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### Optimal Defense Against Jamming Attacks in Cognitive Radio Networks Using the MarkovDecision Process Approach

Agenda Networks

Agenda Networks

Agenda Networks

Agenda Networks

Agenda Networks

Yongle Wu, Beibei Wang, and K. J. Ray Liu

Presenter:WayneHsiao

Advisor:Frank, Yeong-Sung Lin

Agenda Networks

- Introduction
- RelatedWorks
- SystemModel
- OptimalStrategywithPerfectKnowledge
- MarkovModels
- MarkovDecisionProcess

- LearningtheParameters
- SimulationResults

Agenda Networks

- Introduction
- RelatedWorks
- SystemModel
- OptimalStrategywithPerfectKnowledge
- MarkovModels
- MarkovDecisionProcess

- LearningtheParameters
- SimulationResults

Introduction Networks

- Cognitive radio technology has been receiving a growing attention
- In a cognitive radio network
- Unlicensed users (secondary users)
- Spectrumholders(primaryusers)

- Secondary users usually compete for limited spectrum resources
- Game theory has been widely applied as a flexible and proper tool to model and analyze their behavior in the network

Introduction Networks

- Cognitive radio networks are vulnerable to malicious attacks
- Security countermeasures
- Crucial to the successful deployment of cognitive radio networks

- We mainly focus on the jamming attack
- One of the major threats to cognitive radio networks
- Several malicious attackers intend to interrupt the communications of secondary users by injecting interference

Introduction Networks

- Secondary user could hop across multiple bands in order to reduce the probability of being jammed
- Optimal defense strategy
- Markov decision process (MDP)

- The optimal strategy strikes a balance between the cost associated with hopping and the damage caused by attackers

Introduction Networks

- In order to determine the optimal strategy, the secondary user needs to know some information
- the number of attackers

- Maximum Likelihood Estimation (MLE)
- A learning process in this paper that the secondary user estimates the useful parameters based on past observations

Agenda Networks

- Introduction
- RelatedWorks
- SystemModel
- OptimalStrategywithPerfectKnowledge
- MarkovModels
- MarkovDecisionProcess

- LearningtheParameters
- SimulationResults

Related Networks Works

- The problem becomes more complicated in a cognitive radio network
- Primary users’ access has to be taken into consideration

- We consider the scenario
- Asingle-radio secondary user
- Defense strategy is to hop across different bands

- Introduction
- RelatedWorks
- SystemModel
- OptimalStrategywithPerfectKnowledge
- MarkovModels
- MarkovDecisionProcess

- LearningtheParameters
- SimulationResults

System Networks Model

- A secondary user opportunistically accesses one of the predefined M licensed bands
- Each licensed band is time-slotted
- The access pattern of primary users can be characterized by an ON-OFF model

System Networks Model

- Assume all bands share the same channel model and parameters
- But different bands are used by independent primary users

System Networks Model

- Secondary user has to detect the presence of the primary user at the beginning of each time slot

System Networks Model

- Communication gain R
- When the primary user is absent in that band

- The cost associated with hoppingisC
- We assume there are m (m ≥ 1) malicious single-radio attackers
- Attackers do not want to interfere with primary users
- Because primary users’ usage of spectrum is enforced by their ownership of bands

System Networks Model

- On finding the secondary user
- Attacker will immediately inject jamming power which makes the secondary user fail to decode data packets

- We assume that the secondary user suffers from a significant loss L when jammed
- When all the attackers coordinate to maximize the damage
- they detect m channels in a time slot

System Networks Model

- The longer the secondary user stays in a band, the higher risk to be exposed to attackers
- At the end of each time slot the secondary user decides
- to stay
- to hop

- The secondary user receives an immediate payoff U(n) in the nth time slot

System Networks Model

- 1(.) is an indicator function
- Returning 1 when the statement in the parenthesis holds true
- 0 otherwise

System Networks Model

- Average Payoff Ū
- The secondary user wants to maximize
- Malicious attackers want to minimize

- The discount factor δ (0 < δ < 1) measures how much the secondary user values a future payoff over the current one

- Introduction
- RelatedWorks
- SystemModel
- OptimalStrategywithPerfectKnowledge
- MarkovModels
- MarkovDecisionProcess

- LearningtheParameters
- SimulationResults

Optimal Networks StrategywithPerfectKnowledge

- Attackstrategy
- Attackers coordinately tune their radios randomly to m undetected bands in each time slot
- When either all bands have been sensed or the secondary user has been found and jammed

- The jamming game can be reduced to a Markov decision process
- We first show how to model the scenario as an MDP
- Then solve it using standard approaches

Optimal Networks StrategywithPerfectKnowledge

- At the end of the nth time slot
- The secondary user observes the state of the current time slot S(n)
- And chooses an action a(n)
- Whether to tune the radio to a new band or not, which takes effect at the beginning of the next time slot

- S(n) = P
- The primary user occupied the band inthenthtimeslot

- S(n) = J
- The secondary user was jammedinthenthtimeslot

Optimal Networks StrategywithPerfectKnowledge

- a(n) = h
- The secondary user to hop to a new band

- The secondary user has transmitted a packet successfully in the time slot
- ‘to hop’ (a(n) = h)
- ‘tostay’ (a(n) = s)

- S(n) = K
- This is theKthconsecutiveslotwithsuccessfultransmission in thesameband

Optimal Networks StrategywithPerfectKnowledge

- The immediate payoff depends on both the state and the action
- p(S’|S, h)
- The transition probability from an old state S to a new state S’ when taking the action h

- p(S’|S, s)
- The transition probability from an old state S to a new state S’ when taking the action s

Optimal Networks StrategywithPerfectKnowledge

- If the secondary user hops to a new band, transition probabilities do not depend on the old state
- The only possible new states are
- P (the new band is occupied by the primary user)
- J (transmission in the new band is detected by an attacker)
- 1 (successful transmission begins in the new band)

Optimal Networks StrategywithPerfectKnowledge

- When the total number of bands M is large
- M ≫ 1

- Assume that the probability of primary user’s presence in the new band equalthesteady-stateprobabilityoftheON-OFFmodel
- Neglecting the case that the secondary user hops back to some band in very short time,

Optimal Networks StrategywithPerfectKnowledge

- The secondary user will be jammed with the probability m/M
- Each attacker detects one band without overlapping

- Transition probabilities are

Optimal Networks StrategywithPerfectKnowledge

- Note that s is not a feasible action when the state is in J or P
- At state K, only max(M−Km,0) bands have not been detected by attackers
- But another m bands will be detected in the upcoming time slot
- The probability of jamming conditioned on the absence of primary user

Optimal Networks StrategywithPerfectKnowledge

- To sum up, transition probabilities associated with the action s are as follows: ∀K ∈ {1,2,3,...}

- Introduction
- RelatedWorks
- SystemModel
- OptimalStrategywithPerfectKnowledge
- MarkovModels
- MarkovDecisionProcess

- LearningtheParameters
- SimulationResults

Markov Networks DecisionProcess

- If the secondary user stays in the same band for too long, he/she will eventually be found by an attacker
- p(K + 1|K,s) = 0 if K > M/m − 1

- Therefore, we can limit the state S to a finite set ,where

Markov Networks DecisionProcess

- An MDP consists of four important components
- a finite set of states
- a finite set of actions
- transition probabilities
- immediate payoffs

- The optimal defense strategy can be obtained by solving the MDP

Markov Networks DecisionProcess

- A policy is defined as a mapping from a state to an action
- π : S(n) → a(n)

- A policy π specifies an action π(S) to take whenever the user is in state S
- Among all possible policies, the optimal policy is the one that maximizes the expected discounted payoff

Markov Networks DecisionProcess

- The value of a state S is defined as the highest expected payoff given the MDP starts from state S
- The optimal policy is the optimal defense strategy that the secondary user should adopt since it maximizes the expected payoff

Markov Networks DecisionProcess

- After a first move the remaining part of an optimal policy should still be optimal
- The first move should maximize the sum of immediate payoff and expected payoff conditioned on the currentaction
- Bellman equation

Markov Networks DecisionProcess

- Critical state K*(K∗≤ )
- K∗ can be obtained from solving the MDP, and the optimal strategy becomes

- Introduction
- RelatedWorks
- SystemModel
- OptimalStrategywithPerfectKnowledge
- MarkovModels
- MarkovDecisionProcess

- LearningtheParameters
- SimulationResults

Learning Networks theParameters

- A learning scheme
- Maximum Likelihood Estimation (MLE)

- The secondary user simply sets a value as an initial guess of the optimal critical state K∗
- And follows the strategy (10) with the estimate during the whole learning period

Learning Networks theParameters

- This guess needs not to be accurate
- After the learning period,the secondary user updates the critical state K∗ accordingly.
- F
- Thetotal number of transitions from S to S’ with the action h taken

- T
- T
- t

Learning Networks theParameters

- The likelihood that such a sequence has occurred
- A product over all feasible transition tuples
- (S,a,S’) ∈ {P,J,1,2,3,...,KL + 1}×{s,h}×{P,J,1,2,3,...,KL +1}

- Define
- The following proposition gives the MLE of the parameters β, γ, and ρ

Learning Networks theParameters

- Proposition1: Given ,S ∈and,S∈counted from history of transitions, the MLE of primary users’ parameters are

Learning Networks theParameters

- The MLE of attackers’ parameters ρML is the unique root within an interval (0, 1/(KL + 1)) of the following (KL + 1) order polynomial
- Proof

Learning Networks theParameters

- With transition probabilities specified in (4) – (7)
- The likelihood of observed transitions (11) can be decoupled into a product of three terms Λ = ΛβΛγΛρ

Learning Networks theParameters

- BydifferentiatinglnΛβ,lnΛγ,lnΛρandequatingthemto0
- ObtaintheMLE(12)(13)and(14)

- To ensure that the likelihood is positive, ρ has to lie in the interval (0, 1/(K + 1))
- The left-hand side of equation (14) decreases monotonically and approaches positive infinity as ρ goes to 0
- The right-hand side increases monotonically and approaches positive infinity as ρ goes to 1/(KL + 1)

Learning Networks theParameters

- After the learning period, the secondary user rounds M ·ρML to the nearest integer as an estimation of m
- Calculate the optimal strategy using the MDP approach described in the previous section

- Introduction
- RelatedWorks
- SystemModel
- OptimalStrategywithPerfectKnowledge
- MarkovModels
- MarkovDecisionProcess

- LearningtheParameters
- SimulationResults

Simulation Networks Result

- Communication gain R = 5
- Hopping cost C = 1
- Total number of bands M = 60
- Discount factor δ = 0.95
- Primary users’ access pattern
- β = 0.01, γ = 0.1

Simulation Networks Result

- When the threat from attackers are more stronger the secondary user should proactively hop more frequently
- Toavoid being jammed

Simulation Networks Result

- Always hopping:the secondary user will hop every time slot
- Staying whenever possible:the secondary user will always stay in the band unless the primary user reclaims the band or the band is jammed by attackers.

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