Distributed Power Allocation for Multiuser Two-Way Relay Networks Using Stackelberg Game
Fu Jiang, Chaoliang Zhu, Jun Peng,
Yong He, Shuo Li, and Weirong Liu
School of Information Science and Engineering, Central South University, Hunan Engineering Laboratory for Advanced Control and Intelligent Automation, Changsha, Hunan, 410075, China
Recently, two-way relay networks have been regarded as a promising technique that can improve bandwidth utilization. In this paper, the power allocation problem for multiuser two-way relay networks with amplifyand-forward protocol is investigated. In order to describe the self-interestedness of nodes in two-way relay networks, a two-level Stackelberg game is introduced to jointly optimize the benefits of the source pair and the relay nodes, where the relay nodes are modeled as leaders and the source pair is modeled as a follower. To facilitate the power allocation process, a distributed game-theoretic power allocation algorithm is proposed. Then, the existence and optimization of the Stackelberg equilibrium for the proposed power allocation algorithm is proven. The convergence of the presented algorithm is also analyzed by proving that price update is a standard function. Simulation results indicate that the proposed power allocation algorithm can improve energy utilization by jointly optimizing the utilities of both source pair and relay nodes.
-  A. Nosratinia, T. E. Hunter, and A. Hedayat, “Cooperative communication in wireless networks,” IEEE Commun. Mag., Vol.42, No.10, pp. 74- 80, 2004.
-  A. S. Ibrahim, A. K. Sadek, W. F. Su, and K. J. R. Liu, “Cooperative communications with relay-selection: when to cooperate and whom to cooperate with?,” IEEE Trans. Wirel. Commun., Vol.7, No.7, pp. 2814-2827, 2008.
-  T. J. Oechtering and H. Boche, “Bidirectional regenerative halfduplex relaying using relay selection,” IEEE Trans. Wirel. Commun., Vol.7, No.5, pp. 1879-1888, 2008.
-  B. Rankov and A. Wittneben, “Achievable Rate Regions for the Two-way Relay Channel,” Proc. of IEEE Int. Symp. Inf. Theory (ISIT 2006), pp. 1668-1672, 2006.
-  P. Popovski and H. Yomo, “Wireless network coding by amplifyand-forward for bi-directional traffic flows,” IEEE Commun. Lett., Vol.11, No.1, pp. 16-18, 2007.
-  E. Beres and R. Adve, “Selection cooperation in multi-source cooperative networks,” IEEE Trans. Wirel. Commun., Vol.7, No.1, pp. 118-127, 2008.
-  W. Su, A. K. Sadek, and K. J. R. Liu, “Cooperative Communication Protocols in Wireless Networks: Performance Analysis and Optimum Power Allocation,” Wirel. Pers. Commun., Vol.44, No.2, pp. 181-217, 2008.
-  D. Wang, W. Xin, and C. Xiaodong, “Optimal Power Control for Multi-User Relay Networks over Fading Channels,” IEEE Trans. Wirel. Commun., Vol.10, No.1, pp. 199-207, 2011.
-  Z. Yuanyuan, M. Yi, and R. Tafazolli, “Power allocation for bidirectional AF relaying over rayleigh fading channels,” IEEE Commun. Lett., Vol.14, No.2, pp. 145-147, 2010.
-  B. Jiang, F. F. Gao, X. Q. Gao, and A. Nallanathan, “Channel estimation and training design for two-way relay networks with power allocation,” IEEE Trans. Wirel. Commun., Vol.9, No.6, pp. 2022-2032, 2010.
-  V. Havary-Nassab, S. Shahbazpanahi, and A. Grami, “Optimal Distributed Beamforming for Two-Way Relay Networks,” IEEE Trans. Signal Process., Vol.58, No.3, pp. 1238-1250, 2010.
-  X. J. Zhang and Y. Gong, “Adaptive Power Allocation in Two-Way Amplify-and-Forward Relay Networks,” Proc. of IEEE Int. Conf. Commun. (ICC09), pp. 1-5, 2009.
-  R. Shaolei andM. V. Schaar, “Distributed power allocation in multiuser multi-channel cellular relay networks,” IEEE Trans. Wirel. Commun., Vol.9, No.6, pp. 1952-1964, 2010.
-  B. B. Wang, H. Zhu, and K. J. R. Liu, “Distributed Relay Selection and Power Control for Multiuser Cooperative Communication Networks Using Stackelberg Game,” IEEE Trans. Mobile Comput., Vol.8, No.7, pp. 975-990, 2009.
-  R. Yates, “A framework for uplink power control in cellular radio systems,” IEEE J. Sel. Areas Commun., Vol.13, No.7, pp. 1341-1347, 1995.
-  C. U. Saraydar, N. B. Mandayam, and D. J. Goodman, “Efficient Power Control via Pricing inWireless Data Networks,” IEEE Trans. Commun., Vol.50, No.2, pp. 291-303, 2002.