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

2. 2/21 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. 3/21 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. 4/21 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 BS1BS2 PU BS3BS4 PU BS Primary Users Cognitive Radio Base Station PU

5. 5/21 Problem Definition (Cont.) Objective: maximize the number of supported CRs Under 2 Requirements: –R 1 : At each CR, the received SINR must be above a threshold. –R 2 : Total interference caused by all BSs to each PU must not exceed a threshold.

6. 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 1.Initialization: power vector is set to 0 2.Inner loop (iteration): –BS 1 finds P 1 (only noise floor) –BS 2 finds P 2 (noise floor, interference produced by BS 1) –… –BS m finds P m (noise floor, interference produced by BS 1,2,..,m-1) 7/21

8. IWF (cont.) 3.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 4.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 5.Check if (P 1,P 2,…,P m ) satisfies the constraint of protecting PUs: –If not satisfied: power vector is set to zero 8/21

9. 9/21 Non-Cooperative Game: NE For all channel assignments CH = (ch 1,ch 2,...ch N ): 1.If two CRs in one cell have the same channel: drop this assignment, otherwise continue 2.Find power allocation P = (P 1,P 2,...P N ) using IWF: for k = 1 : K do find all CRs with allocated channel k call IWF 3.Check if ch i is the best response of CR i for all i: If P i =0 and by changing ch i, P i can be made > 0: ch i is not the best response of CR i If ch i is the best response of CR i for all i: CH is a NE

10. Non-Cooperative Game 1.Counter = 0 2.Each BS assigns channels to its CRs uniformly at random 3.BSs find the corresponding power vector 4.If this channel/power assignment is a NE: Return this NE; break 5.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 10/21

11. 11/21 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 P max = 50mW

12. 12/21 Many NE Number of NE versus number of PUs

13. 13/21 Non-Optimal NE Number of supported CRs in NE versus number of PUs

14. 14/21 Protecting PUs Maximum total transmit power in NE versus number of PUs

15. 15/21 Convergence of the game Percentage of times the game converges versus number of PUs (Max number of iterations = 100)

16. 16/21 Convergence Time Average convergence time versus number of PUs

17. 17/21 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. 18/21 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) is obtained 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. 19/21 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. 20/21 Nash Bargaining Solution (NBS) Unique NBS NBS and one of the optimal NE of the non-cooperative game coincides

21. 21/21 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