1838 IEEE COMMUNICATI ONS LETTERS, VOL. 17, NO. 9, SEP TEMBER 2013 Adaptive Spectrum Sensing Algorithm Under Different Primary User Utilizations Nan… [630633]

1838 IEEE COMMUNICATI ONS LETTERS, VOL. 17, NO. 9, SEP TEMBER 2013
Adaptive Spectrum Sensing Algorithm
Under Different Primary User Utilizations
Nan Wang, Student: [anonimizat], IEEE, Yue Gao, Member, IEEE, Xing Zhang, Member, IEEE
Abstract —Spectrum sensing is one of the key technologies
to realize dynamic spectrum access in cognitive radio (CR)systems. In this letter, a novel adaptive threshold spectrumsensing algorithm is proposed to achieve an efficient trade-offbetween the detection and false alarm probability. The proposedadaptive threshold algorithm demonstrates a better spectrumefficiency for both primary users (PUs) and secondary users(SUs) in comparison with the conventional fixed one. A closed-from expression between PUs’ spectrum utilization ratio and theproposed adaptive threshold is derived and simplified.
Index Terms —Cognitive radio, spectrum sensing, energy de-
tection, adaptive threshold.
I. I NTRODUCTION
COGNITIVE radio (CR) is being viewed as a new intel-
ligent 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 inCR systems as it requires hig h accuracy and low complexity
for dynamic spectrum access [3]. The spectrum sensing per-
formance metric is usually measured as a trade-off between
selectivity and sensitivity, and can be quantified by the lev-
els of detection and false alarm probability. The higher thedetection probability, the better primary users (PUs) can be
protected. The lower the false alarm probability, the more
chances a channel can be utilized by secondary users (SUs).
The performance of spectrum sensing depends greatly
on the setting of a detection threshold. Most conventional
spectrum sensing methods adopt a fixed decision threshold
to distinguish PU signals from the noise. For example, an
experimental threshold is set in [4] by measuring the noise
power. However, it is difficult to guarantee the detectionand false alarm probability with the fixed threshold setting
method, especially when the noise power fluctuates [5], [6].
A number of optimal threshold setting algorithms have beenproposed [7], [8] to minimize the required missed detection
probability and false alarm probability. In [7], 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 [7], aspectrum utilization factor was considered in [8] to minimize
the total error sensing probability. All these work has assumed
that the impact factor (weighted factor or spectrum utilization)
Manuscript received June 26, 2013. The associate editor coordinating the
review of this letter and approving it for publication was D. B. Da Costa.
N. Wang and Y . Gao are with the School of Electronic Engineering and
Computer Science, Queen Mary University of London, London E1 4NS,
United Kingdom (e-mail: {nanw, yue.gao }@eecs.qmul.ac.uk).
X. Zhang is with the School of Information and Communication Engineer-
ing, Beijing University of Posts and Telecommunications, Beijing, 100876,China (e-mail: [anonimizat]).
Digital Object Identifier 10.1109/LCOMM.2013.081313.131468is 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 analyzed to pro-
vide guidance for future CR network designs. In this letter, an
adaptive threshold setting al gorithm is proposed to maximize
the spectrum efficiency for both PUs and SUs for different PU
spectrum utilizations.
The main contributions are that an adaptive threshold setting
algorithm is proposed to achieve better spectrum efficiency for
PUs and SUs. The closed-form expression between PUs’ spec-
trum utilization ratio and the pr oposed adaptive threshold is
derived and simplified. The impacts of different PU utilizations
on the sensing performance are quantified.
The remainder of this paper is organized as follows: a
generic CR system model is provided in Section II. The
proposed adaptive threshold se tting algorithm is described in
Section III. In Section IV , theoretical and numerical resultsof both proposed and conventional algorithms are compared
and analyzed at different PUs’ spectrum utilizations. The
conclusions are drawn in Section V .
II. S
YSTEM MODEL
SUs with the energy detection technique is used to detect the
presence of PU signals. The energy detector firstly measures
the power of the input PU signals over a time interval T,t h e n
the received power is compared to a predefined fixed threshold
to decide whether the frequency band is occupied or not. The
sensing decision can be formulated into a binary hypothesis
by
H0:y(n)=w(n)( signal absent )
H1:y(n)=h(n)s(n)+w(n)(signal present )(1)
whereH0andH1denote the hypothesis PU absent and
present, respectively. After bandpass filtering over a bandwidth
W, the received signal is denoted as y(n) (n = 0,1,…,N-1) .w(n)
represents the additive white Gaussian noise and assumed to
be independent and identically distributed (iid) with zero meanand variance of σ
2
n.s(n) is the PU signal and also assumed to
be an iid random process with zero mean and variance of σ2
s.
h(n) is the channel gain. With the signal and noise variance, the
signal to noise ratio (SNR) can be defined as SNR =σ2
s/σ2
n.
The performance metric of spectrum sensing can be mea-
sured by the detection probability Pdand the false alarm
probability Pf. When sample points Nis large enough, Pd
can be derived as [9], [10], [11], [12]
Pd=P(Y>λ|H1)=Q/parenleftBigg
λ−(σ2
n+σ2
s)
(σ2n+σ2s)//radicalbig
N/2/parenrightBigg
(2)
1089-7798/13$31.00 c/circlecopyrt2013 IEEE

WANG et al. : ADAPTIVE SPECTRUM SENSING ALGORITHM UNDER DIFFERENT PRIMARY USER UTILIZATIONS 1839
andPfcan be given as
Pf=P(Y>λ|H0)=Q/parenleftBigg
λ−σ2
n
σ2n//radicalbig
N/2/parenrightBigg
(3)
It can be seen in (2) and (3) that both PdandPfare
mainly dependent on the threshold λ, if the signal variance
σ2
s, the noise variance σ2
nand the sample points Nare known.
Therefore, the decision threshold can be derived for a targetP
dorPf. Under hypothesis H1, the threshold λPdcan be set
for a constant detection rate (CDR) as [13]
λPd=(σ2
n+σ2
s)/parenleftBigg
1+Q−1(Pd)
/radicalbig
N/2/parenrightBigg
(4)
Similarly, under hypothesis H0, the threshold λPfcan be
set for a constant false alarm rate (CFAR) as
λPf=σ2
n/parenleftBigg
1+Q−1(Pf)
/radicalbig
N/2/parenrightBigg
(5)
It has shown in (4) and (5) that the threshold derivation
results are similar for both CDR and CFAR. The threshold
based on CFAR is commonly applied in conventional energydetection algorithms. However, the conventional threshold
derivation process faces one problem that it only considers
one aspect every time in the favor of either PUs or SUs. If
the CR network is designed to guarantee PUs’ safety use of
the spectrum, the CDR method should be used and the targetdetection probability P
dshould be set as high as possible.
The higher the detection probability, the better the PUs can
be protected. If the CR network is designed to guarantee thespectrum efficiency of the SUs, the CFAR method should
be implemented and the target false alarm probability P
f
should be set as small as possible. The lower the false alarm
probability, the more chances a channel can be utilized by
SUs. In order to maximize the benefit for both PUs and SUs,an adaptive threshold setting a lgorithm is proposed to achieve
the best trade-off between P
dandPfin this letter.
III. P ROPOSED THRESHOLD SETTING ALGORITHM
A. Threshold Setting Optimization
In this letter, the trade-off between PdandPfis formu-
lated to an equivalent form of minimizing the error decision
probability Pein function of PUs’ spectrum utilization ratio
α(0<α< 1)and the threshold λas
min(Pe(λ)) = min {(1−α)Pf+α(1−Pd)} (6)
where (1−Pd)represents the missed detection probability that
indicates PUs being absent while actually present. α(1−Pd)
indicates the error decision probability for PUs being present
with spectrum utilization α. Similarly, (1−α)Pfis the error
decision probability for PUs being absent. Therefore, our
objective is to find an adaptive threshold to minimize the total
error decision probability as much as possible.
Substitute Pdin (2) and Pfin (3) into (6),
Pe(λ)=( 1−α)Pf+α(1−Pd)
=( 1−α)Q/parenleftbigg
λ−σ2
n
σ2n/√
N/2/parenrightbigg
+α/bracketleftbigg
1−Q/parenleftbigg
λ−(σ2
n+σ2
s)
(σ2n+σ2s)/√
N/2/parenrightbigg/bracketrightbigg
=1−α
√
π/integraltext∞
a
√
2e−z2dz−α
√
π/integraltext∞
b
√
2e−z2dz+α
(7)wherea=(λ−σ2
n)
σ2
n·/radicalbig
N/2andb=λ−(σ2
n+σ2
s)
σ2
n+σ2
s·/radicalbig
N/2.I f
a spectrum utilization ratio αis specified, the probability of
error decision Pe(λ)becomes a convex function changing with
varying threshold λ. Then, let∂Pe(λ)
∂λ=0,
(2σ2
n+σ2
s)λ2
2σ2n(σ2n+σ2s)−λ−2σ2
n(σ2
n+σ2
s)
σ2sNln(1−α)(σ2
n+σ2
s)
ασ2n=0
(8)
The solutions are
λ1=1+/radicalbigg
1+4(2σ2n+σ2s)
Nσ2s·ln/parenleftBig
(1−α)(σ2s+σ2n)
ασ2n/parenrightBig
(2σ2n+σ2s)/σ2n(σ2n+σ2s)(9)
λ2=1−/radicalbigg
1+4(2σ2n+σ2s)
Nσ2s·ln/parenleftBig
(1−α)(σ2s+σ2n)
ασ2n/parenrightBig
(2σ2n+σ2s)/σ2n(σ2n+σ2s)(10)
Since a decision threshold should be real and positive. The
optimal threshold λ∗that can minimize the error decision
probability is λ1. Substitute SNR =σ2
s/σ2
ninto (9), we have
λ∗=σ2
n·1+/radicalbigg
1+4
N·/parenleftbig
1+2
SNR/parenrightbig
·ln/parenleftBig
(1−α)
α·(1 +SNR )/parenrightBig
(2 +SNR )/(1 +SNR )
(11)
B. Numerical Analysis
Equation (11) can be further simplified when the sample
pointsNis approaching to positive infinite,
λ∗≈2σ2
n·(1 +SNR )
(2 +SNR )(N→+∞) (12)
Fig. 1 shows the proposed adaptive threshold with N=
65537 for different PUs’ spectrum utilizations α. The noise
varianceσ2
nis set to 1. The SNR ranges from -25 dB to -10
dB. It can be seen that the adaptive threshold decreases as
the spectrum utilization increases. The spectrum utilizations
with 10% and 90% exhibit a symmetry property centered atthe 50% utilization. An ideal case when the sample points N
†
become positive infinity (N†/greatermuch100·N)is also illustrated in
Fig. 1. The red square line for sample points N†is overlapped
with the blue star line for the 50% spectrum utilization.
This is because (1−α)/αis equal to 1 when α= 50% .
The spectrum utilization has no effect on the setting of the
adaptive threshold, which is only determined by the sample
points and SNR. Therefore, equation (12) can be regardedas a simplified expression of the proposed adaptive threshold
setting algorithm when the spectrum utilization is 50%.
The proposed adaptive threshold of a given spectrum uti-
lization ratio αcan be obtained with the knowledge of the
SNR and sample points N. Therefore, for a given SNR and
sample points N, the impacts of different spectrum utilization
αon the performance of the error decision probability can be
analyzed by substituting (11) into (7).
Fig. 2 shows the error decision probability P
ewith N=
65537 against different SNRs. The noise variance is σ2
n=1.
The spectrum utilization increases from 0to1. A higher Pe
means a lower spectrum effici ency for both PUs and SUs.
Al o w e rPeleads to a higher spectrum e fficiency. Therefore,
Peshould be minimized as much as possible to improve the

1840 IEEE COMMUNICATI ONS LETTERS, VOL. 17, NO. 9, SEP TEMBER 2013
-25 -20 -15 -100.960.970.980.991.001.011.021.031.041.051.06
SNR(dB)10%α=
90%α=
50%α=
†N→+ ∞*λ
Fig. 1. Adaptive threshold λ∗versus SNR
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.050.10.150.20.250.30.350.4
Spectrum utilizations PeSNR = -24dB
SNR = -22dB
SNR = -20dB
SNR = -18dB
SNR = -16dB
α
Fig. 2.Peversus spectrum utilizations α
spectrum efficiency of the overall system including both PUs
and SUs.
It can be observed in Fig. 2 that the value of error decision
probability Peincreases with the decr easing of SNR values.
This is because the decreasin g of SNR greatly degrades
SUs’ sensing ability. The CR system suffers a low detection
probability and a high false alarm probability, and therefore thetotal error decision probability is definitely increased. Fig. 2
also shows that the highest P
ealways appears when α= 50% .
In addition, Peshows a symmetry property around the 50%
spectrum utilization. Pedecreases by either decreasing or
increasing α. The three cases for Pe=0 areα=0,α=1
and SNR greater than -16 dB. α=0 indicates the extreme
case when all the channels are available to be used by SUs.
Similarly, if all the channels are occupied by PUs, α=1 and
Pe=0. Furthermore, if the SNR is higher than -16 dB, Pe
becomes 0. This is due to the better the channel condition,
PUs and SUs can be more clearly differentiated.-25 -20 -15 -100.20.30.40.50.60.70.80.91
SNR(dB)Pd
Fixed Simulation
Fixed Theory
Adaptive Simulation
Adaptive Theory
Fig. 3.PdversusSNR α = 50%
IV . P RIMARY USER SPECTRUM UTILIZATION EFFECTS
A. Experiment Setup
In simulations, the number of sample points is set as N
= 65537 , which is same as that in theoretical analysis in
Section III. The energy detection employed in this letter is
based on the sensing algorithm [14]. Monte-carlo simulations
are carried out to obtain the detection provability Pdagainst
SNRs for fixed and adaptive threshold setting at 50% spectrum
utilization, as shown in Fig. 3. It can be seen that both sim-
ulation results are very closed t o the analytical results, which
approve our theoretical analysis in Section III. Fig. 3 also
shows that the proposed adaptive threshold achieves higherdetection probability than the conventional fixed one in the
lower SNR region. Based on the same simulation platform, the
study are then extended to a range of PU spectrum utilizationsvarying from 10% to 90%.
B. Results and Analysis
Fig. 4 illustrates the error decision probability P
efor both
the proposed adaptive threshold (blue solid curves) and con-versional fixed threshold (red dotted curves) setting algorithm
at deferent spectrum utilizations αranging from 10% to 90%.
It can be seen that different PUs’ spectrum utilizations do havea significant impact on the P
eperformance. The highest error
decision probability Pecan be achieved at α= 50% for the
proposed adaptive threshold setting algorithm. This highest Pe
point indicates the lowest total spectrum utilization ratio for
b o t hP U sa n dS U s .N om a t t e r αdecreases or increases, the
error decision probability Pealways decreases. The Pefor
the adaptive threshold at the spectrum utilization αof 10% is
the same as that for the spectrum utilization αof 90%. By
comparing the Peat 10% and 90% spectrum utilizations in
Fig. 2 with those in Fig. 4, Peat -20 dB shows almost the
same results for both theretical derivation and simulations.By observing all the P
eagainst SNR, it can be found that
the symmetry property shown in Fig. 4 exactly matches the
theoretical derivation in Section III.
The effect of spectrum utilizations αon the error decision
probability Pefor the conventional fixed threshold setting

WANG et al. : ADAPTIVE SPECTRUM SENSING ALGORITHM UNDER DIFFERENT PRIMARY USER UTILIZATIONS 1841
-25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -1500.10.20.30.40.50.60.7
SNR(dB)Pe= 10% Fixed Threshold
= 50% Fixed Threshold
= 90% Fixed Threshold
= 10% Adaptive Threshold
= 50% Adaptive Threshold
= 90% Adaptive Thresholdα
α
α
α
α
α
Fig. 4.Peversus SNR
algorithm is also illustrated by the red dotted curves in Fig. 4.
ThePeincreases greatly as the increasing of αwhen SNR is
lower than -18.3 dB, and then maintain a almost constant level
when SNR is greater than -18. 3 dB. However, by comparing
the results of both fixed and proposed adaptive threshold,the proposed adaptive threshol d setting algorithm can always
obtain a lower P
efor anyαvalues ranging from 0 to 1.
Therefore, a higher spectru m efficiency can be obtained for
both PUs and SUs by adopting the proposed adaptive threshold
setting algorithm.
V. C ONCLUSION
Previous research has usually been limited to a fixed
PUs’ spectrum utilization and lacks consideration of effects
of different utilizations. In this letter, an adaptive threshold
setting algorithm was proposed to minimize the total error
decision probability for both PUs and SUs at different PUs’
spectrum utilizations. The cl osed-from expression between
PU’s spectrum utilization ra tio and the proposed adaptive
threshold has been derived and verified by simulations. The
numerical analysis demonstrated that the significant influenceof PUs’ spectrum utilization on the total system spectrumefficiency. Both analytical and s imulation results have shown
that a lower error decision probability can be obtained for theproposed adaptive threshold setting algorithm in comparison
with the conventional fixed one. Overall, it can be concluded
that historical PUs spectrum utilizations should be taken intoaccount when designing CR systems.
R
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