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

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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

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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

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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

BS1 BS2

PU

BS3 BS4

PU

PU

PU

PU PU

PU

PU

PU

PU

BS

Primary Users

Cognitive Radio

Base Station

PU

PU

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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.

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

BS1 BS2

PU

BS3 BS4

PU

PU

PU

PU PU

PU

PU

PU

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 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)

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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 (P1,P2,…,Pm) satisfies the constraint of protecting PUs:

– If not satisfied: power vector is set to zero

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Non-Cooperative Game: NE

• For all channel assignments CH = (ch1,ch2,...chN):

1. If two CRs in one cell have the same channel: drop this assignment, otherwise continue

2. Find power allocation P = (P1,P2,...PN) using IWF:

• for k = 1 : K do

• find all CRs with allocated channel k

• call IWF

3. Check if chi is the best response of CR i for all i:

• If Pi =0 and by changing chi , Pi can be made > 0: chi is not the best response of CR i

• If chi 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

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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

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Many NE

• Number of NE versus number of PUs

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Non-Optimal NE

• Number of supported CRs in NE versus number of PUs

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Protecting PUs

• Maximum total transmit power in NE versus number of PUs

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Convergence of the game

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

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Convergence Time

• Average convergence time versus number of PUs

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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

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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).

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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

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Nash Bargaining Solution (NBS)

• Unique NBS

• NBS and one of the optimal NE of the non-cooperative game coincides

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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