Downlink Channel Assignment and Power Control in Cognitive Radio Networks Using Game Theory

1. Downlink Channel Assignment and Power Control in Cognitive Radio Networks Using Game Theory Ghazale Hosseinabadi Tutor: Hossein Manshaei January, 29th, 2008 Security and Cooperation in Wireless Networks

2. Next Generation Wireless Networks • Current spectrum allocation is inefficient • Dynamic or opportunistic access • Next Generation networks: • Cognitive Radio (CR) • Opportunistic access to the licensed bands without interfering with the existing users

3. IEEE 802.22 Wireless Regional Area Networks (WRAN) 802.22 Network Architecture: Primary networks: UHF and VHF TV channels Secondary Networks: CR: sense the spectrum Base Station: manages the spectrum and provides service to CRs Our Goal: Evaluate the interaction between primary and secondary users using game theory CR

4. PU PU PU PU PU PU PU PU PU Problem Definition (A 802.22 Scenario) • Multiple cells • Each cell: one BS and a set of CRs • Single or multiple primary users • FDMA • BS needs exactly one channel to support each CR PU BS1 BS2 Primary Users PU PU Cognitive Radio Base Station BS3 BS4 BS

5. Problem Definition (Cont.) • Objective: maximize the number of supported CRs • Under 2 Requirements: • R1: At each CR, the received SINR must be above a threshold. • R2 : Total interference caused by all BSs to each PU must not exceed a threshold.

6. PU BS1 BS2 PU PU PU PU BS3 BS4 PU PU PU PU Game Model • Players: BSs • Strategies: channel and power selection • Utility: number of supported CRs • Constraints: • All PUs must be protected • SINR of all CRs must be above the threshold

7. Iterative Water Filling (IWF) • Distributed method for power allocation • m BSs transmitting toward m CRs • Initialization: power vector is set to 0 • Inner loop (iteration): • BS 1 finds P1 (only noise floor) • BS 2 finds P2(noise floor, interference produced by BS 1) • … • BS m finds Pm(noise floor, interference produced by BS 1,2,..,m-1)

8. IWF (cont.) • Outer loop: power vector is adjusted: • If of any CR is greater than the power of its BS is decreased • If of any CR is less than the power of its BS is increased • Confirmation step: • If the target SINR of all CRs are satisfied, go to 5. • Otherwise, go back to 2: • Each BS considers the noise floor and the interference produced by all other BSs • Check if (P1,P2,…,Pm) satisfies the constraint of protecting PUs: • If not satisfied: power vector is set to zero

9. Non-Cooperative Game: NE • For all channel assignments CH = (ch1,ch2,...chN): • If two CRs in one cell have the same channel: drop this assignment, otherwise continue • Find power allocation P = (P1,P2,...PN)using IWF: • for k = 1 : K do • find all CRs with allocated channel k • call IWF • Check if chiis the best response of CR ifor all i: • If Pi =0 and by changing chi , Pi can be made > 0: chi is not the best response of CR i • If chiis the best response of CR i for all i: CH is a NE

10. Non-Cooperative Game • Counter = 0 • Each BS assigns channels to its CRs uniformly at random • BSs find the corresponding power vector • If this channel/power assignment is a NE: Return this NE; break • While counter < max_counter: • For i = 1 : N do • counter = counter + 1 • BS supporting CR i assigns the next channel to it • BSs find the corresponding power vector • If this channel/power assignment is a NE: return this NE; break • end for • end while

11. Simulation • 4 cells • Number of CRs: N = 6 • Number of PUs: M = 1-5 • Number of channels: K = 4 • Path-loss exponent = 4 • Maximum interference to each PU = -110 dBm • N0 = -100 dBm • Required SINR = 15 dB • Pmax = 50mW

12. Many NE • Number of NE versus number of PUs

13. Non-Optimal NE • Number of supported CRs in NE versus number of PUs

14. Protecting PUs • Maximum total transmit power in NE versus number of PUs

15. Convergence of the game • Percentage of times the game converges versus number of PUs (Max number of iterations = 100)

16. Convergence Time • Average convergence time versus number of PUs

17. Cooperative Game: Nash Bargaining • N players • S: set of possible joint strategies • Nash Bargaining: a method for players to negotiate on which point of S they will agree • U: multiuser utility function • d: disagreement point • B = (U,d): a bargaining problem

18. Nash Bargaining (cont.) • A function is called the Nash Bargaining function if it satisfies: • Linearity: if we perform the same linear transformation on the utilities of all players then the solution is transformed accordingly. • Independence of irrelevant alternatives: if the bargaining solution of a large game (T,d) isobtained in a small set S, then the bargaining solution assigns the same solution to the smaller game, i.e. the irrelevant alternatives in T\S do not affect the outcome of the bargaining. • Symmetry: If two players are identical then renaming them will not change the outcome. • Pareto optimality: If s is the outcome of the bargaining, then no other state t exists such that U(s) < U(t).

19. Nash Bargaining (cont.) • Nash proved that there exists a unique function satisfying these 4 axioms: • Nash Bargaining Solution (NBS): • s: Unique solution of the bargaining problem

20. Nash Bargaining Solution (NBS) • Unique NBS • NBS and one of the optimal NE of the non-cooperative game coincides

21. Conclusion • Channel assignment/power control problem in a cognitive radio network • IWF: distributed power allocation • Non-cooperative game: non-convergence or many undesirable NE • To enhance the performances: Nash bargaining solution is used