Abstract
In wireless communications, power allocation plays a paramount role in sustainable network lifetime prolongation with quality-of-service and network interference reduction. This paper investigates a distributed power allocation problem in wireless parallel amplify-and-forward (AF) relay transmissions. Particularly, the objective is set to minimize the total transmit power while guaranteeing the signal-to-noise ratio (SNR) requirement at the destination node. The distributed SNR-based power allocation problem is formulated and modeled as a Cournot game. Moreover, a distributed SNR-based power allocation algorithm is proposed to solve the Cournot game. The proposed distributed SNR-based power allocation algorithm is proved to converge to a unique equilibrium. To evaluate the distributed method, a centralized optimal SNR-based power allocation algorithm is also proposed. Numerical results show that the proposed distributed SNR-based power allocation algorithm can achieve comparable performance to the centralized optimal SNR-based power allocation algorithm.
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Xia B., Wang J. (2005) Effect of channel-estimation error on QAM systems with antenna diversity. IEEE Transactions on Communications 53(3): 481–488
Wang X., Wang J. (2004) Effect of imperfect channel estimation on transmit diversity in CDMA systems. IEEE Transactions on Vehicular Technology 53(5): 1400–1412
IEEE 802.16m. (2011). IEEE standard for local and metropolitan area networks-Part 16: Air interface for broadband wireless access systems: Advanced air interface.
3GPP TR 36.813 V0.1.1. (2008). Future advancements for E-UTRA, physical layer aspects.
van der Meulen E. C. (1971) Three-terminal communication channels. Advances in Applied Probability 3(1): 120–154
Cover T. M., Gamal A. A. El. (1979) Capacity theorems for the relay channel. IEEE Transactions on Information Theory IT-25(5): 572–584
Farhadi G., Beaulieu N. (2008) On the ergodic capacity of wireless relaying systems over rayleigh fading channels. IEEE Transactions on Wireless Communications 7(11): 4462–4467
Ding Y., Zhang J. K., Wong K. M. (2009) Ergodic channel capacities for the amplify-and-forward half-duplex cooperative systems. IEEE Transactions on Information Theory 55(2): 713–730
Kwon U.-K., Choi C.-H., Im G.-H. (2009) Full-rate cooperative communications with spatial diversity for half-duplex uplink relay channels. IEEE Transactions on Wireless Communications 8(11): 5449–5454
Zhao X., Wang J.-B., Wang J.-Y., Chen M., Feng M., Sheng M. (2011) System outage probability analysis in unlink multi-hop cellular systems over composite channels. EURASIP Journal on Wireless Communications and Networking 2011(1): 35
Ding Z., Leung K. K., Goeckel D. L., Towsley D. (2009) On the study of network coding with diversity. IEEE Transactions on Wireless Communications 8(3): 1247–1259
Luo J., Blum R. S., Cimini L. J., Greenstein L. J., Haimovich A. M. (2007) Decode-and-forward cooperative diversity with power allocation in wireless networks. IEEE Transactions on Wireless Communications 6(3): 793–799
Ng T. C. -Y., Yu W. (2007) Joint optimization of relay strategies and resource allocations in cooperative cellular networks. IEEE Journal on Selected Areas in Communications 25(2): 328–339
Host-Madsen A., Zhang J. (2005) Capacity bounds and power allocation for wireless relay channels. IEEE Transactions on Information Theory 51(6): 2020–2040
Madan, R., Mehta, N. B., Molisch, A. F., & Zhang, J. (2006). Energy-efficient cooperative relaying over fading channels with simple relay selection. In IEEE Global Telecommnications Conference. San Francisco: IEEE.
Seddik K. G., Sadek A. K., Su W., Liu K. J. R. (2007) Outage analysis and optimal power allocation for multimode relay networks. IEEE Signal Processing Letters 14(6): 377–380
Brown, D. R., III. (2004). Resource allocation for cooperative transmission in wireless networks with orthogonal users. In The 38th Asilomar conference on signals, systems and computers (pp. 1473–1477). California: IEEE.
Cai J., Shen X., Mark Joh. W. (2008) Semi-distributed user relaying algorithm for amplify-and-forward wireless relay networks. IEEE Transactions on Wireless Communications 7(4): 1348–1357
Chen M., Yener A. (2008) Distributed power allocation strategies for parallel relay networks. IEEE Transactions on Wireless Communications 7(2): 552–561
Ma Y., Yi N., Tagazolli R. (2008) Bit and power loading for OFDM-Based three-node relaying communications. IEEE Transactions on Signal Processing 56(7): 3236–3247
Phan, K. T., Le, L. B., Vorobyov, S. A., & Tho, L.-N. (2009). Centralized and distributed power allocation in multi-user wireless relay networks. In IEEE international conference on communications. Dresden: IEEE.
Yu W., Ginis G., Cioffi J. (2002) Distributed multiuser power control for digital subscriber lines. IEEE Journal on Selected Areas in Communications 20(5): 1105–1115
Agustin, A., Munoz, O., & Vidal, J. (2004). A game theoretic approach for cooperative MIMO systems with cellular reuse of the relay slot. In IEEE international conference on acoustics, speech, and signal processing (pp. 581–584). Montreal: IEEE.
Huang J., Han Z., Chiang M., Poor H. V. (2008) Auction-based resource allocation for cooperative communications. IEEE Journal on Selected Areas in Communications 26(7): 1226–1237
Shi Y., Wang J., Letaief K. B., Mallik R. (2009) A game-theoretic approach for distributed power control in interference relay channels. IEEE Transactions on Wireless Communications 8(6): 3151–3161
Ren S., Schaar M. (2010) Distributed power allocation in multi-user multi-channel cellular relay networks. IEEE Transactions on Wireless Communications 9(6): 1952–1964
Wang B., Han Z., Liu K. J. R. (2009) Distributed relay selection and power control for multiuser cooperative communication networks using Stackelberg Game. IEEE Transactions on Mobile Computing 8(7): 975–990
Yu, X., Wu, T., Huang, J., & Wang, Y. (2008). A non-cooperative game approach for distributed power allocation in multi-cell OFDMA-relay networks. In IEEE vehicular technology conference (pp. 1920–1924). Marina Bay: IEEE.
Colander D. C. (2008) Microeconomics (7th ed.). McGraw-Hill, New York
Tirole J. (1998) The theory of industrial organization. MIT Press, Cambridge
Saraydar C. U., Mandayam N. B., Goodman D. J. (2002) Efficient power control via pricing in wireless data networks. IEEE Transactions on Communications 50(2): 291–303
Rosen J. B. (1965) Existence and uniqueness of equilibrium points forconcave N-person Games. Econometrica 33(3): 520–534
Droste E., Hommes E., Tuinstra J. (2002) Endogenous fluctuations under evolutionary pressure in Cournot competition. Games and Economic Behavior 40(2): 232–269
Theocharis R. D. (1960) On the stability of the Cournot solution on the oligopoly problem. Review of Economic Studies 27(2): 133–134
Thorlund-Petersen L. (1990) Iterative computation of Cournot equilibrium. Games and Economic Behavior 2(1): 61–75
Yates R. D. (1995) A framework for uplink power control in cellular radio systems. IEEE Journal on Selected Areas in Communications 13(7): 1341–1347
Press W. H., Flamery B. P., Teukolsky S. A., Vetterling W. T. (1992) Numerical recipes in C. Cambridge University Press, Cambridge
Sundaram R. K. (1996) A first course in optimization theory. Cambridge University Press, Cambridge
UMTS 30. 03. (1998). Annex B: test environments and deployment models.
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Wang, JB., Wang, JY., Song, X. et al. Distributed SNR-Based Power Allocation in Wireless Parallel Amplify-and-Forward Relay Transmissions Using Cournot Game. Wireless Pers Commun 70, 1285–1306 (2013). https://doi.org/10.1007/s11277-012-0747-7
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DOI: https://doi.org/10.1007/s11277-012-0747-7