically decreasing with τ
when PD (τ ) > 0.5. So PD (τ ) is increasing and convex for
the range of τ when PD (τ ) > 0.5.
It is clear that PD (τ ) < 0 based on Theorem 1. Since
Pc1 τ can be transformed from PD (τ ) through linear operation, we can drive Pc1 (τ ) is increasing and convex. The
function log(1 + αx), a > 0 is also increasing and convex.
So R(τ ) is increasing and convex.
Theorem 2 There exists an optimal sensing time
which yields the maximum achievable throughput for the
active SU pair.
Proof From Eqs.(13)–(15) we can get the derivative
of C :
1
lim C (τ ) = − ((T − τ )R (τ ) − R(τ )) ≤ 0
τ →T
T
lim C (τ ) = ∞
τ →0
(16)
(17)
Hence, there is a maximum point of C(τ ) within interval (0, T ). The secondary derivative of C(τ ) can be shown
as:
1
C (τ ) = − ((T − τ )R (τ ) − 2R (τ ))
(18)
T
Because R(τ ) is increasing and convex, R (τ ) > 0 and
R (τ ) ≤ 0. It can be derived that C (τ ) ≤ 0. The maximum point of C(τ ) is unique.
The optimal sensing time is a convex problem which
can develop plenty efficient search algorithms such as
Newton’s iteration method to obtain the optimal sensing
time.
IV. Simulation Results
Fig. 3. Throughput of SU against the sensing time with different inactive cooperative SUs
Fig.3 represents the throughput of SU against the
sensing time with different inactive cooperative SUs. The
transmission power of PU and interference is 36dBm and
30dBm, respectively. It is clear the throughput of SU is
a convex function with τ . The optimal sensing time decreases with the increasing of number of cooperative SUs.
At the beginning, the throughput of the SU is increasing
with the longer sensing time. It is because that the probability of detection is increasing which makes SU send
data with a higher power. When probability of detection
is large enough, the benefit of the increasement of sensing time is less than the loss which make the transmission
time short. The more inactive cooperative SUs will bring
the better sensing performance, the throughput of SU will
have a higher value with the same sensing time.
Fig.4 represents throughput of SU against the sensing time with different transmission power of PU-T and
interference. It is clear that the throughput of SU and
the optimal sensing time will decrease when transmission
power of interference increases. At this case, I-T will generate much interference to PU-R. SU need to transmit
Optimal Sensing Time Strategy Under Primary Outage Constraint in Cognitive Radio Networks
with lower power. The higher transmission power of I-T
makes SUs easy to sense. So the optimal sensing time will
decrease. When PU transmits with a lower power, the
throughput of SU will decrease. It is because that interference received at PU-R though the γth is fixed. SU-T
have to transmit with lower power. It also needs much
sensing time to satfiy the outage probability.
[8]
[9]
[10]
[11]
[12]
[13]
Fig. 4. Throughput of SU against the sensing time with different transmission power of PU-T and interference
V. Conclusion
The sensing time against throughput trade-off was optimised using a probabilistic constraint on the channeldependent probability of detection. After we developed
the pilot sensing scheme, the active SU can transmit with
the proper power. Consider the probability of interference source’s activity is unknown, the relationship between throughput of the SU pair and the sensing time is
established. Simulation results show that the maximum
throughput of CRN can be obtained by using the optimal
sensing time.
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LIU Xinyi was born in 1986, he received the Ph.D degree at State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, China. He received
the B.E. degrees in 2004 in information and
communication engineering. He was a visiting student to the Texas A&M University
from 2010 to 2011. His research interest is
the cooperative sensing policy in cognitive
radio system. (Email: [email protected])
LI Jiandong was born in 1962, he
received the B.E., M.S. and Ph.D. degrees
from Xidian University, Xi’an, China, in
1982, 1985 and 1991 respectively, all in information and communication engineering.
He has been a faculty member of Telecommunications Engineering at Xidian University since 1985, where he is currently a vice
president of Xidian University and director of State Key Laboratory of Integrated
Service Networks. Prof. Li is a senior member of IEEE. He was
a visiting professor to the Department of Electrical and Computer
Engineering at Cornell University from 2002 to 2003. He was a member of Personal communication networks (PCN) specialist group for
China 863 Communication High Technology Program during 1993–
1994 and again 1999-2000. He also served as the General Vice Chair
for COMSOCs Chinacom 2009. He was awarded as Distinguished
Young Researcher and Changjiang Scholar from Ministry of Science
and Technology, China. His major research interests include wireless
communication theory, cognitive radio and signal processing.
JIANG Jian was born in 1986, she
received the Ph.D degree at State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, China. She received
the B.E. degrees in 2004 in information and
communication engineering. Her main area
of research includes performance analysis
for the network selection strategy based on
the delay and prediction in heterogeneous
wireless networks.