Spectrum auction with interference constraint for cognitive radio networks with multiple primary and secondary users

Extensive research in recent years has shown the benefits of cognitive radio technologies to improve the flexibility and efficiency of spectrum utilization. This new communication paradigm, however, requires a well-designed spectrum allocation mechanism. In this paper, we propose an auction framework for cognitive radio networks to allow unlicensed secondary users (SUs) to share the available spectrum of licensed primary users (PUs) fairly and efficiently, subject to the interference temperature constraint at each PU. To study the competition among SUs, we formulate a non-cooperative multiple-PU multiple-SU auction game and study the structure of the resulting equilibrium by solving a non-continuous two-dimensional optimization problem, including the existence, uniqueness of the equilibrium and the convergence to the equilibrium in the two auctions. A distributed algorithm is developed in which each SU updates its strategy based on local information to converge to the equilibrium. We also analyze the revenue allocation among PUs and propose an algorithm to set the prices under the guideline that the revenue of each PU should be proportional to its resource. We then extend the proposed auction framework to the more challenging scenario with free spectrum bands. We develop an algorithm based on the no-regret learning to reach a correlated equilibrium of the auction game. The proposed algorithm, which can be implemented distributedly based on local observation, is especially suited in decentralized adaptive learning environments as cognitive radio networks. Finally, through numerical experiments, we demonstrate the effectiveness of the proposed auction framework in achieving high efficiency and fairness in spectrum allocation.

1. In our study, we assume that SUs are honest, and indeed make the payments. We do not consider the issue of payment enforcement, which may require a separate mechanism and is beyond the scope of the paper.

2. From the perspective of auction theory, the reserved bid β _n set by PU n can be seen as a bid made by PU n. By bidding β _n , PU n has a way of declaring a reservation value for its spectrum resource and prevents the possibility of the SUs colluding to purchase the resource for an arbitrarily small amount of money.

3. For the sake of simplicity, in case of non-ambiguity, we note S _i ((a ^* _i , b ^* _i ), s _−i ) as a function of s _i , i.e., S _i (s _i ) or S _i (a ^* _i , b ^* _i ).

4. Throughout the paper, the inequality between two vectors is defined as the inequality in all components of the vectors.

5. For the free band, there is no bidding game, or alternatively, we can define a dumb bidding game for the free band, at the NE of which each SU choosing the free band submits 0 as bid and the utility is given by (13).

6. The rationale of the choice is that choosing the furthest PU causes the least interference at the PU.

This work is supported by the project TEROPP (technologies for TERminal in OPPortunistic radio applications) funded by the French National Research Agency (ANR). Part of the work was presented at the 29th IEEE Conference on Computer Communications (IEEE Infocom 2010) [1].

Authors and Affiliations

1. Laboratoire de Recherche en Informatique (LRI), CNRS, University of Paris-Sud XI and INRIA, 91405, Orsay, France

   Lin Chen

2. Department of Computer Science and Networking, TELECOM ParisTech, LTCI CNRS 5141, 46 Rue Barrault, 75013, Paris, France

   Stefano Iellamo, Marceau Coupechoux & Philippe Godlewski

Corresponding author

Correspondence to Lin Chen.

Part of this work is done when Stefano Iellamo was a master student in Department of Electronics and Information, Politecnico di Milano, Piazza L. da Vinci 32, Milan, Italy.

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