Communications and Network, 2013, 5, 276-279
http://dx.doi.org/10.4236/cn.2013.53B2051 Published Online September 2013 (http://www.scirp.org/journal/cn)
A Diffusion-Based Distributed Collaborative Energy
Detection Algorithm for Spectrum Sensing
in Cognitive Radio*
Junfang Li1, Wen xi a o Che n2, Shaoli Kang3, Yongming Guo1
1The National Institute of Radio Spectrum Management, Xi’an, China
2School of Communication and Information Engineering, Xi’an University of Posts & Telecommunications, Xi’an, China
3State Key Lab of Wireless Mobile Communication, China Academy of Telecommunication Technology, Beijing, China
Received July, 2013
ABSTRACT
Spectrum sensing is one of the most important steps in cognitive radio. In this paper, a new fully-distributed collabora-
tive energy detection algorithm based on diffusion cooperation scheme and consensus filtering theory is proposed,
which doesn’t need the center node to fuse the detection results of all users. The secondary users only exchange infor-
mation with their neighbors to obtain the detection data, and then make the corresponding decisions independently ac-
cording to the pre-defined threshold. Simulations show that the proposed algorithm is more superior to the existing cen-
tralized collaborative energy detection algorithm in terms of the detecting performance and robustness in the insecurity
situation.
Keywords: Collaborative Energy Detection; Data Diffusion; Cognitive Radio; Spectrum Sensing
1. Introduction
Cognitive radio (CR) [1] is a spectrum sharing technol-
ogy that allows unlicensed (secondary) users to operate
in the licensed spectrum bands. It effectively improves
the spectrum utilization in wireless communications [2].
Spectrum sensing is one of the key technologies of
cognitive radio systems, and its purpose is to timely de-
tect ‘spectrum holes’ and makes use of it. At present, the
spectrum sensing algorithms mainly include matched
filtering [3], cyclostationary feature detection [4] and
energy detection [5]. The energy detection is the simplest
method, which doesn't need the prior knowledge of pri-
mary user and is simple to implement [6].Since the de-
tection problem such as ‘hidden terminal’ may be ap-
peared relying on solely one terminal or node, the
multi-node cooperative strategy in cognitive radio is re-
searched and become one of the effective measures to
solve the problem [7-11].
Based on whether depending on center node or not,
multiple node energy detection algorithms can be divided
into two kinds of cooperative models, that is, centralized
and distributed. Currently, most collaborative spectrum
sensing algorithms can be viewed as centralized one. It
means that center node (i.e. fusion center) can use the
observed data or detection results of secondary users, and
then decides whether the primary user is present. But
there are some limits for the performance when the
channels to the center node are under deep fading [10].
And this approach requires sufficient communications
resources to transmit the data, which could easily lead to
network congestion and increase the risk of the network
collapse due to the presence of the central node [11].
However，in the distributed approach, where all nodes
are in equal position and there is no center node, every
node exchanges information only with its neighborhoods
to achieve cooperative energy detection. [12] proposes a
diffusion cooperation strategy based on peer-to-peer dif-
fusion protocol, which attracts widespread concern due
to its simple distributed architecture and low computa-
tional complexity.
In this paper, a distributed cooperative energy detec-
tion algorithm based on the diffusion strategy is proposed,
in which the diffusion collaboration strategy is applied
into spectrum sensing, and combines with consensus
filtering theory to obtain a fully distributed energy detec-
tion algorithm. The proposed algorithm is simulated and
compared with the existing collaborative algorithms.
*This work is supported by National Science and Technology Major
Project (2012ZX03003005-002).
C
opyright © 2013 SciRes. CN

J. F. LI ET AL. 277
2. Energy Detectioin and Network Topology
2.1. Energy Detection Model
In this paper, we assume all users experience independ-
ent and identically distributed (iid) fading communica-
tion environment. Figure 1 depicts the block-diagram of
an energy detector.
In the diagram, the received signal is filtered by
a bandpass filter with the center frequency
()yt
s
f
, and the
bandwidth of interest B. This filter is followed by a
squaring device to measure the received energy
and an integrator 0 is operated over the observation
interval
Ｔ . At last, the detection statistic of the integra-
tor’s output, Y, is compared with a threshold, λ, to decide
whether primary user is present.
2
()
T

For implementation simplicity, the goal of spectrum
sensing is viewed as two hypotheses test,
0
1
(),
() () (),
tH
tht tH



n
ysn (1)
where is the received signal by secondary user and
()yt
()
s
t is transmitted signal of the primary user, h is the
channel amplitude and is the additive white Gaus-
sian noise (AWGN) with mean zero and variance
()nt
2

.
0
H
and 1
H
represent the absence and the presence of
the primary user, respectively. We also denote by

the
signal-to-noise ratio (SNR). Correspondingly, the deci-
sion statistic Y has the following form [5],
2
2
2
21
(2 )
TB
TB
0
H
Y
H








(2)
where 2
2TB

denotes the central chi-square distribution
with 2TB degrees of freedom, 2
2(2 ) TB

 denotes the
non-central chi-square distribution with 2TB degrees of
freedom and the parameter of 2

.
In the centralized collaborative scheme, center node
uses the observed data or detection results of all secon-
dary users to get the fusion result, and then compares
with the pre-defined threshold

to make a final deci-
sion.
2.2. The Diffusion-based Collaborative
Distributed Network Model
In the distributed energy detection scenario with diffu-
sion collaborative strategy [12], the network formed by
the secondary users can be represented by an undirected
graph (Figure 2).The graph consists of a set
of nodes and a set of edges
(, )GVE
{1,2 ,V, }n
()yt 2 ()
0
T

BPF
Y
Threshold Device
01
or
H
H
Figure 1. Block diagram of an energy detector.
{( ,),}EijijV.
If two secondary users are connected by an edge, it
means that they satisfy and can mutually ex-
change information. For convenience of description, we
often refer node i as i-th secondary user. Denote the
neighbors of node i by
(, )ij E
{(,)}
i
Nj
N
VijEV
, and
the number of elements in i is denoted by i (also
called the degree of node i). E.g., the neighbor of node 1
is
d
1{1,2 ,}Nn

and 13d

.
In the above distributed network, at time 0k

, every
user i sets i
(0)
i
x
kY


*()
i
as its local state variable. The
collaboration strategy of diffusion is represented by Fig-
ure 3, where every node i in the network continuously
combines the measurement results from its neighbor-
hoods, and gains a fusion result. Those iterations are
done repeatedly until a common result (i.e. steady state)
is reached,
x
xk, for any user i at a certain time k.
This process may be considered as the consensus filter-
ing problem. Therefore, we can make use of consensus
filter theory to attain collaborative spectrum sensing.
2.3. Consensus Filtering Theory
By achieving consensus, the individual variable i
x
progressively converges to the common value *
x
, for
each iV

i.e.
() ,
i
xkx k

 
)
j
(3)
Our scheme is based on the recent results in weighting
consensus algorithms [15], which the iterative formula is
as follows:
(1) ()(
i
iiii ij
jN
x
kwxk wx

 
k (4)
Node 1
1
Y
Node n
n
Y
Node i
i
Y
Node j
j
Y
Node 3
3
Y
Node 2
2
Y
1
N
3
N
\
\
Figure 2. Distributed network with n nodes.
Consensus
filter
i
1(1) i
xk


1(1)xk

1(1) i
xk


(1)
i
xk

()
i
x
k
{( 1)}
i
N
xk
\
\
//
(1)
n
xk

Figure 3. Network with a diffusion cooperation strategy.

J. F. LI ET AL.
278
where, it is assumed that state variable of the user
i is the measurement i
Y at discrete time
(0)
i
x
0k

,
and ij are denoted the weighting factors. ij
ii
w
0w w

means that nodes i and j are not connected. Currently,
possible choices for the weighting coefficients w are the
Metropolis, the Laplacian and the nearest neighbor rules
[16-18]. For simplicity, we choose to use the nearest
neighbor rule which the combiner matrix is defined
as follows:
w
1,
||
0,
i
i ij
jN
N w





otherwise
(5)
According to the weighting factors, the diffusion co-
operative scheme (4) can be interpreted as that every
node i exchanges information with its neighbors, and
then updates itself measurement based on its own previ-
ous states and its neighbors.
3. Diffusion-Based Algorithm for Spectrum
Sensing
When the network topology is setup, every node estab-
lishes communication links with its neighborhoods. The
proposed diffusion-based collaborative spectrum sensing
algorithm includes three stages, energy measurement,
diffusion cooperative and decision.
1. Let n denotes the number of users collaborating.
Each node utilizes the spectrum sensing model (Figure 1)
to make its measurements about primary users signal. i
is denoted the measurement result of user i, and all
are random variables with independent
and identical distribution by equation (2).
Y
(1,2,,)
i
Yi n
2. According to the network topology, every user uses
the neighbors’ measurements to coopera-
tively fuse. Those iterations are done repeatedly until a
steady state is reached. Finally, we can obtain the deci-
sion statistic of the proposed algorithm which is the
,ij Yj N
d
T
average measurements of all users, i.e. 1
1n
D
i
i
TY
n
.
We define , therefore
1
n
ii M
T


Y1
D
M
n
TT. According
to the characteristic of the chi-square distribution, there is
no primary signal present under 0
H
, we have
2
2
~
M
nTB
T  (6)
12
2
~
D
nTB
n
T  (7)
Under the hypothesis of 1
H
, all secondary users ex-
perience the same fading environment, and the detection
threshold is determined only by the distribution of
D
T
under 0
H
. So, there is no need to derive the distribution
of
D
T under 1
H
.
3. Every secondary user compares the average meas-
urement result with the pre-defined threshold λ (
Figure
1), and then makes a corresponding decision independ-
ently to get the final result of fusion locally,
0
1
,
,
D
D
HT
HHT






(8)
where the decision threshold λ is determined by the
equation ()
D
Td df
f
tdtP

 
 and the probability
density function
D
T
f
of the random variable TD can be
derived from equation (7).
4. Simulation Results and Discussions
The performance of spectrum sensing algorithm is evalu-
ated in terms of detection probability d and false alarm
probability
P
f
P. As expected, the larger detection prob-
ability indicates that the performance of the algorithm is
the better under a certain false alarm probability. In the
simulation, we assume that and
0.1
f
P5TB

at the
selected center frequency
s
f
. There are 100000 times
Monte Carlo simulation.
The detection performance of the proposed diffusion-
based scheme for different number of collaborative spec-
trum sensors is shown in Figure 4. In the comparison,
we can see that the performance of proposed scheme
have a significant improvement with increasing number
of collaborative spectrum sensors. For example, the de-
tection probability of only one user is about 52% when
SNR is -5dB, while the number of the secondary users
increases to 5 and 10, the detection probability raises to
about 67% and 75%, respectively.
As to the network model with 10 users (Figure 2),
Figure 5 shows the performance of the proposed diffu-
sion-based scheme, the existing OR-rule and AND-rule
collaborative scheme, respectively. From the simulation
results, it can be observed that the proposed diffusion-
based compares with the existing two kinds of algorithm
-5 -4 -3 -2-10 12 3 45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Average SNR/dB
Detection Probability
n=1
n=5
n=10
Figure 4. Detection performance comparison for different
number of collaborative spectrum sensors.

J. F. LI ET AL.
279
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-5 -4 -3-2-10 1 2345
0.4
0.5
0.6
0.7
0.8
0.9
1
Average SNR/dB
Dete c tion Proba b ilit y
OR-rule-b ased Col l aborati ve Energy Detecti on
AND-rul e-b ased Coll aborati ve Energy Detecti on
Diffusi on-based Collab orati ve Ene rgy Detecti on
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5. Conclusions
In this paper, we have proposed a novel fully-distributed
collaborative spectrum sensing algorithm in cognitive
radios, in which every node exchanges information only
with its neighbors and then makes the corresponding
decision independently without fusion center. Simulation
results demonstrate the validity of the proposed scheme,
and show that it is more superior to the existing collabo-
rative energy detection algorithms in terms of the detect-
ing performance and robustness.
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