Trust based channel preference in cognitive radio
networks under collaborative selfish attacks
Shameek Bhattacharjee and Mainak ChatterjeeElectrical Engineering & Computer Science, University of Central Florida, Orlando,
Email: {shameek, mainak}@eecs.ucf.edu.
Abstract—Secondary spectrum data falsification (SSDF) is acommon attack in cognitive radio networks, where dishonest
nodes share spurious local sensing data. This behavior misleads
the collective inference on spectrum occupancy. The situation ismore aggravated when a collaborative SSDF attack is launchedby a coalition of selfish nodes. Defense against such collaborative
attacks is difficult with popularly used voting based inference
models.
This paper proposes a method based on Bayesian inference
that indicates how much the collective decision on a channel’s occupancy can be trusted. Using an anomaly monitoring technique,we check if the reports sent by a node match with the expectedoccupancy and classify the outcomes into three categories: i)if there is a match, ii) if there is a mismatch, and iii) if itcannot be decided. Based on the measured observations overtime, we estimate the parameters of the hypothesis of match andmismatch events using a multinomial Bayesian based inference.
We quantitatively define the trust as the difference between theposterior beliefs associated with matches and that of mismatches.
The posterior beliefs are updated based on a weighted averageof the prior information on the belief itself and the recently
observed data. We conduct simulation experiments that showthat the proposed trust model is able to distinguish the attacked
channels from the non-attacked ones. Also, a node is able torank the channels based on how trustworthy the inference on achannel is. We are also able to show that attacked channels havesignificantly lower trust values than channels that are not.

I. I NTRODUCTION
In cognitive radio networks, secondary users (i.e., unlicensed users) cooperate with each other by sharing theirlocally sensed information on spectrum occupancy facilitating
more accurate inference on spatio-temporal spectrum usage
statistics. The fused information is then used by the secondaryusers to dynamically access channel based on some mutuallyagreed upon channel access etiquettes. [1].
Oftentimes, to reduce the adverse effect of wireless channel
characteristics like signal fading and noise, data gathered at
multiple locations are fused together [7]. Thus, the cognitive radios employ cooperative sensing where the spectrum
decision is made after fusing the individual spectrum reports
sent by a number of radios at various locations. Such fusion
has been proven to effectively mitigate shadowing and multipath effects and significantly improve spectrum usage throughcoordination among competing cognitive radios [7]. Popularfusion techniques are usually based on 𝑘 out of 𝐾 fusion
or majority voting [12]. However, reliance on cooperation
has also opened up potential vulnerabilities [4]. An example
c978-1-4799-4912-0/14/$31.00 ⃝2014
IEEE

could be the case where dishonest radios provide misleading
information resulting in wrong decisions by the other radios.
An easy manipulation can be achieved through secondary
spectrum data falsification (SSDF) attacks where spurious
occupancy information is sent by the rogue radios. From now,
we use the terms ‘radio’ and ‘nodes’ interchangeably.
To counter SSDF attacks, the common approach has beenon the identification or isolation of dishonest nodes [5], [10].
But, there has not been much effort on distinguishing between
selfish and malicious rationale of rogue nodes, or the effectof a coalition formation. While a malicious attacker’s only
objective is maximum damage to other nodes in a network,
selfish attacks are launched by rational nodes on a few strategic
channels so as to gain some tangible benefit. A classic example
of a collaborative selfish SSDF attack is a group of nodes
belonging to a certain network provider which wants accessto some selected channel(s); hence all nodes belonging tothat provider send false information for those channels while
truthfully reporting on all other channels in order to remain
undetected. Compared to the number of malicious nodes, thenumber of selfish nodes can be high, considering every node
has a natural proclivity to maximize its benefits. Hence selfish
attacks are more plausible form of a vulnerability. But total
isolation of all such selfish nodes is perhaps not the rightapproach. This is because in such a case the fusion process
loses the correct information that the selfish nodes mightshare [3]. This loss is even more pronounced when the selfish
nodes collaboratively falsify (on same channel sets) with alow probability and tell the truth more often [4]. In fact, it isoften difficult to detect such selfish behavior of nodes throughmalicious node detection techniques. Thus, instead of isolating
and not considering the selfish nodes at all, we ought toconsider shared information on specific channels and discountor completely ignore information on other channels. Thus, we
argue for the need of a channel-centric defense instead of anode-centric defense.
In this paper, we propose a trust based channel centric
approach towards evading selfish collaborative SSDF attacks.
We discuss two variants of selfish collaboration: static anddynamic. In the static case, the set of channels that is attacked
does not change over time, while in the dynamic case, it
does. First, we present a 3 step monitoring technique thatgathers channel centric evidence by capturing the anomalies
in the advertised occupancy of a channel. First we estimate
the lower and upper bounds on the received power level froma neighbor. The bounds are then compared with some predefined threshold that results in a predicted ternary decision:
occupied, not occupied, or cannot be decided. This predicted
decision is compared with what a neighboring node actually
advertised. The comparison yields three possible outcomes–
match, mismatch or undecided. The observation data formedby the outcomes from all neighbors on a particular channel
gives the frequency of occurrence of matches, mismatches
or undecided. More matches is indicative of agreement onchannel occupancy while more mismatches means presenceof mis-leading advertisements.
The outcomes can be conceptualized as multinomial hypothesis of a Bayesian inference model with three parameters. We
seek to build a Bayesian inference based trust model, wherea value is assigned to each channel that indicates the level oftrustworthiness of the occupancy inference of that channel.
We do this by calculating the posterior Bayesian belief ofthe hypothesis based on incrementally incoming observation
data and prior belief of the hypothesis itself. The difference
between the posterior beliefs associated with a match and amismatch is reported as the net trust. We use the net trust
for ranking the channels allowing the nodes to choose thechannels based on how trustworthy the cooperative inference
on a channel is. Such a choice enables less policy violations
and better spectrum utilization.
Our results show that for both variants (i.e., static anddynamic) the channels that were attacked have a significantly
lower trust value than channels that were not. Moreover,for static attacks it is also possible to identify the channels
that were selected by the adversarial group. We also showthat the proposed trust model is effective even for a highdensity of selfish nodes. We demonstrate that the proposed
channel centric defense mechanism is not effected by node
mobility and does not require knowledge of the locationsof secondary nodes, thus obviating the need for addressing
location falsification.
II. S YSTEM M ODEL AND A SSUMPTIONS
We consider a distributed secondary cognitive radio networkwith honest nodes denoted by 𝐻 and a set of selfish nodes
denoted by 𝐷. Each node 𝑖 fuses the spectrum sensing data it
receives from its neighboring nodes, denoted by 𝑁 𝑖 . For any
channel 𝑘, there are 𝑁𝑘𝑖 advertised opinions on the occupancy
of channel 𝑘 at node 𝑖. We assume all secondary nodes
continuously undergo spectrum sensing to determine whether
a channel is occupied or not by comparing the sensed energy
with some common threshold, 𝛾𝑡ℎ . Let us assume secondary
node 𝑖 constructs its observed binary occupancy vector as𝑖= [𝑑1 , 𝑑2 , ⋅ ⋅ ⋅ , 𝑑𝐾 ], where 𝑑𝑘 is 1 or 0 depending
𝐵𝑎𝑐𝑡on whether the channel is occupied or unoccupied, and 𝐾𝑖denotesis the number of channels being monitored. 𝐵𝑎𝑐𝑡the actual binary occupancy vector that was formed at 𝑖.
Once this binary vector is created, a secondary node would𝑖.
advertise this information to its neighboring nodes as 𝐵𝑎𝑑𝑣
𝑖
𝑖∕= 𝐵𝑎𝑐𝑡
and for honest nodes both
For a selfish node, 𝐵𝑎𝑑𝑣
of them are equal. Similarly, a secondary node would also

hear broadcast messages (binary occupancy vectors) from its
neighbors. Based on the vectors a node receives, the node will
employ a majority voting based fusion technique to obtain abetter estimate about the spectrum usage.
We consider that the selfish nodes do not report theiroccupancy vectors truthfully; rather they inject errors in theiroccupancy vectors by flipping the bits in the vector collaboratively. Flipping 0 to 1 implies that the channel is occupied
when in reality it is unoccupied. Flipping 1 to 0 implies that an
occupied channel is reported as unoccupied. The selfish nodes
collaborate to attack (i.e., flip) the same set of channels to
mislead the voting based fusion technique. We denote 𝐼𝑎𝑡𝑡𝑎𝑐𝑘 ,as the fraction of channels that a selfish node flips/changes
from its observed vector. Unlike the attacks from malicious
nodes, selfish nodes attack on fewer but a specific channels(based on certain statistical criteria).
We assume the transmit power level of all secondary nodes
during sharing of binary vectors is equal and takes placethrough a common control channel. Given this, along withchannel losses, and antenna gains with the appropriate pathloss model we can compute the distance between the two
nodes using received signal strength (RSS) of reporting signal
through localization or lateration [2], [9]. Hence, location
falsification is no more a limiting factor and location privacy
preserved.
As for the primary users, each primary transmitter, transmits
on one channel; so the channel associated with a primarytransmitter is known. The primary transmitter that transmits
on channel 𝑘, is referred as 𝑇𝑘 , and has fixed coordinates(𝑥𝑇𝑘 , 𝑦𝑇𝑘 ) which are known to the nodes.
III. G ATHERING T RUST E VIDENCE
Consider Fig. 1. Let 𝑂 be the position of any node 𝑖. Let
𝑗 be its neighbor whose exact location is not known, but themutual distance can be estimated through RSS localization.
Through RSS localization, whenever node 𝑗 sends an advertisement, we can estimate the mutual distance 𝑠𝑖𝑗 and the locus
of neighbor 𝑗 is anywhere on the circle centered around node
𝑖 with a radius 𝑠𝑖𝑗 when transmit powers are same for all
nodes. (See Fig. 1) Using commonly used propagation modelfor RSS [8], we know RSS at node 𝑖 on channel 𝑘 due toprimary tower 𝑇𝑘 is:
𝛾𝑘𝑖 = 𝑃𝑘 ×

𝐴2
;
𝑠𝜔
𝑖,𝑘

(1)

where 𝐴 is a constant, 𝜔 is path loss factor, 𝑠𝑖,𝑘 is the distance
between 𝑇𝑘 and node 𝑖, and 𝑃𝑘 is the transmit power of
𝑇𝑘 . On any channel 𝑘, the highest and lowest bounds on thereceived power for neighbor 𝑗 due to the primary transmitter
𝑇𝑘 transmitting on channel 𝑘 is given by:[𝛾𝑘𝑗 ]ℎ𝑖𝑔ℎ = 𝑃𝑘 ×
[𝛾𝑘𝑗 ]𝑙𝑜𝑤 = 𝑃𝑘 ×

𝐴2𝑠𝜔
𝑗𝑚𝑖𝑛 ,𝑘𝐴2𝑠𝜔
𝑗𝑚𝑎𝑥 ,𝑘(2)(3)

where the minimum and maximum distances are 𝑠𝑗𝑚𝑖𝑛 ,𝑘 and𝑠𝑗𝑚𝑖𝑛 ,𝑘 from 𝑇𝑘 respectively (also shown in Fig. 1). The detailsof this procedure are given in [3].
Locus of Neighbor j

Tk( x T , yT )k

[ Yk ]

high

s ij

s
j
,k
min

k

j

j

[ Yk ]

H

o
L

(x
s

low

Node i

i

, y

i

)

ik

s
j
,k
max

Fig. 1.

Bounds of RSS on channel 𝑘 of neighbor node 𝑗

Thus the predicted power vector for node 𝑗 on channel 𝑘
as calculated[ by 𝑖 is given as𝑗= ([𝛾1𝑗 ]𝑙𝑜𝑤 , [𝛾1𝑗 ]ℎ𝑖𝑔ℎ ), ([𝛾2𝑗 ]𝑙𝑜𝑤 , [𝛾2𝑗 ]ℎ𝑖𝑔ℎ ), ⋅ ⋅ ⋅ ,𝑃𝑝𝑟𝑒𝑑𝑖𝑐𝑡]𝑗𝑗]𝑙𝑜𝑤 , [𝛾𝐾]ℎ𝑖𝑔ℎ ) .
([𝛾𝐾
The inference drawn by node 𝑖 for node 𝑗 on channel 𝑘 isgiven as⎧𝑗𝑗
⎨ 0 if both [𝛾𝑘 ]𝑙𝑜𝑤 and [𝛾𝑘 ]ℎ𝑖𝑔ℎ ≤ 𝛾𝑡ℎ𝑗𝑗
𝑑𝑘 ∣𝑖𝑛𝑓 𝑒𝑟 =(4)
1 if both [𝛾𝑘 ]𝑙𝑜𝑤 and [𝛾𝑘𝑗 ]ℎ𝑖𝑔ℎ ≥ 𝛾𝑡ℎ⎩
𝑋 otherwise
where 𝑋 denotes that no inference could be drawn, and 𝛾𝑡ℎ is
the common threshold used by all nodes to decide if a channel
is occupied or not.
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 , ......, 𝑑𝑗𝐾 ∣𝑖𝑛𝑓 𝑒𝑟 ];𝑑𝑗𝑘 ∣𝑖𝑛𝑓 𝑒𝑟 ∈ {0, 1, 𝑋} (5)𝑗We compare 𝐷𝑖𝑗 from Eqn. (5) with received 𝐵𝑎𝑑𝑣=𝑗𝑗𝑗[𝑑1 , .., 𝑑𝑘 ..𝑑𝐾 ]. We record the results of comparison in a vector
Trust Evidence 𝑄𝑘𝑗 , where a match (denoted as 𝛼), a mismatch(denoted by 𝛽), and channels with value 𝑋 in 𝐷𝑖𝑗 are recorded
as 𝜇 based on Eqn. (6): If 𝑄𝑗𝑘 is the result of the comparison,

then

⎧
⎨ 𝛼
𝑄𝑗𝑘 =
𝛽
⎩
𝜇

if 𝑑𝑗𝑘 ∣𝑖𝑛𝑓 𝑒𝑟 = 𝑑𝑗𝑘
if 𝑑𝑗𝑘 ∣𝑖𝑛𝑓 𝑒𝑟 ∕= 𝑑𝑗𝑘(6)otherwise

From Eqn. (6), for each channel 𝑘 and for each neighbor 𝑗,
we have one of three categories of outcomes: match, mismatch,
undecided. We arrange the 𝑄𝑗𝑘 for all neighbors and look for
total number of occurrences for each category with respect tochannel 𝑘. The number of matches, mismatches and undecided
observed for channel 𝑘 are given by 𝑛𝛼𝑘 , 𝑛𝛽𝑘 , and 𝑛𝜇𝑘
respectively. Also, 𝑛𝛼𝑘 + 𝑛𝛽𝑘 + 𝑛𝜇𝑘 = 𝑁𝑘 equals the total
number of opinions from 𝑁 neighbors on channel 𝑘. Note
this is equally valid for all nodes and therefore we drop theindex 𝑖 for the node concerned.

IV. T RUST BASED C HANNEL P REFERENCE
From the previous section, we get 𝑁𝑘 independantly monitored observations on channel 𝑘, comprising one of thethree possible outcomes per observation. We seek to obtain
the Bayesian belief (also called subjective probability) of
occurrence of each possible outcome known as bayesian belief
parameters based on prior observations gathered from theobserved trust evidence. With more observations, we update
the Bayesian belief parameter for the hypothesis increasing
the accuracy of the parameters. Since a match indicates a nonanomalous behavior, a channel with higher posterior belief formatch is considered more trustworthy.
To model how node 𝑖 can compute the belief on channel 𝑘,
we use the observation counts to calculate the Bayesian estimate of each of the parameters. Since the following analysis
is valid for any channel 𝑘, we drop the suffix 𝑘 for simplicity.
¯ denote the hypothesis described by the underlying
Let 𝑋(𝜃)unknown bayesian probability parameter of a random trial
yielding match, mismatch or undecided as 𝜃¯ = {𝜃𝛼 , 𝜃𝛽 , 𝜃𝜇 }.
¯Here, 𝜃𝛼 , 𝜃𝛽 , and 𝜃𝜇 are the unknown probability of 𝑋(𝜃)exhibiting a match, mismatch or undecided respectively. Since
these observation outcomes are exhaustive and mutually exclusive, 𝜃𝛼 +𝜃𝛽 +𝜃𝜇 = 1. Let 𝐷𝛼 , 𝐷𝛽 , 𝐷𝜇 denote the randomvariables that represent the number of times, the outcomes 𝛼,𝛽 and 𝜇 occur. The observation data can be represented as
random observation vector 𝐷(𝑁 ) = {𝐷𝛼 , 𝐷𝛽 , 𝐷𝜇 } having a
multinomial distribution with 3 tuple parameter described by𝜃𝛼 , 𝜃𝛽 , and 𝜃𝜇 .
Our objective is to estimate and update the probability¯ based on observation evidence 𝐷(𝑁 )parameters in 𝑋(𝜃)¯ itself.
and prior information on the hypothesis parameter 𝜃,¯
Since there is no information about 𝜃 initially, we consider it
to be uniformly distributed a-priori. Subsequent observations
dictates how these parameters are updated. Our first step is to¯calculate the Bayesian estimate of 𝜃.
First, we show the case of estimating belief that a matchoccurs (𝜃𝛼 ). Since in Bayesian inference, the assumption isthat prior and posterior probability have the same distribution,
we can formally define the probability parameters as:¯ = 𝛼∣𝜃)¯ = 𝜃𝛼𝑃 (𝑋(𝜃)¯ = 𝛽∣𝜃)¯ = 𝜃𝛽𝑃 (𝑋(𝜃)¯ = 𝜇∣𝜃)¯ = 𝜃𝜇𝑃 (𝑋(𝜃))(7)

This assumption is due to the well known fact that a Dirichlet
distribution acts as a conjugate prior to multinomial distributions. Hence prior and posterior preserve the same form [11].
The observations data 𝐷(𝑁 ) can be treated as a multinomial
distribution with probability parameter 𝜃𝛼 ,𝜃𝛽 , and 𝜃𝜇, where
the probability mass function is given by:¯ = 𝑃 (𝐷(𝑁 )∣𝜃)¯𝑃 (𝐷𝛼 = 𝑛𝛼 , 𝐷𝛽 = 𝑛𝛽 , 𝐷𝜇 = 𝑛𝜇 ∣𝜃)𝑁!
𝑛𝜃𝑛𝛼 𝜃 𝛽 𝜃𝑛𝜇=𝑛𝛼 !𝑛𝛽 !𝑛𝜇 ! 𝛼 𝛽 𝜇(8)Given this we can use Bayes theorem to calculate the¯ = 𝛼,
ˆ 𝜃)
posterior belief estimate on the event of a match 𝑋(

given observation data 𝐷(𝑁 ) as:¯ = 𝛼∣𝐷(𝑁 )) =
ˆ 𝜃)
𝑃 (𝑋(

¯ = 𝛼, 𝐷(𝑁 ))
ˆ 𝜃)
𝑃 (𝑋(
𝑃 (𝐷(𝑁 ))(9)

Denominator of the above equation is the marginal probability that can be conditioned or marginalized on all possible
outcomes for 𝜃¯ and since probabilities are continuous∫¯ (𝜃)𝑑(¯ 𝜃)¯(10)𝑃 (𝐷(𝑁 )) = 𝑃 (𝐷(𝑁 )∣𝜃)𝑓¯ˆ 𝜃),Assuming conditional independence between the 𝑋(¯
𝐷(𝑁 ) and 𝜃, we calculate the numerator of Eqn. (9),¯ = 𝛼, 𝐷(𝑁 )), as:
ˆ 𝜃)
𝑃 (𝑋(
∫
¯ = 𝛼, 𝐷(𝑁 )∣𝜃)𝑓¯ (𝜃).𝑑(¯ 𝜃)¯𝑃 (𝑋(𝜃)=¯
𝐷(𝑁 )(𝜃)∫=¯
𝐷(𝑁 )(𝜃)¯
𝐷(𝑁 )(𝜃)Since there is no prior information on 𝜃¯ (before any observations) in Eqn. (10), we can assume it to be uniformly¯ = 1 and we can put Eqn. (8) in
distributed such that 𝑓 (𝜃)Eqn. (10), and get∫𝑁!
𝑛
𝑃 (𝐷(𝑁 )) =𝜃𝛼𝑛𝛼 𝜃𝛽 𝛽 𝜃𝜇𝑛𝜇 𝑑𝜃𝛼 𝑑𝜃𝛽 𝑑𝜃𝜇 (11)𝑛𝛼 !𝑛𝛽 !𝑛𝜇 !
𝐷(𝑁 )(𝜃𝛼 ,𝜃𝛽 ,𝜃𝜇 )For simplicity, let∫𝑛 𝑛𝜃𝛼𝑛𝛼 𝜃𝛽 𝛽 𝜃𝜇 𝜇 𝑑𝜃𝛼 𝑑𝜃𝛽 𝑑𝜃𝜇 = 𝐼1
𝐷(𝑁 )(𝜃𝛼 ,𝜃𝛽 ,𝜃𝜇 )To solve for 𝐼1 we use the multivariate generalization of theEulerian integral of first kind. Note that 𝐷(𝑁 )(𝜃𝛼 , 𝜃𝛽 , 𝜃𝜇 )denotes a space and we know that a space of 𝑚(= 3)parameters has only 𝑚 − 1(= 2) degrees of freedom due tothe additivity constraint 𝜃𝛼 + 𝜃𝛽 + 𝜃𝜇 = 1. Therefore when
we integrate over this space, the integration has 𝑚 − 1 = 2
dimensions. Hence∫ 1∫ 1−𝜃𝛼 −𝜃𝛽(𝑛 +1)−1𝐼1 =𝜃𝛼(𝑛𝛼 +1)−1 𝜃𝛽 𝛽
(1 − 𝜃𝛼 − 𝜃𝛽 )(𝑛𝜇 +1)−1 𝑑𝜃𝛼 𝑑𝜃𝛽
0

0

(12)
Eqn. (12) is a known form for the multivariate extensionof the Beta function which in this case is defined as 𝐵(𝑛𝛼 +1, 𝑛𝛽 + 1, 𝑛𝜇 + 1). The proof can be found in Lemma 2.4.1of [6]. In general 𝐵(𝛼1 , ⋅ ⋅ ⋅ , 𝛼𝑚 )∫𝑚−1∑𝑥1𝛼1 −1 ...(1 −𝑥𝑖 )𝛼𝑚 −1 𝑑𝑥1 ...𝑑𝑥𝑚−1=
𝑖=1
𝐷(𝑥1 ,⋅⋅⋅ ,𝑥𝑚−1 )∏𝑚Γ(𝛼 )Γ(𝛼1 ) ⋅ ⋅ ⋅ Γ(𝛼𝑚 )𝑖=1∑𝑚 𝑖 ==
Γ(𝛼1 + ⋅ ⋅ ⋅ + 𝛼𝑚 )Γ( 𝑖=1 𝛼𝑖 )

(13)

=
=

𝐵(𝑛𝛼 + 1, 𝑛𝛽 + 1, 𝑛𝜇 + 1)
Γ(𝑛𝛼 + 1)Γ(𝑛𝛽 + 1)Γ(𝑛𝛽 + 1)
Γ(𝑛𝛼 + 1 + 𝑛𝛽 + 1 + 𝑛𝜇 + 1)

(14)

Putting Eqn. (14) in Eqn. (11) we get:𝑁!
Γ(𝑛𝛼 + 1)Γ(𝑛𝛽 + 1)Γ(𝑛𝛽 + 1)
𝑛𝛼 !𝑛𝛽 !𝑛𝜇 ! Γ(𝑛𝛼 + 1 + 𝑛𝛽 + 1 + 𝑛𝜇 + 1)
(15)
Since the parameters in gamma functions 𝑛𝛼 + 1 etc. are allnon zero positive values, we can use the result Γ(𝑧) = (𝑧 −1)!
to calculate Eqn. (15) as𝑃 (𝐷(𝑁 )) =𝑃 (𝐷(𝑁 )) =𝑁!
(𝑁 + 2)!

=𝑁!
𝑛𝛼 !𝑛𝛽 !𝑛𝜇 !

∫𝑛𝜃𝛼 𝜃𝛼𝑛𝛼 𝜃𝛽 𝛽 𝜃𝜇𝑛𝜇 𝑑𝜃𝛼 𝑑𝜃𝛽 𝑑𝜃𝜇𝐷(𝑁 )(𝜃𝛼 ,𝜃𝛽 ,𝜃𝜇 )=𝑁!
𝑛𝛼 !𝑛𝛽 !𝑛𝜇 !

∫𝑛𝜃𝛼𝑛𝛼 +1 𝜃𝛽 𝛽 𝜃𝜇𝑛𝜇 𝑑𝜃𝛼 𝑑𝜃𝛽 𝑑𝜃𝜇(17)𝐷(𝑁 )(𝜃𝛼 ,𝜃𝛽 ,𝜃𝜇 )The above integral has the same form as Eqns. (11), (12),and (13). Hence the integral portion of Eqn. (17) can be
rewritten as∫ ∫1 1−𝜃𝛼 −𝜃𝛽(𝑛 +1)−1𝜃𝛼(𝑛𝛼 +2)−1 𝜃𝛽 𝛽
(1 − 𝜃𝛼 − 𝜃𝛽 )(𝑛𝜇 +1)−1 𝑑𝜃𝛼 𝑑𝜃𝛽=0 0which can be solved using Eqn. (13).
Using the above result, Eqn. (17) can be simplified as¯ = 𝛼, 𝐷(𝑁 )) = 𝑁 !(𝑛𝛼 + 1)
ˆ 𝜃)
𝑃 (𝑋(
(𝑁 + 3)!

(18)

Thus, Eqn. (9), can be solved by dividing Eqn. (18) by
Eqn. (16), which gives¯ = 𝛼∣𝐷(𝑁 )) =
ˆ 𝜃)
𝑃 (𝑋(

𝑛𝛼 + 1𝑁 +3(19)¯ = 𝛽∣𝐷(𝑁 )) = 𝑛𝛽 +1 and 𝑃 (𝑋(
¯ =
ˆ 𝜃)
ˆ 𝜃)
Similarly, 𝑃 (𝑋(
𝑁 +3
𝑛𝜇 +1
𝜇∣𝐷(𝑁 )) = 𝑁 +3 . These equations are the expressions forposterior belief of matches, mismatches, and undecided. For
any channel 𝑘, we again use the suffix 𝑘, for example 𝑛𝛼𝑘 .
For simplicity of notations, we rewrite the left hand side of
𝑛 +1
𝑛 +1
Eqn. (20) for channel 𝑘 as 𝑅𝛼𝑘 = 𝑁𝛼𝑘𝑘+3 ; 𝑅𝛽𝑘 = 𝑁𝛽𝑘𝑘+3 ; and𝑛𝜇𝑘 +1𝑅𝜇𝑘 = 𝑁𝑘 +3 respectively. Of course, it can be verified that𝑅𝛼𝑘 + 𝑅𝛽𝑘 + 𝑅𝜇𝑘 = 1 and it satisfies the Cromwell’s rule.
A. Trust Updates

Using the above result, we can write Eqn. (12) as𝐼1¯ = 𝛼∣𝜃)𝑃¯ (𝐷(𝑁 )∣𝜃)𝑑(¯ 𝜃)¯𝑃 (𝑋(𝜃)(16)

A node observes channels over several time slots. Let at any
time 𝑡 the number of matches, mismatches, and undecided forchannel 𝑘 are 𝑛𝛼𝑘 (𝑡), 𝑛𝛽𝑘 (𝑡) and 𝑛𝜇𝑘 (𝑡) respectively. The
total number of neighbors advertising on channel 𝑘 at time 𝑡
is 𝑁𝑘 (𝑡). The time window after which a trust update is mademay vary depending on the user requirement and computational resource availability. The system under question may
have selfish nodes that employ static attacks, where channels
attacked remain the same over time, or a dynamic variation,
where channel sets that are attacked may change with time.
If we assume a dynamic variation of collaborative attack,then channel attacked in previous slot may not be attacked
in subsequent slots, and since channel usage is based on thecurrent spectrum scenario, the weightage to old observations

where 0 < 𝜆 < 1 is a sensitivity factor that determines theextent to which old observations are weighted. 𝑡 = 1 denotes
the oldest observation and 𝑡 = 𝑛 denotes the latest. Smaller
values of 𝜆 implies that old observations have less weight andvice-versa. 𝑅𝛽𝑡𝑛𝑘 and 𝑅𝜇𝑡𝑛𝑘 can be calculated in similar ways
from Eq. (20).
B. Net Trust
To capture the effect of both the updated beliefs for matches
as well as mismatches into a single parameter, we define net
𝑡𝑛
and 𝑅𝛽𝑡𝑛𝑘 . More formally,
trust as the difference between 𝑅𝛼
𝑘
𝑡𝑛
𝑡𝑛
𝑅𝑛𝑒𝑡
= 𝑅𝛼
− 𝑅𝛽𝑡𝑛𝑘
𝑘
𝑘

(21)

𝑡𝑛
Note, the range of 𝑅𝑛𝑒𝑡lies between −1 and 1. We use net𝑘trust to rank channels from the best to worst. The greater theposterior belief for mismatch, the lesser is its net trust. Thisis consistent with the idea that mismatches indicate dishonest
opinions. Hence we expect channels that were attacked to havesignificantly lower trust.

decision on channel 8 can be trusted the most followed by 2
and so on. The strategy for node 12 will be to check whether
channel 8 can be used to communicate with its intended
receiver. If not, it will check channel 2 and so on.
0.8
0.7
Trust Value
0.6

Trust Value of channels

should be minimal. Hence we propose an update model withhigh sensitivity to latest observations and low sensitivity to
old observations. This not only addresses dynamic attacks but
automatically consider static attacks.
We also recommend that the length of the window for atrust update should be small, so as to capture frequent changes
in the attacked channel sets. However, it may also be notedthat frequent changes in collaborative channel sets increase thecost of attack for the adversary. Hence it is unlikely that thechannel sets attacked will be changed on every slot.
Let the current time slot be denoted as 𝑡𝑛 . The updated
belief corresponding to match on a channel 𝑘 at time 𝑡𝑛 is∑𝑛
1 + 𝑡=1 𝜆𝑡𝑛 −𝑡 𝑛𝛼𝑘 (𝑡)𝑡𝑛∑𝑛𝑅 𝛼𝑘 =(20)
3 + 𝑡=1 𝜆𝑡𝑛 −𝑡 𝑁𝑘 (𝑡)

0.5
0.4
0.3
0.2
0.1
0

15 7

5 1

3 9 16 19

8 2 17 14 13 12 4 18 0 6 10 11

−0.1
−0.2

Fig. 2.

Channel preference order by node 12 and 𝜔 = 3.5

B. Channel Preference with more selfish nodes
Now, we set the number of selfish nodes to 60% of the total
number of nodes i.e., 18. In Fig. 3(a), we show the net trust of
the channels sorted in an descending manner as calculated by
the honest node 14. As per most previous works, it is difficult
to distinguish dishonest behavior when the adversary density
is higher than 50% [10]. It is to be noted that node 14 is able
to identify the 9 channels that were attacked inspite of theincreased number of selfish nodes. The trust values for thosechannels are even lower– enabling a better differentiation of
the channels. However, the order is different from what wasobserved by node 12 because of being at a different location.
Fig. 3(b), shows that results hold true for a higher value of𝜔 = 5.0, which is applicable to dense urban scenarios.
0.8

1
Trust Value

0.7
0.8

A. Trust Based Channel Preference
We consider 40% of the nodes as selfish which collaboratively attacked the channels 𝑆 = {1, 3, 5, 7, 9, 11, 15, 16, 19}.
The channels attacked remained static over time. In Fig. 2,
we show the net trust of the channels sorted in an descending
manner as calculated by an honest node 12. As expected, the9 channels that were attacked have significantly lower trust
values than others. For node 12, the best channel is 8 and thesecond best is 2. The worst channel is 19. Therefore, the fused

0.5

Trust Value of Channels

To validate the trust model and to compute the net trust
for each channel, we simulate a distributed network over a3000 × 3000 m grid. 20 primaries are considered; thus 20
channels. We consider a total of 30 (honest and malicious)
mobile secondary nodes. The received power at each receiverdepends on the path loss factor 𝜔 which was varied between 3
and 5. We show the results for different nodes that belong todifferent parts of the network. As for the update periodicity,
we update the beliefs every 3 time slots which we refer to asa window. The sensitivity factor 𝜆 was kept at 0.2.

Trust Value of Channel

0.6
Trust Value of Channels

V. S IMULATION M ODEL AND R ESULTS

0.4
0.3
0.2
0.1
0

0.6

0.4

0.2

0

19 11 7 15 1 16 9 5 3
2 17 8 14 13 4 12 18 0 6 10

11 15 7 1 16 9 5 19 3
8 2 17 14 13 4 12 18 0 6 10

−0.2

−0.1
−0.2

−0.4

(a)

(b)

Fig. 3. Channel preference of node no. 14 with 18 selfish nodes: (a) For
𝜔 = 3.5 (b) For 𝜔 = 5.0

C. Trust propagation under static attacks
In Fig. 4, we observe how trust values evolve over time withthe proposed trust update model for static attacks. It clearly
exhibits the difference between a channel that was attacked
and a channel that was not. We consider two channels: one
from the attacked channel set (i.e., 1) and another from the
non-attacked channel set (i.e., 4). We plot the weighted moving
average of the net trust after every 3 time slots. As time
progresses, we see a clear difference in the trust values forchannels 1 and 4.

1
1
1

Trust Values: Channel 12

0.8

0.8
Trust value of channel

Trust Value

Channel 1: Under Static Attack
Channel 4: No Attack

0.4

0.2

Trust value of channel

Ch 9 Trust

0.6

0.5

0

0.4
0.2
0
−0.2

0
−0.5
0

−0.2

−0.4
0

2

Fig. 4.

4

6
8Time Window Number

10

12

Fig. 6.

Net trust for attacked and not-attacked channels

20

30
40
Time Window

50

60

−0.4
0

10

20

30
40
Time Window

50

60

(b)

Net trust updates for dynamic attacks (a) Channel 12 (b) Channel 9

VI. C ONCLUSIONS

We investigate how the trust values for channels vary withdifferent fractions of selfish nodes. In Fig. 5, we show theaverage trust values for attacked channel set and the nonattacked channel set, for increasing number of attackers. As
expected, there is hardly any change on channels that are notattacked, whereas, the average trust value for the channels
that were attacked decreases. This result is in contrast withthe commonly used voting schemes or Kullback-Leibler divergence based defense models that fail to detect anomaly when
the number of attackers is more than 50%.
0.8
0.7

10

(a)

14

D. Effect of fraction of selfish nodes

Avg Trust for Channels Attacked
Avg Trust for Channels Not Attacked

0.6

Average Trust Value

0.6

0.5
0.4

In this paper, we address the importance of anomalies inadvertised spectrum usage reports that could occur due toattacks by a coalition of selfish nodes Based on observations from the proposed monitoring techique, we presented
a Bayesian inference model that can be used for deciding
how much trustworthy the the collective decision on a channel
is. We test our proposed method under static and dynamic
variants of collaborative SSDF attack; results show that thechannels that were attacked could be quantified based on
the net trust metric. The net trust also allows a node to
select the best channels based on the trustworthiness of thechannel occupancy decision. We show how our model is able
to distinguish among channels even when the population ofselfish nodes is more than 50%– a shortcoming of most voting
or entropy divergence based models.
R EFERENCES

0.3
0.2
0.1
0
−0.1
−0.2
20

Fig. 5.

25

30

35

40
45
50
55
Percentage of Selfish Nodes

60

65

70

Avg. trust with increasing number of selfish nodes

E. Trust variation under dynamic attacks
To prove that our model is able to capture the frequentchanges in the attacked channel set, we vary the attacked
channel set every 10 time slots on an average. We show how
the net trust is updated for two specific channels (12 and 9)
in Fig. 6(a) and Fig. 6(b) respectively. Note, the plots areshown in time windows (3 time slots = 1 window). These
two representative channels were intermittently and randomly
chosen by the coalition of selfish nodes. Trust of channel
12 starts with a high value for 10 time windows, but thenattacked consistently for next 15 windows (i.e., 45 time slots);hence its trust exhibits a steady decrease. After that channel
12, is intermittently chosen for attack, which causes the rapid
fluctuations of the trusts values. Channel 9 is not attacked for
22 windows then attacked for a few windows. Hence, its trust
value is initially high followed by a sudden decrease whichstays unchanged for 4 windows and then increases for theremaining windows.

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