1. Optimal Defense Against Jamming Attacks in Cognitive Radio Networks Using the Markov Decision Process Approach Presenter: Wayne Hsiao Advisor: Frank, Yeong-Sung Lin Yongle Wu, Beibei Wang, and K. J. Ray Liu

2. Agenda Introduction Related Works System Model Optimal Strategy with Perfect Knowledge o Markov Models o Markov Decision Process Learning the Parameters Simulation Results

3. Agenda Introduction Related Works System Model Optimal Strategy with Perfect Knowledge o Markov Models o Markov Decision Process Learning the Parameters Simulation Results

4. Introduction Cognitive radio technology has been receiving a growing attention In a cognitive radio network o Unlicensed users (secondary users) o Spectrum holders (primary users) Secondary users usually compete for limited spectrum resources o Game theory has been widely applied as a flexible and proper tool to model and analyze their behavior in the network

5. Introduction Cognitive radio networks are vulnerable to malicious attacks Security countermeasures o Crucial to the successful deployment of cognitive radio networks We mainly focus on the jamming attack o One of the major threats to cognitive radio networks o Several malicious attackers intend to interrupt the communications of secondary users by injecting interference

6. Introduction Secondary user could hop across multiple bands in order to reduce the probability of being jammed o Optimal defense strategy o Markov decision process (MDP) The optimal strategy strikes a balance between the cost associated with hopping and the damage caused by attackers

7. Introduction In order to determine the optimal strategy, the secondary user needs to know some information o the number of attackers Maximum Likelihood Estimation (MLE) o A learning process in this paper that the secondary user estimates the useful parameters based on past observations

8. Agenda Introduction Related Works System Model Optimal Strategy with Perfect Knowledge o Markov Models o Markov Decision Process Learning the Parameters Simulation Results

9. Related Works The problem becomes more complicated in a cognitive radio network o Primary users’ access has to be taken into consideration We consider the scenario o A single-radio secondary user o Defense strategy is to hop across different bands

10. Agenda Introduction Related Works System Model Optimal Strategy with Perfect Knowledge o Markov Models o Markov Decision Process Learning the Parameters Simulation Results

11. System 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

12. System Model Assume all bands share the same channel model and parameters But different bands are used by independent primary users

13. System Model Secondary user has to detect the presence of the primary user at the beginning of each time slot

14. System Model Communication gain R o When the primary user is absent in that band The cost associated with hopping is C We assume there are m (m ≥ 1) malicious single-radio attackers Attackers do not want to interfere with primary users o Because primary users’ usage of spectrum is enforced by their ownership of bands

15. System Model On finding the secondary user o 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 o they detect m channels in a time slot

16. System 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 o to stay o to hop The secondary user receives an immediate payoff U(n) in the nth time slot

17. System Model 1(.) is an indicator function o Returning 1 when the statement in the parenthesis holds true o 0 otherwise

18. System Model Average Payoff Ū o The secondary user wants to maximize o 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

19. Agenda Introduction Related Works System Model Optimal Strategy with Perfect Knowledge o Markov Models o Markov Decision Process Learning the Parameters Simulation Results

20. Optimal Strategy with Perfect Knowledge Attack strategy o Attackers coordinately tune their radios randomly to m undetected bands in each time slot o 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 o We first show how to model the scenario as an MDP o Then solve it using standard approaches

21. Optimal Strategy with Perfect Knowledge At the end of the nth time slot o The secondary user observes the state of the current time slot S(n) o 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 o The primary user occupied the band in the nth time slot S(n) = J o The secondary user was jammed in the nth time slot

22. Optimal Strategy with Perfect Knowledge a(n) = h o The secondary user to hop to a new band The secondary user has transmitted a packet successfully in the time slot o ‘to hop’ (a(n) = h) o ‘to stay’ (a(n) = s) S(n) = K o This is the Kth consecutive slot with successful transmission in the same band

23. Optimal Strategy with Perfect Knowledge The immediate payoff depends on both the state and the action p(S’|S, h) o The transition probability from an old state S to a new state S’ when taking the action h p(S’|S, s) o The transition probability from an old state S to a new state S’ when taking the action s

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

25. Optimal Strategy with Perfect Knowledge When the total number of bands M is large o M ≫ 1 Assume that the probability of primary user’s presence in the new band equal the steady-state probability of the ON- OFF model o Neglecting the case that the secondary user hops back to some band in very short time,

26. Optimal Strategy with Perfect Knowledge The secondary user will be jammed with the probability m/M o Each attacker detects one band without overlapping Transition probabilities are

27. Optimal Strategy with Perfect Knowledge 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 o But another m bands will be detected in the upcoming time slot o The probability of jamming conditioned on the absence of primary user

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

29. Agenda Introduction Related Works System Model Optimal Strategy with Perfect Knowledge o Markov Models o Markov Decision Process Learning the Parameters Simulation Results

30. Markov Decision Process If the secondary user stays in the same band for too long, he/she will eventually be found by an attacker o p(K + 1|K,s) = 0 if K > M/m − 1 Therefore, we can limit the state S to a finite set, where

31. Markov Decision Process An MDP consists of four important components o a finite set of states o a finite set of actions o transition probabilities o immediate payoffs The optimal defense strategy can be obtained by solving the MDP

32. Markov Decision Process A policy is defined as a mapping from a state to an action o 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

33. Markov Decision Process 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

34. Markov Decision Process 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 current action o Bellman equation

35. Markov Decision Process Critical state K * (K ∗ ≤ ) K ∗ can be obtained from solving the MDP, and the optimal strategy becomes

36. Agenda Introduction Related Works System Model Optimal Strategy with Perfect Knowledge o Markov Models o Markov Decision Process Learning the Parameters Simulation Results

37. Learning the Parameters A learning scheme o 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

38. Learning the Parameters This guess needs not to be accurate After the learning period, the secondary user updates the critical state K ∗ accordingly. F o The total number of transitions from S to S’ with the action h taken T t

39. Learning the Parameters The likelihood that such a sequence has occurred o A product over all feasible transition tuples o (S,a,S’) ∈ {P,J,1,2,3,...,K L + 1}×{s,h}×{P,J,1,2,3,...,K L +1} Define The following proposition gives the MLE of the parameters β, γ, and ρ

40. Learning the Parameters Proposition1: Given, S ∈ and, S ∈ counted from history of transitions, the MLE of primary users’ parameters are

41. Learning the Parameters The MLE of attackers’ parameters ρ ML is the unique root within an interval (0, 1/(K L + 1)) of the following (K L + 1) order polynomial Proof

42. Learning the Parameters With transition probabilities specified in (4) – (7) The likelihood of observed transitions (11) can be decoupled into a product of three terms Λ = Λ β Λ γ Λ ρ

43. Learning the Parameters By differentiating ln Λ β, ln Λ γ, lnΛ ρ and equating them to 0 o Obtain the MLE (12) (13) and (14) To ensure that the likelihood is positive, ρ has to lie in the interval (0, 1/(K + 1)) o The left-hand side of equation (14) decreases monotonically and approaches positive infinity as ρ goes to 0 o The right-hand side increases monotonically and approaches positive infinity as ρ goes to 1/(K L + 1)

44. Learning the Parameters After the learning period, the secondary user rounds M ·ρ ML to the nearest integer as an estimation of m Calculate the optimal strategy using the MDP approach described in the previous section

45. Agenda Introduction Related Works System Model Optimal Strategy with Perfect Knowledge o Markov Models o Markov Decision Process Learning the Parameters Simulation Results

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

47. Simulation Result When the threat from attackers are more stronger the secondary user should proactively hop more frequently o To avoid being jammed

48. Simulation Result o Always hopping: the secondary user will hop every time slot o 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.