1. On Spectrum Selection Games in Cognitive Radio Networks
Ilaria Malanchini, Matteo Cesana, Nicola Gatti
Dipartimento di Elettronica e Informazione
Politecnico di Milano, Milan, Italy

2. Summary Introduction Spectrum Selection in Cognitive Networks
Cognitive Radio Networks
Goals and Contributions
Spectrum Selection in Cognitive Networks
The static game model
Dynamic spectrum management
Formulation to solve the games
Experimental evaluation
Conclusion and Future Work

3. Cognitive Radio Networks
Cognitive Radio Networks (CRNs) are a viable solution to solve spectrum efficiency problems by an opportunistic access to the licensed bands
The “holes” in the radio spectrum may be exploited for use by wireless users (secondary users) other than the spectrum licensee (primary users)
CRNs are based on cognitive devices which are able to configure their transmission parameters on the fly depending on the surrounding environment

4. Cognitive Capabilities
Secondary users will be able to exploit the spectrum “holes” using the cognitive radio technology, that allows to:
detect unused spectrum portions (spectrum sensing)
characterize them on the basis of several parameters (spectrum decision)
coordinate with other users in the access phase (spectrum sharing)
handover towards other holes when licensed users appear or if a better opportunity becomes available (spectrum mobility)

5. Goals Goals: Evaluation of the spectrum management functionalities
Comparison of different quality measures for the evaluation of the spectrum opportunities
Interaction among secondary users
Analysis of the dynamic evolution of this scenario

6. Contributions Contributions:
Non-cooperative game theoretic framework that accounts for:
availability/quality of the spectrum portions (s. decision)
interference among secondary users (s. sharing)
cost associated to spectrum handover (s. mobility)
Static analysis
Dynamic analysis
We take here a constructive approach by analyzing, at first, a static game in which spectrum mobility is neglected, and secondary users evaluate different spectrum opportunities, considering both the quality-of-service and the corresponding congestion level. Then, we move to a dynamic game formulation which accounts for the temporal evolution of the system, the corresponding time-varying primary users activity, and the costs associated to spectrum mobility. In both cases, we characterize and derive the Nash equilibria of the games, and we thoroughly comment on their quality.

7. Scenario Secondary Interference Range Inactive Primary Secondary Users

8. Spectrum Selection Game Model
SOP1
(W1,T1)
SOP2
(W2,T2)
SOP3
(W3,T3)
Spectrum occupied by primary users
Spectrum opportunities available for secondary users
Players: secondary users
Strategies: available spectrum opportunities (SOPs)
Cost function: we define different cost functions that depend on the number of interferers, the achievable bandwidth and the expected holding time
We consider a scenario composed of primary and secondary users sharing a given portion of the spectrum, which is subdivided into orthogonal channels (sub-bands), throughout the paper referred to as Spectrum OPportunities (SOP) (see Fig. 1). Each primary user is licensed to transmit arbitrarily on a specific sub-band (SOP). Time is divided into epochs which can be defined as the time period where the activity of primary users does not change. Secondary users can opportunistically access SOP which are vacant in a given epoch, with the firm constraint to handover whenever the SOP gets occupied by a licensed primary user.

9. Spectrum Selection Game Model
Spectrum Selection Game (SSG) can be defined:
The generic user i selfishly plays the strategy:
SSG belongs to the class of congestion games
It always admits at least one pure-strategy Nash equilibrium
From this equivalence it directly comes that also our game does admit at least one pure-strategy Nash equilibrium for any cost function ci(k, xki ) that is increasing in the level of the congestion. Therefore, we can safely limit us to search for pure strategy equilibria.
A Nash equilibrium is a set of strategies such that no player has incentive to unilaterally change her action.

10. Static Analysis Interference-based cost function
Linear combination cost function
Product-based cost function
In this section, we consider the static game, representing a single time epoch, in which available spectrum opportunities for each user are a fixed subset of B.
In general, neither of these two cost functions overcomes the other, a priori. In fact, we can observe that the cost function (3), represents the total amount of bandwidth that can be used by each user, defined as: [Bandwidth ・ Time/Interfering Users] whereas cost function (2) does not reflect this property. On the other side, cost function (2) allows users to give a preference between bandwidth and holding time, whereas the other does not.

11. Dynamic Spectrum ManagementB
SOP(T3W3)
SOP(T1W1)
SOP (T2W2) T
Spectrum occupied by primary users
Spectrum opportunities available for secondary users
Primary activity is time-varying
The subset of SOPs available for each user can change
We consider a repeated game

12. The Multi-Stage Game
Time is divided in epochs which can be defined as the time period where primary activity does not change
At each epoch users play the previous game, but using the following cost function:
where K represents the switching cost that a user has to pay if it decides to change the spectrum opportunity
Experimental evaluation aims at comparing the optimal solution and the equilibrium reached by selfish users

13. Solving the games
General model to characterize best/worst Nash equilibria and optimal solution in our congestion game
The following model can be used (and linearized) for each one of the presented cost function
Parameters:
Variables:

14. Solving the games
Constraints:
Objective Function:

15. Experimental Setting 1 2 3 4 5 6 … 18 p q High Holding Time Low HT
Primary Users Activity
Inactive
Active
High Bandwidth
Low Bandwidth
Low/Medium/High activity
(larger p  higher primary activity)
Low/High Opportunity
p>q  low AND p<q  high q

16. Static Evaluation High Bandwidth High Holding Time
Low primary Activity

17. Dynamic Evaluation

18. Conclusion and Future Work
We propose a framework to evaluate spectrum management functionalities in CRN, resorting to a game theoretical approach
This allows a SU to characterize different spectrum opportunities, share available bands with other users and evaluate the possibility to move in a new channel
New simulation scenarios
different kind of users
different available information set/cost functions