Hierarchical Competition for Downlink Power Allocation in OFDMA Femtocell Networks

This paper considers the problem of downlink power allocation in an orthogonal frequency-division multiple access (OFDMA) cellular network with macrocells underlaid with femtocells. The femto-access points (FAPs) and the macro-base stations (MBSs) in the network are assumed to compete with each other to maximize their capacity under power constraints. This competition is captured in the framework of a Stackelberg game with the MBSs as the leaders and the FAPs as the followers. The leaders are assumed to have foresight enough to consider the responses of the followers while formulating their own strategies. The Stackelberg equilibrium is introduced as the solution of the Stackelberg game, and it is shown to exist under some mild assumptions. The game is expressed as a mathematical program with equilibrium constraints (MPEC), and the best response for a one leader-multiple follower game is derived. The best response is also obtained when a quality-of-service constraint is placed on the leader. Orthogonal power allocation between leader and followers is obtained as a special case of this solution under high interference. These results are used to build algorithms to iteratively calculate the Stackelberg equilibrium, and a sufficient condition is given for its convergence. The performance of the system at a Stackelberg equilibrium is found to be much better than that at a Nash equilibrium.

[1]  C.E. Shannon,et al.  Communication in the Presence of Noise , 1949, Proceedings of the IRE.

[2]  Mohammad Kaykobad,et al.  Positive solutions of positive linear systems , 1985 .

[3]  S. Barbarossa,et al.  Asynchronous Iterative Waterfilling for Gaussian Frequency-Selective Interference Channels: A Unified Framework , 2007, 2007 Information Theory and Applications Workshop.

[4]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[5]  Mihaela van der Schaar,et al.  Conjectural Equilibrium in Multiuser Power Control Games , 2009, IEEE Transactions on Signal Processing.

[6]  Mehdi Bennis,et al.  Spectrum sharing games on the interference channel , 2009, 2009 International Conference on Game Theory for Networks.

[7]  J. Goodman.  Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games , 1965 .

[8]  Heechang Kim,et al.  WiMAX femtocells: a perspective on network architecture, capacity, and coverage , 2008, IEEE Communications Magazine.

[9]  Zhi-Quan Luo,et al.  A Stackelberg game approach to distributed spectrum management , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[10]  J. Rabaey,et al.  A Revenue Enhancing Stackelberg Game for Owners in Opportunistic Spectrum Access , 2008, 2008 3rd IEEE Symposium on New Frontiers in Dynamic Spectrum Access Networks.

[11]  Francisco Facchinei,et al.  Distributed Power Allocation With Rate Constraints in Gaussian Parallel Interference Channels , 2007, IEEE Transactions on Information Theory.

[12]  Wei Yu,et al.  Distributed multiuser power control for digital subscriber lines , 2002, IEEE J. Sel. Areas Commun..

[13]  Sudarshan Guruacharya,et al.  Hierarchical Competition in Femtocell-Based Cellular Networks , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[14]  Kenneth W. Shum,et al.  Convergence of Iterative Waterfilling Algorithm for Gaussian Interference Channels , 2007, IEEE Journal on Selected Areas in Communications.

[15]  Guoan Bi,et al.  Distributed optimization for cognitive radio networks using Stackelberg game , 2010, 2010 IEEE International Conference on Communication Systems.

[16]  Ronny Yongho Kim,et al.  WiMAX femtocell: requirements, challenges, and solutions , 2009, IEEE Communications Magazine.

[17]  Qian Zhang,et al.  Stackelberg game for utility-based cooperative cognitiveradio networks , 2009, MobiHoc '09.

[18]  Mihaela van der Schaar,et al.  A new perspective on multi-user power control games in interference channels , 2007, IEEE Transactions on Wireless Communications.

[19]  Wei Yu,et al.  Dual methods for nonconvex spectrum optimization of multicarrier systems , 2006, IEEE Transactions on Communications.

[20]  Sachin Agarwal,et al.  A stackelberg game for pricing uplink power in wide-band cognitive radio networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[21]  W. A. Kirk,et al.  Topics in Metric Fixed Point Theory , 1990 .

[22]  Sergios Theodoridis,et al.  A Novel Efficient Cluster-Based MLSE Equalizer for Satellite Communication Channels with-QAM Signaling , 2006, EURASIP J. Adv. Signal Process..

[23]  Jeffrey G. Andrews,et al.  Femtocell networks: a survey , 2008, IEEE Communications Magazine.

[24]  Dusit Niyato,et al.  Microeconomic Models for Dynamic Spectrum Management in Cognitive Radio Networks , 2007 .

[25]  Mihaela van der Schaar,et al.  Stackelberg Contention Games in Multiuser Networks , 2008, EURASIP J. Adv. Signal Process..

[26]  S. T. Chung,et al.  A game-theoretic approach to power allocation in frequency-selective gaussian interference channels , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[27]  Michael Bloem,et al.  A stackelberg game for power control and channel allocation in cognitive radio networks , 2007, Valuetools 2007.

[28]  Zhi-Quan Luo,et al.  Analysis of Iterative Waterfilling Algorithm for Multiuser Power Control in Digital Subscriber Lines , 2006, EURASIP J. Adv. Signal Process..