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

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

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

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)

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

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.

Scenario Secondary Interference Range Inactive Primary Secondary Users

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.

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.

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.

Dynamic Spectrum Management B 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

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

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:

Solving the games Constraints: Objective Function:

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

Static Evaluation High Bandwidth High Holding Time Low primary Activity

Dynamic Evaluation

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