Abstract
In this paper, an energy efficiency (EE) game in a MIMO multiple access channel (MAC) communication system is considered. The existence and the uniqueness of the Nash Equilibrium (NE) is affirmed. A bisection search algorithm is designed to find this unique NE. Despite being sub-optimal for deploying the \(\varepsilon \)-approximate NE of the game when the number of antennas in transmitter is unequal to receiver’s, the policy found by the proposed algorithm is shown to be more efficient than the classical allocation techniques. Moreover, compared to the general algorithm based on fractional programming technique, our proposed algorithm is easier to implement. Simulation shows that even the policy found by proposed algorithm is not the NE of the game, the deviation w.r.t. to the exact NE is small and the resulted policy actually Pareto-dominates the unique NE of the game at least for 2-user situation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The generalized inequality for matrix defined here is referred to its diagonal and takes the non-negative orthant as the underlying cone.
References
Zappone, A., Björnson, E., Sanguinetti, L., Jorswieck, E.: Globally optimal energy-efficient power control and receiver design in wireless networks. IEEE Trans. Sig. Process. 65, 2844–2859 (2017)
Zappone, A., Jorswieck, E.: Energy efficiency in wireless networks via fractional programming theory. Found. Trends® Commun. Inf. Theory 11(3–4), 185–396 (2015)
Zappone, A., Chong, Z., Jorswieck, E.: Energy-aware competitive power control in relay-assisted interference wireless networks. IEEE Trans. Wirel. Commun. 12, 1860–1871 (2013)
Zhang, C., Lasaulce, S., Agrawal, A., Visoz, R.: Distributed power control with partial channel state information: performance characterization and design. IEEE Trans. Veh. Technol. 68(9), 8982–8994 (2019)
Belmega, E.V., Lasaulce, S.: Energy-efficient precoding for multiple-antenna terminals. IEEE Trans. Sig. Process. 59(1), 329–340 (2011)
Saraydar, C.U., Mandayam, N.B., Goodman, D.J.: Pricing and power control in a multicell wireless data network. IEEE J. Sel. Areas Commun. 19(10), 1883–1892 (2001)
Debreu, G.: A social equilibrium existence theorem. Natl. Acad. Sci. 38, 886–893 (1952)
Dinkelbach, W.: On nonlinear fractional programming. Manag. Sci. 13(7), 492–498 (1967)
Varma, V., Lasaulce, S., Debbah, M., Elayoubi, S.: An energy efficient framework for the analysis of MIMO slow fading channels. IEEE Trans. Sig. Process. 61(10), 2647–2659 (2013)
Raghavendra, P.S., Daneshrad, B.: An energy-efficient water-filling algorithm for OFDM systems. In: 2010 IEEE International Conference on Communications (ICC), pp. 1–5, May 2010
Richter, F., Fehske, A.J., Fettweis, G.: Energy efficiency aspects of base station deployment strategies for cellular network. In: IEEE Proceedings of VTC, Fall 2009
Ng, D.W.K., Lo, E.S., Schober, R.: Energy-efficient resource allocation in multi-cell OFDMA systems with limited backhaul capacity. IEEE Trans. Wirel. Commun. 11(10), 3618–3631 (2012)
He, S., Huang, Y., Jin, S., Yang, L.: Coordinated beamforming for energy efficient transmission in multicell multiuser systems. IEEE Trans. Commun. 61(12), 4961–4971 (2013)
Venturino, L., Zappone, A., Risi, C., Buzzi, S.: Energy-efficient scheduling and power allocation in downlink OFDMA networks with base station coordination. IEEE Trans. Wirel. Commun. 14(1), 1–14 (2015)
Du, B., Pan, C., Zhang, W., Chen, M.: Distributed energy-efficient power optimization for CoMP systems with max-min fairness. IEEE Commun. Lett. 18(6), 999–1002 (2014)
Daskalakis, C., Goldberg, P.W., Papadimitriou, C.H.: The complexity of computing a Nash equilibrium. SIAM J. Comput. 39(3), 195–259 (2009)
Nash, J.: Equilibrium points in n-person game. Proc. Natl. Acad. Sci. 36(1), 48–49 (1950)
Belmega, E.V., Lasaulce, S., Debbah, M.: Power allocation games for MIMO multiple access channels with coordination. IEEE Trans. Wirel. Commun. 8(6), 3182–3192 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Zou, H., Zhang, C., Lasaulce, S., Saludjian, L., Panciatici, P. (2020). Energy-Efficient MIMO Multiuser Systems: Nash Equilibrium Analysis. In: Habachi, O., Meghdadi, V., Sabir, E., Cances, JP. (eds) Ubiquitous Networking. UNet 2019. Lecture Notes in Computer Science(), vol 12293. Springer, Cham. https://doi.org/10.1007/978-3-030-58008-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-58008-7_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-58007-0
Online ISBN: 978-3-030-58008-7
eBook Packages: Computer ScienceComputer Science (R0)