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

2/21 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

3/21 IEEE Wireless Regional Area Networks (WRAN)  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

4/21 Problem Definition (A 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

5/21 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.

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

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

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

9/21 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

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

11/21 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

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

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

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

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

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

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

18/21 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).

19/21 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

20/21 Nash Bargaining Solution (NBS) Unique NBS NBS and one of the optimal NE of the non-cooperative game coincides

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