1. Research on cognitive radios Presented by George Fortetsanakis

2. Network paradigm We consider a geographical region Λ, in which a set of service providers P, sell Internet access. – Each provider p ∈ P owns a cellular network consisting of Base station that are located on the sites of a triangular grid. – The Bandwidth of the provider p is distributed among its Base station according to a frequency reuse scheme with factor k p. – The set of all Base stations in the region of interest is denoted by B. The medium access scheme is TDMA – All channels that are available to a Base station are divided into a number of time-frequency slots.

3. Secondary users A set of secondary users U, that are scattered at various locations in the region Λ try to buy Internet access from Base stations in their vicinity. A secondary user can connect to a base station using a unique time-frequency slot.

4. Game-theoretical problem formulation We describe the system as a game in which: – The players are the service providers and the secondary users. – Each service provider can choose among a discrete set of prices S p ={pr 1, pr 2, …, pr N } for the services he offers. – A secondary user can choose to connect to specific base station or not to buy Internet access at all. The set of strategies for a secondary user is denoted by S u = B ∪ {e}. – The strategy e corresponds to the case that a secondary device does not buy Internet access.

5. Channel model The channel gain between a secondary user x ∈ U and a Base station y ∈ B is given by a path loss model. Where – L(x) and L(y) are the locations of x and y respectively. – d 0 is a reference distance. – PL(d 0 ) is the path loss at distance d o from the transmitter. – N is the path loss exponent.

6. Interference power When a secondary user x ∈ U communicates with a Base station y ∈ B we take into consideration the worst case of interference from Base stations that function at the same channels as y. – x and y can communicate only if their distance is lower than the threshold Where: – D p : Distance between y and the closest interfering Base station. – γ: Required SINR for successful communication.

7. Example of a cellular network Red spots: Interfering Base stations. Frequency reuse factor is K p = 7. D p : Distance of closest interferers. : Cell radius.

8. Required transmission power The required transmission power for a secondary user x ∈ U to communicate with a Base station y ∈ B is equal to: Where: – T max : maximum allowable transmission power.

9. Payoff of a secondary user The payoff function of a secondary user x ∈ U is defined as follows: Where: – k: The Base station with which x chooses to connect. – σ(k): The price offered by the Base station y. – : Maximum price that x can tolerate. – τ x : Significance of transmission power for x. – κ x : Significance of price for x.

10. Payoff of a service provider The payoff function of a service provider p ∈ P when he interacts with a secondary user x ∈ U is defined as follows: if BS k belongs to y Where: – σ(p): Price that all the Base stations of the provider p offer. – k: The Base station with which x chooses to connect.

11. Game evolution Each secondary user reconsiders his strategy at time instances that are produced by a Poisson process of mean l u. – At the time instances the secondary user chooses to connect to a Base station that maximizes his payoff function. Each service provider reconsiders his price at time instances that are also produced by a Poisson process of mean l p. – At these time instances a service provider chooses a price that maximizes his payoff. Usually l p << l u.

12. Simulation testbed In a region of 5.4Km x 5.6Km, three cellular networks function that belong to different service providers. 400 secondary users are scattered in this region with a uniform spatial distribution. We study two scenarios: – Scenario a: All secondary users are value transmission power more than price (t x >>k x ). – Scenario b: All secondary users are value price more than transmission power (t x <<k x ).

13. Results of scenario a 1/2

14. Results of scenario a 2/2

15. Results of scenario b 1/2

16. Results of scenario b 2/2