Coalitional Games for Transmitter Cooperation in MIMO Multiple Access Channels

Cooperation between nodes sharing a wireless channel is becoming increasingly necessary to achieve higher throughputs in a wireless network. The problem of determining the feasibility and stability of cooperation between rational nodes in a wireless network is of great importance in understanding cooperative behavior. This paper addresses the stability of the grand coalition of transmitters signaling over a multiple access channel using the framework of cooperative game theory. The external interference experienced by each TX is represented accurately by modeling the cooperation game between the TXs in partition form. Single user decoding and successive interference cancelling strategies are examined at the receiver. Transmitter cooperation is stable, if and only if the core of the game (the set of all divisions of grand coalition utility such that no coalition deviates) is nonempty. Determining the stability of cooperation is a co-NP-complete problem in general. For a single user decoding receiver, transmitter cooperation is shown to be stable at both high and low SNRs, while for an interference cancelling receiver with a fixed decoding order, cooperation is stable only at low SNRs and unstable at high SNR. When time sharing is allowed between decoding orders, it is shown using an approximate lower bound to the utility function that TX cooperation is also stable at high SNRs. Thus, this paper demonstrates that ideal zero cost TX cooperation over a MAC is stable and improves achievable rates for each individual user.

[1]  W. Lucas,et al.  N‐person games in partition function form , 1963 .

[2]  Wei Yu,et al.  Iterative water-filling for Gaussian vector multiple-access channels , 2001, IEEE Transactions on Information Theory.

[3]  Luigi Palopoli,et al.  On the Complexity of the Core over Coalition Structures , 2011, IJCAI.

[4]  Zhu Han,et al.  Coalitional game theory for communication networks , 2009, IEEE Signal Processing Magazine.

[5]  W. Lucas.  Solutions for Four-Person Games in Partition Function Form , 1965 .

[6]  Mai H. Vu.  The Capacity of MIMO Channels with Per-Antenna Power Constraint , 2011, ArXiv.

[7]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[8]  Hesham El Gamal,et al.  The Water-Filling Game in Fading Multiple-Access Channels , 2005, IEEE Transactions on Information Theory.

[9]  U. Mitra,et al.  Stability of transmitter cooperation over a multiple access channel , 2012, 2012 International Conference on Signal Processing and Communications (SPCOM).

[10]  Dong In Kim,et al.  Game Theoretic Approaches for Multiple Access in Wireless Networks: A Survey , 2011, IEEE Communications Surveys & Tutorials.

[11]  Eitan Altman,et al.  A Bayesian Game-Theoretic Approach for Distributed Resource Allocation in Fading Multiple Access Channels , 2010, EURASIP J. Wirel. Commun. Netw..

[12]  Walid Saad,et al.  Author manuscript, published in "IEEE Transactions on Wireless Communications (2009) Saad-ITransW-2009" A Distributed Coalition Formation Framework for Fair User Cooperation in Wireless Networks , 2022 .

[13]  Richard J. La,et al.  DIMACS Series in Discrete Mathematics and Theoretical Computer Science A Game-theoretic Look at the Gaussian Multiaccess Channel , 2022 .

[14]  Massimo Franceschetti,et al.  Cooperation in multi-access networks via coalitional game theory , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[15]  Vincent Conitzer,et al.  Complexity of constructing solutions in the core based on synergies among coalitions , 2006, Artif. Intell..

[16]  E. Larsson,et al.  Game theory and the flat-fading gaussian interference channel , 2009, IEEE Signal Processing Magazine.

[17]  Elza Erkip,et al.  User cooperation diversity. Part I. System description , 2003, IEEE Trans. Commun..

[18]  Mérouane Debbah,et al.  Power allocation games in wireless networks of multi-antenna terminals , 2010, Telecommun. Syst..

[19]  S. Lasaulce,et al.  Methodologies for analyzing equilibria in wireless games , 2009, IEEE Signal Process. Mag..

[20]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[21]  Seung-Jean Kim,et al.  On the Convexity of log det (I + K X^{-1}) , 2006, ArXiv.

[22]  Mokshay M. Madiman,et al.  Cores of Cooperative Games in Information Theory , 2008, EURASIP J. Wirel. Commun. Netw..

[23]  Urbashi Mitra,et al.  Capacity of ad-hoc networks with node cooperation , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[24]  Isa Emin Hafalir,et al.  Efficiency in coalition games with externalities , 2007, Games Econ. Behav..

[25]  Aris L. Moustakas,et al.  Distributed Learning Policies forPower Allocation in Multiple Access Channels , 2012, IEEE J. Sel. Areas Commun..

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

[27]  Aris L. Moustakas,et al.  Dynamic power allocation games in parallel multiple access channels , 2010, VALUETOOLS.

[28]  Narayan B. Mandayam,et al.  Coalitions in Cooperative Wireless Networks , 2008, IEEE Journal on Selected Areas in Communications.

[29]  Urbashi Mitra,et al.  Coalition games for transmitter cooperation in wireless networks , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.