IEEE ICC 2013 - Cognitive Radio and Networks Symposium

Utilizing Misleading Information for Cooperative
Spectrum Sensing in Cognitive Radio Networks
Shameek Bhattacharjee, Saptarshi Debroy and Mainak Chatterjee

Kevin Kwiat

Department of Electrical Engineering & Computer Science
University of Central Florida
Orlando, Florida 32816
Email: {shameek, saptarsh, mainak}@eecs.ucf.edu

Air Force Research Laboratory
Information Directorate
Rome, NY 13441
Email: kevin.kwiat@rl.af.mil

Abstract—In cognitive radio networks, the radios continuously
scan the radio spectrum and create a spectrum usage report. Dueto channel uncertainty, there are inaccuracies in these reports.
Oftentimes, the radios share and fuse the observed data inorder to increase the accuracy of the spectrum usage. However,malicious nodes tend to send false information (i.e., attack) inorder to mislead the construction of the spectrum usage report.
In this paper, we use a trust model to evaluate the trustworthiness of every node and use the trust values to effectively fuse
the information from all nodes. A node compares the information
sent by a neighboring node with the predicted information. Basedon the ratio of matches (or mismatches), the neighboring node is
assigned a trust value. Then, we propose a log-weighted metricutilizing trust values to distinguish malicious nodes from others.
Subsequently, we propose threshold based Selective Inversion (SI)fusion and Complete Inversion (CI) fusion to effectively combine
not only the information sent by honest nodes but also utilize
misleading information sent by malicious nodes. We also propose
a combination of the two inversion schemes. We compare theperformance of the inversion based fusion schemes with blindand trust-based fusions. Results reveal better performance forinversion based fusion schemes for various intensities of attack.
We also conduct simulations to evaluate the optimal thresholds
that are used for invoking the inversion based fusion schemes.1

I. I NTRODUCTION
Cognitive radio networks are poised to bring about radical
changes in the wireless communications paradigm. Unlike
traditional radios, cognitive radios constantly monitor the spectrum and intelligently use the radio spectrum in an opportunistic manner, both in licensed and unlicensed bands. Cognitive
radios determine which portions of the spectrum are available
and dynamically access the best available bands/channels.
Usually, a stand alone cognitive radio cannot accurately
measure the true spectrum occupancy due to typical wirelesschannel impairments like channel fading, noise, multipath
shadowing and fading. Thus, multiple radios engage in cooperative spectrum sensing [3], [4] where locally generated
reports by a radio are sent to all its neighboring radios. A
node receiving such reports fuses the information to generate amore accurate spectrum usage report. However, dependence on
information from other radios introduces a vulnerability known
as Spectrum Sensing Data Falsiﬁcation [2] where a radio
participating in cooperative spectrum sensing intentionally
1 Approved for Public Release; Distribution Unlimited: 88ABW-2013-0878,
22Feb13.

978-1-4673-3122-7/13/$31.00 ©2013 IEEE

alters the observed spectrum occupancy. A malicious radiochanges sensed usage on a channel before broadcasting; sayfor example, if the channel is sensed empty denoted by a value
0, the radio advertises a value 1 on that channel, and viceversa. Such malicious intent could be to gain unfair share of
the spectrum or deny spectrum to legitimate radios. Regardless, of the intent, falsiﬁcation of data cripples the utility ofcooperative sensing and induces wrong spectrum decisions.
For example, a radio might be tempted to use a channel thatis being used by the licensed user which is a violation of
the regulatory aspects. Alternatively, a radio might be denied
access to a channel that is usable. As far as combating suchfalsiﬁcation attacks are concerned, there is a considerable
amount of work that deals with either isolation of malicious
nodes [6] or fault tolerant fusion by disregarding the reports
from malicious nodes [2]. To the best of our knowledge, there
is no effort that utilizes misleading information for information
fusion.
In this paper, we introduce a new approach that utilizes
our previous work [1] on trust computation through anomaly
detection. We propose a framework where instead of disregarding falsiﬁed information from malicious nodes, we utilize
their information to our advantage. First, we propose a trustmodel to evaluate the trustworthiness of every node. This isdone by comparing the information sent by each node withthe predicted information. Based on the ratio of matches (ormismatches), every node is assigned a trust value. Once thetrust values are known, we use a log-weighted metric to distinguish the malicious nodes from others. Then, we use weighted
threshold based Selective Inversion (SI) fusion and Complete
Inversion (CI) fusion schemes to effectively fuse data obtained
from all nodes. We also propose a combination of the two
inversion schemes which provides better performance for any
attack intensity. We ﬁnd the conditions for which the combination works better. The fraction of mismatches (false alarms
and missed detections) for different intensities of attack andnode densities is considered as a performance metric. We showthat fraction of mismatches for the proposed fusion techniques
is always less than trust based fusion that completely ignoresthe malicious nodes. In the end, we demonstrate that we could
utilize false information sent by malicious nodes to increase
the gain in cooperative spectrum sensing.

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TABLE I
N OTATIONS

II. S YSTEM M ODEL AND A SSUMPTIONS
We consider an ad-hoc secondary network with 𝑁 nodes; 𝐻
is the set of honest nodes and 𝑀 malicious/dishonest nodes.
The malicious nodes launch independent attacks without collaboration. We assume that the number of malicious nodes(𝜂(𝑀 )) is less than the number of regular nodes (𝜂(𝐻)). Eachnode 𝑖 fuses the spectral sensing data it receives from its
neighbors. We make the following assumptions.
∙ We assume all secondary nodes continuously undergo spectrum sensing to determine whether a channel is occupied ornot. Let us assume secondary node 𝑖 constructs its observed𝑖= [𝑑1 , 𝑑2 , ⋅ ⋅ ⋅ , 𝑑𝑛 ],(actual) binary occupancy vector as: 𝐵𝑎𝑐𝑡where 𝑑𝑘 is 1 or 0 depending on whether the channel is
occupied or unoccupied, and 𝑛 is the number of channels being
monitored. Once this binary vector is created, a secondary
node would broadcast (advertise) this information to its neigh𝑖𝑖𝑖. For a malicious node, 𝐵𝑎𝑑𝑣∕= 𝐵𝑎𝑐𝑡
boring nodes as 𝐵𝑎𝑑𝑣
and for honest nodes both of them are equal. Similarly, asecondary node would also hear broadcast messages (binary
occupancy vectors) from its neighbors. Based on the vectors
a node receives, the node employs a fusion technique toobtain a better estimate about the spectrum usage that cansigniﬁcantly improve the performance of spectrum sensing.
Such cooperative sensing has other beneﬁts such as mitigating
shadowing and multi-path effects.
∙ We consider that the malicious nodes do not report theiroccupancy vectors truthfully; rather they inject errors in theiroccupancy vectors by ﬂipping the bits in the vector. Flipping
0 to 1 implies that the channel is occupied when in reality it isunoccupied. Flipping 1 to 0 implies that an occupied channel
is reported as unoccupied. We denote probability of attack
𝑃𝑎𝑡𝑡𝑎𝑐𝑘 , as the percentage of channels that a malicious nodechanges from its actual observed vector. 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 also denotes
the intensity of attack; hence these terms are used alternatively.
∙ The nodes need not know the geographical coordinates ofother nodes involved in cooperation. We assume the transmit
power level of all secondary nodes are same. Knowledge ofthe transmitter output power, channel losses, and antenna gains
with the appropriate path loss model allow us to ﬁnd distance
between the two nodes using received signal strength (RSS)
through localization or lateration [7].
∙ Each primary transmitter whether it chooses to transmit ornot, transmits only on one channel; so the channel associatedwith a primary transmitter is known. The primary transmitterthat transmits on channel 𝑘, is referred to as 𝑇𝑘 , and since it
is ﬁxed, its coordinates (𝑥𝑇𝑘 , 𝑦𝑇𝑘 ) are known to the nodes. A
comprehensive table for notations used is tabulated in Table I.
III. T RUST M ODEL
Consider Fig. 1. Let 𝑂 be the position of any node 𝑖.
Let 𝑗 be a neighbor whose exact location is not known, but
its distance from 𝑖 is known through RSS localization. On
any channel 𝑘, the bounds on the received power due to theprimary transmitter 𝑇𝑘 is given by [𝛾𝑘𝑗 ]ℎ𝑖𝑔ℎ and [𝛾𝑘𝑗 ]𝑙𝑜𝑤 . Using

Symbol
𝑛
𝑁𝑖
𝐻
𝑀
𝛾𝑡ℎ
𝑠𝑇𝑖𝑘
𝑑𝑘
𝑗
𝑃𝑖
𝑖
𝐵𝑎𝑐𝑡
𝑖
𝐵𝑎𝑑𝑣
𝑖𝑗
𝑃𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐷𝑖𝑗
𝑑𝑗𝑘 ∣𝑝𝑟𝑒𝑑𝑖𝑐𝑡(𝛼, 𝛽, 𝑋)𝑗𝑗
𝐸𝑡𝑟𝑢𝑠𝑡𝑖
𝑇 𝐵𝐹 𝑖

Meaning
Number of channels
Neighbor set of node 𝑖
Set of honest nodes
Set of malicious nodes
Common threshold used to normalize power vectors
Distance between node 𝑖 and primary tower 𝑇𝑘 for channel 𝑘
Binary Decision on a channel 𝑘, 𝑑𝑘 ∈ 0, 1
Set of all neighbors of 𝑖, 𝑗 ∈ 𝑁𝑖
Measured power vector on 𝑛 channels at node 𝑖Actual binary occupancy vector formed at 𝑖
Advertised binary occupancy vector by node 𝑖
Vector of power ranges for neighbor 𝑗 predicted by 𝑖
Binary occupancy of node 𝑗, predicted by 𝑖
Predicted decision on any channel 𝑘, for 𝐷𝑝𝑗
Three tuple trust evidence
Reputation or trust of neighbor 𝑗 calculated by node 𝑖
Fusion result Based on selective inclusion of 𝑗 based on trust

commonly used model for RSS [5], we get
𝛾𝑘𝑖 = 𝑃𝑘 ×

𝐴2
;
𝑠𝛼
𝑖𝑘

(1)

where 𝐴 = frequency constant, 𝛼 is path loss factor, 𝑠𝑖𝑘 isthe distance between 𝑇𝑘 and node 𝑖, and 𝑃𝑘 is the transmit
power of 𝑇𝑘 . It has been shown in [1], that the upper andlower bounds are:[𝛾𝑘𝑗 ]ℎ𝑖𝑔ℎ = 𝑃𝑘 ×
[𝛾𝑘𝑗 ]𝑙𝑜𝑤 = 𝑃𝑘 ×

𝐴2

;

(2)

𝛼;

(3)

𝛼
𝑠𝑘𝑚𝑖𝑛𝑗𝐴2
𝑠𝑘𝑚𝑎𝑥𝑗where the minimum and maximum distances are 𝑠𝑘𝑚𝑖𝑛𝑗 and𝑠𝑘𝑚𝑎𝑥𝑗 respectively (also shown in Fig. 1).
Locus of Node j
T
k

(x

y )
Tk, T k( γjj
( γk ))

k high

P

R
s

min

ik

O

s ij

Q

(x ,y)
i i

k
j

s

max

Fig. 1.

s

low

k
j

Bounds of RSS on channel 𝑘 of neighbor node 𝑗

Thus the[ predicted power vector is given as𝑖𝑗= ([𝛾1𝑗 ]𝑙𝑜𝑤], [𝛾1𝑗 ]ℎ𝑖𝑔ℎ ), ([𝛾2𝑗 ]𝑙𝑜𝑤 , [𝛾2𝑗 ]ℎ𝑖𝑔ℎ ), ......,
𝑃𝑝𝑟𝑒𝑑𝑖𝑐𝑡([𝛾𝑛𝑗 ]𝑙𝑜𝑤 , [𝛾𝑛𝑗 ]ℎ𝑖𝑔ℎ ) .
The inference drawn by node 𝑗 on channel 𝑘 is given as⎧𝑗⎨ 0 if [𝛾𝑘 ]ℎ𝑖𝑔ℎ ≤ 𝛾𝑡ℎ ;𝑗𝑑𝑘 ∣𝑖𝑛𝑓 𝑒𝑟 =(4)
1 if [𝛾𝑘𝑗 ]𝑙𝑜𝑤 ≥ 𝛾𝑡ℎ ;⎩𝑋 otherwise

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where 𝑋 denotes that no inference could be drawn. Though
we discuss with respect to a single node 𝑖, the analysis applies
to all other nodes as well.
A. Formation of Trust Evidence
The predicted occupancy vector, given the mutual distance
between node 𝑖 and 𝑗, is given as
𝐷𝑖𝑗 = [𝑑𝑗1 ∣𝑖𝑛𝑓 𝑒𝑟 , ......, 𝑑𝑗𝑛 ∣𝑖𝑛𝑓 𝑒𝑟 ];𝑑𝑗𝑘 ∣𝑖𝑛𝑓 𝑒𝑟 ∈ 0, 1, 𝑋

A. Log Weighted metric based on TrustFirst, we need to ﬁgure out how much weight do we give toeach node. Note, due to the variability in the trust values, wecannot treat all nodes equally. If node 𝑗 ′ 𝑠 trust as computed𝑗, we denote its corresponding weight as:
by node 𝑖 is 𝐸𝑡𝑟𝑢𝑠𝑡𝑖
𝑊𝑖𝑗 = 𝑙𝑜𝑔𝑒

(5)𝑗
We compare 𝐷𝑖𝑗 with received 𝐵𝑎𝑑𝑣
= [𝑑𝑗1 , .., 𝑑𝑗𝑘 ..𝑑𝑗𝑛 ]. We
deﬁne a vector called Invert Sequence 𝐼𝑆𝑖𝑗 which records thevalues of 𝑘 on which a mismatch (denoted by 𝛽) occurs, amatch (denoted as 𝛼) occurs, and channels with value 𝑋 in
𝐷𝑖𝑗 are kept as 𝑋. If 𝑄𝑗 is the result of the comparison, then⎧𝑗𝑗
⎨ 𝛼 if 𝑑𝑘 ∣𝑖𝑛𝑓 𝑒𝑟 = 𝑑𝑘 ;
𝑗
𝑗
(6)
𝑄 =
𝛽 if 𝑑𝑘 ∣𝑖𝑛𝑓 𝑒𝑟 ∕= 𝑑𝑗𝑘 and 𝐼𝑆𝑖𝑗 = 𝑘;⎩
𝑋 otherwise𝑗[ 𝐸𝑡𝑟𝑢𝑠𝑡𝑖𝑗
1 − 𝐸𝑡𝑟𝑢𝑠𝑡
𝑖

]

(9)

The above equation ensures negative weights for nodes
whose trusts values are below 0.5 and positive otherwise; thus
distinguishing the two classes of nodes. Also, the weights
monotonically increase for honest nodes and monotonicallydecrease for malicious nodes as shown in Fig. 2. We use theseweights to decide the criterion for inversion.
5
Log weight

Weight

The total number of matches, mismatches and undecided
for each node 𝑗 is denoted as 𝜂(𝛼𝑗 ), 𝜂(𝛽 𝑗 ) and 𝜂(𝑋 𝑗 ). We
argue that the trust value should be proportional to the numberof matches. Also, a similar proportion of the undecided ones
must be considered as matches. Thus, the instantaneous valueof trust is obtained as:

0

𝑗

𝑗
=
𝐸𝑡𝑟𝑢𝑠𝑡𝑖)
𝜂(𝛼𝑗 ) ∗ (1 + 𝜂(𝛼𝜂(𝑋𝑗 )+𝜂(𝛽 𝑗 ) )𝜂(𝛼𝑗 ) + 𝜂(𝛽 𝑗 ) + 𝜂(𝑋 𝑗 )

(7)

−5
0

which indicates the probability of whether a node is honest or
dishonest. A value closer to 1 indicates high trustworthinessand a value closer to 0 indicates low trustworthiness ormalicious intent.
B. Trust based Fusion

We use a simple trust based fusion scheme whereby we𝑗is higher
consider only the neighboring nodes whose 𝐸𝑡𝑟𝑢𝑠𝑡𝑖than some trust threshold, Γ𝑜𝑝𝑡 .
{≥ Γ𝑜𝑝𝑡 Node 𝑗 Trusted ;𝑗
If 𝐸𝑡𝑟𝑢𝑠𝑡(8)𝑖< Γ𝑜𝑝𝑡 Node 𝑗 is not trusted𝑖]
We deﬁne Trust based fusion as 𝑇 𝐵𝐹 𝑖 = ∇[𝑇 𝐹 𝑆𝑖 ⊕ 𝐵𝑎𝑐𝑡where 𝑇 𝐹 𝑆𝑖 is the trusted fusion set of binary vectors accumulated by node 𝑖 using equation (8). ∇ is the operator
for majority vote decision rule and the ⊕ operator is used for𝑗less than the threshcombination. The nodes for which 𝐸𝑡𝑟𝑢𝑠𝑡𝑖old are the non-trusted nodes (𝑁 𝑇 𝑆𝑖 ) in the neighborhoodof 𝑖. Most approaches as in [1], [2], [6] use an exclusionary
policy of disregarding the nodes that are deemed malicious.
We deviate from this notion of ﬁltering out possible outliers;
rather, we take a more inclusive approach to exploit malicious
information so as to increase the cooperation gain.

IV. I NVERSION BASED F USION S CHEMAS
Our objective is to intelligently invert elements of theoccupancy vector that are sent by malicious nodes. That way,
we make use of the information sent by malicious nodes.

0.2

0.4

0.6

0.8

1

Trust

𝑗
where 0 ≤ 𝐸𝑡𝑟𝑢𝑠𝑡≤ 1. The trust is a value between 0 and 1
𝑖Fig. 2.

Relation between Trust and Weight

B. Criterion for Inversion
We deﬁne two thresholds: minimum (𝑊𝑚𝑖𝑛 ) and optimal(𝑊𝑜𝑝𝑡 ). Nodes for which the weights are more than 𝑊𝑜𝑝𝑡 areconsidered honest and no change is made to their advertised
vectors. Nodes for which the weights are less than 𝑊𝑚𝑖𝑛
are deemed malicious; thus every element in their advertised
vectors is inverted. The elements in the advertised vectors are
selectively inverted for the nodes whose weights lie between
𝑊𝑚𝑖𝑛 and 𝑊𝑜𝑝𝑡 . That is,⎧
No Inversion⎨ > 𝑊𝑜𝑝𝑡
Complete Inversion (10)≤ 𝑊𝑚𝑖𝑛If 𝑊𝑖𝑗⎩≤ 𝑊𝑜𝑝𝑡 and ≥ 𝑊𝑚𝑖𝑛 Selective Inversion
The challenge lies in determination of these thresholds– which
will be determined through simulations.
1) Complete Inversion (CI): For all malicious neighborsof 𝑖 (identiﬁed by Eqn. (8)), we invert all elements of theadvertised vector. In this case, the expected number of channels on which we get the correct opinion is proportional to𝑃𝑎𝑡𝑡𝑎𝑐𝑘 . For example, if a malicious nodes modiﬁes 80% of
the observed data, we get back the actual sensed opinion on
80% of the channels after inversion. Of course, the hind sideof complete inversion is that the correct information becomesincorrect. Thus it works better for higher 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 . Hence it isused when weights are very low (i.e., lower than 𝑊𝑚𝑖𝑛 ). We
prove this claim in the simulation section.

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corresponds to weight threshold of 0. From the above two
observations, we can infer that for all 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 , 𝑊𝑜𝑝𝑡 is 0.
2
1

Avg. for Honest Nodes
Avg. for Malicious Nodes
Malicious Node 18

0

Log Weight2) Selective Inversion (SI): For all neighbors 𝑖, we get
the invert sequence 𝐼𝑆𝑖𝑗 from the Eqn. (6). 𝐼𝑆𝑖𝑗 indicates
all channels with mismatches. For neighbors whose weights
lie between 𝑊𝑜𝑝𝑡 and 𝑊𝑚𝑖𝑛 , we seek to selectively invert𝑗
the advertised values in 𝐵𝑎𝑑𝑣
for channels comprising the𝑗
set 𝐼𝑆𝑖 . Such inversion forms a new vector for all nontrusted neighbors. This scheme is applicable for lower 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 .
The reason for using a combination of two inversion based
fusion is because the network does not know 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 . However, the trust weights depend on 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 and as trust changes,
the type of inversion scheme that works better is employed.

−1
−2
−3
−4

C. Ideal Fusion and Blind Fusion: For comparisons−5
0.5

Ideal fusion refers to the case when all nodes know andadvertise the actual spectrum usage. We measure the deviation(fraction of mismatches) from the ideal result. The lesser
the deviation, the better is the performance of the proposed
scheme. We use fraction of mismatches from the ideal result asa performance metric We also compare the proposed schemes
when there is no defense mechanism and the fusion is donein a blind manner. Later, we show huge improvements of the
proposed schemes compared to blind fusion.

Fig. 3.

A. Log Weight Measurement
In Fig. 3, we see a signiﬁcant difference between the average
weights for all honest nodes and the average weight for all
malicious nodes. As shown earlier in Fig. 2, the malicious
nodes’ weights lie on the negative 𝑦-axis and the weights ofhonest node lie on the positive 𝑦-axis. As expected, the average
weight for the malicious nodes decreases with increasing
𝑃𝑎𝑡𝑡𝑎𝑐𝑘 . We also show how the weight of a single malicious
node (Node no. 18) varies with 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 . Obviously, the actionsof the honest nodes have nothing to do with 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 ; hence a
ﬂat line.
B. Optimal threshold for Inversion based Fusion
In trust based fusion, we discarded nodes whose trust was
lower than the threshold of 0.50. From Fig. 4, it is evident thatthe minimum possible mismatch is achieved at 0.0 for all probabilities of attack. As we lower the threshold, more malicious
nodes will be included for inversion; hence the higher numberof mismatches. We show the results for mismatch fraction
over different 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 considering different weight thresholds
in Fig. 5. We observe that the lowest mismatch is the one that

0.7
0.8
Probability of Attack

0.9

1

Weights for malicious and honest nodes

0.12
Pattack=0.55

Fraction of Mismatch from ideal

0.11

V. S IMULATION M ODEL AND R ESULTS
We simulate an area of 100x100 units with 100 randomly
scattered nodes with 30% of them programmed to be malicious. All nodes continuously scan 50 channels, record thesignal power on each of them, and create the binary occupancy
vector which they then advertise. The malicious nodes attack(i.e., change the bits in the channel occupancy vector) witha probability between 0.5 to 1.0. It is to be noted that lower
attack probability does not signiﬁcantly affect the network.
Transmission range of all nodes is considered to be 20 units.

0.6

P

=0.60

attack0.1

Pattack=0.65
P

0.09

=0.70

attackPattack=0.75

0.08

Pattack=0.80

0.07

Pattack=0.85

0.06
0.05
0.04
0.03
−1.5

Fig. 4.

−1−0.5
0Weight Thresholds

0.5

1

Fraction of mismatches from ideal vs. weight thresholds

C. Selective Inversion and Complete Inversion
The nodes whose weights are below or equal to 0 are
considered potentially malicious node and they are candidates
for the inversion schemes. Using the entire range for 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 ,we found that for lower values of 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 , selective inversion
performs better as evident from Fig. 6. As 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 takes
higher values, the undecided channels (i.e., neither matches
nor mismatches) are not taken into account in selective inversion and hence the mismatches increase. However, for thecomplete inversion the reverse happens. As 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 increases,
more channels are inverted and the inverted vector from amalicious node is closer to the actual occupancy. This leads
to a gain in cooperation even from the malicious nodes. The
point where the two inversion schemes 𝑆𝐼 and 𝐶𝐼 crossis termed as ‘crossover point’. Before the crossover point,
selective inversion works better and after the crossover pointcomplete inversion works better. From simulations, we ﬁndthat the crossover point occurs at 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 = 0.65. In the next
subsection we justify the choice of crossover point from Fig. 7.
With the crossover point known, we are able to back-calculate
the threshold 𝑊𝑚𝑖𝑛 .
D. Threshold selection for Complete and Selective Inversion
In order to examine the nature of the crossover point, weconsider different densities of malicious nodes for both thefusion schemes and see whether there is a consensus on

2615

0.12

6

Average Mismatch from ideal/Node

5

Fraction of mismatch per node from ideal

weight threshold = 0.0
weight threshold = − 0.5
weight threshold = − 1.0
weight threshold = − 1.5

4

3

2

1

0
0.5

Fig. 5.

0.55

0.6

0.65

0.7

0.75
0.8
Probability of attack

0.85

0.9

0.95

Fraction of mismatches from ideal vs. probability of attack

0.07

Mismatch per node

Fraction of Mismatch from ideal per nodeComplete Inversion
Trust based Fusion
Selective Inversion

0.08

0.06
0.05
0.04
0.03
0.02
0.01
0
0.5

Fig. 6.

0.6

0.7
0.8
Probability of attack

0.9Comparison of proposed fusion schemes with Trust based Fusion

the crossover point. Fig. 7 conﬁrms that 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 = 0.65 isthe cross-over point for both inversion schemes for 𝜌𝑚𝑎𝑙 =0.2, 0.3 and 0.4. Though it is obvious to use an inversion
scheme based on the probability of attack, the problem is thatthe regular nodes would not know the probability of attack.
However, using the log-weight based trust evaluation, they cancompute the weights, 𝑤𝑖 , which indirectly captures the probability of attack. Thus, there is a one-to-one correspondence
between 𝑝𝑎𝑡𝑡𝑎𝑐𝑘 and 𝑤𝑖𝑚𝑎𝑙 .
It is interesting to ﬁnd that the average 𝑊𝑖 for malicious
nodes that corresponds to 𝑃𝑎𝑡𝑡𝑎𝑐𝑘 = 0.65 is almost thesame. For instance, for 𝜌𝑚𝑎𝑙 = 0.2, 0.3 and 0.4 𝑊𝑖 =−1.023909, −1.009977, and −1.037043 respectively. We callthis 𝑊𝑐𝑟𝑜𝑠𝑠𝑜𝑣𝑒𝑟 and make 𝑊𝑐𝑟𝑜𝑠𝑠𝑜𝑣𝑒𝑟 = 𝑊𝑚𝑖𝑛 = −1.0
the threshold which decides which inversion scheme is to
be invoked. Knowing 𝑊𝑚𝑖𝑛 and noting that 𝑝𝑎𝑡𝑡𝑎𝑐𝑘 and 𝑊𝑖
are inversely related, we simply use selective inversion for
𝑊𝑖 > 𝑊𝑚𝑖𝑛 and complete inversion for 𝑊𝑖 < 𝑊𝑚𝑖𝑛 . The
result of the combined inversion fusion is compared with blindfusion and trust based fusion in Fig. 8. It is apparent thatthe combined inversion based inclusive technique works better
than a single trust based technique.
VI. C ONCLUSIONSIn this paper, we proposed a technique that utilizes misleading information sent by malicious nodes for the purposeof cooperative sensing in cognitive radio networks. Contrary
to common approaches, where information sent by malicious
nodes are simply excluded for any decision making, we follow

Fig. 8.

=0.2

mal

CI at ρ=0.3

SI at ρ=0.3

mal

CI at ρ=0.4

SI at ρ

=0.4

mal

0.06

mal

0.04
0.02

0.6

0.7
0.8
Probability of attack

0.9

Crossover point for different malicious node densities

0.25

0.2

Combined Inversion based fusion
Trust based fusion
Blind Fusion

0.15

0.1

0.05

0
0.5

1

=0.2

SI at ρmal

Fig. 7.

0.09

crossover point between
CI and SI at 0.65

0.08

0
0.5

1

CI at ρ

mal

0.1

0.6

0.7
0.8
Probability of attack

0.9

1

Combined inversion compared with Trust based and Blind Fusion

inclusive approaches to exploit even the misleading information. We argue that if the trustworthiness of each malicious
node can be computed, then we can appropriately negate
the false information. To this end, we use a log-weighted
function to compute the trust value of every node. We present
two schemes (selective inversion and complete inversion) for
inverting the occupancy information of the channels. The
combination of these two inversion schemes is also proposed
which yields better spectrum occupancy estimates than trustbased and blind fusion schemes for all probabilities of attack.
We also ﬁnd the conditions for which one scheme works better
than the other.
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