Abstract
In this paper, we propose piecewise mixed integer linear programming (PWMIP) models for joint subcarrier and power allocation in downlink wireless orthogonal frequency division multiple access (OFDMA) networks. In particular, we consider the problem of maximizing the total capacity of an OFDMA system subject to user power, subcarrier and quality of service constraints. For this purpose, we model the problem as a (0-1) mixed integer nonlinear programming problem. Then, we obtain two PWMIP models by means of a convex combination approach [17] and with the approach proposed in [21]. The latter consists of reducing the cardinality of a subset of binary variables to a logarithmic number of binary variables. Finally, we propose a variable neighborhood search (VNS) procedure [10, 11]. Our preliminary numerical results indicate that the first model is more effective and that the VNS approach allows to obtain feasible solutions in less computational cost.
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References
Amzallag, D., Armarnik, T., Livschitz, M., Raz, D.: Multi-cell slots allocation in OFDMA systems. In: 16th Mobile and Wireless Communications Summit (IST), pp. 1–5 (2007)
Balas, E.: Projection, lifting and extended formulation in integer and combinatorial optimization. Ann. Oper. Res. 140, 125–161 (2005)
Beale, E., Tomlin, J.: Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. In: Lawrence, J. (ed.) Proceedings of the Fifth International Conference on Operational Research, pp. 447–454. Tavistock Publications, London (1970)
Bixby, R.: Solving Real-World Linear Programs: A Decade and More of Progress. Oper. Res. 50(1), 1–13 (2002)
Cao, Z., Tureli, U., Liu, P.: Optimum subcarrier assignment for OFDMA uplink. In: IEEE International Conference on Communications, pp. 11–15 (2003)
Croxton, K., Gendron, B., Magnanti, T.: Comparison of mixed-integer programming models for nonconvex piecewise linear cost minimization problems. Manage. Sci. 49, 1268–1273 (2003)
Dantzig, G.: Linear programming and extensions. Princeton University Press (1963)
Geiler, B., Martin, A., Morsi, A., Schewe, L.: Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and its Applications, vol. 154, pp. 287–314 (2012)
Gray, F.: Pulse code communication, March 17, 1953 (filed November 1947). U.S. Patent 2,632,058
Hansen, P., Mladenovic, N.: Variable neighborhood search: Principles and applications. Eur. J. Oper. Res. 130, 449–467 (2001)
Hansen, P., Mladenovic, N., Perez Brito, D.: Variable Neighborhood Decomposition Search. J. Heuristics. 7, 335–350 (2001)
Hernández, A., Guio, I., Valdovinos, A.: Interference management through resource allocation in multi-cell OFDMA networks. In: IEEE 69th Vehicular Technology Conference VTC, pp. 1–5 (2009)
Keha, A., de Farias, I., Nemhauser, G.: Models for representing piecewise linear cost functions. Oper. Res. Lett. 32(1), 44–48 (2004)
Markowitz, H., Manne, A.: On the solution of discrete programming-problems. Ecometrica 25, 84–110 (1957)
Padberg M., Rijal, M.: Location, Scheduling, Design and Integer Programming. International Series in Operations Research & Management Science, vol. 3. Springer, Boston (1996)
Shannon, C.E.: A Mathematical Theory of Communication. AT&T Tech. J. 27, 379–423 (1948)
Srikrishna, S., Linderoth, J., Luedtke, J.: Locally ideal formulations for piecewise linear functions with indicator variables. Oper. Res. Lett. 41(6), 627–632 (2013)
Sternad, M., Svensson, T., Ottosson, T., Ahlen, A., Svensson, A., Brunstrom, A.: Towards Systems Beyond 3G Based on Adaptive OFDMA Transmission. Proceedings of the IEEE 95, 2432–2455 (2007)
Venturino, L., Risi, C., Buzzi, S., Zappone, A.: Energy-efficient coordinated user scheduling and power control in downlink multi-cell OFDMA networks. In: IEEE 24th International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), pp. 1655–1659 (2013)
Vielma, J., Ahmed, S., Nemhauser, G.: Mixed-integer models for nonseparable piecewise-linear optimization: unifying framework and extensions. Oper. Res. 58, 303–315 (2009)
Vielma, J., Nemhauser, G.: Modeling disjunctive constraints with a logarithmic number of binary variables and constraints. Math Program 128, 49–72 (2009)
Wong, I., Zukang, C., Evans, B., Andrews, J.: A low complexity algorithm for proportional resource allocation in OFDMA systems. In: IEEE Workshop on Signal Processing Systems, pp. 1–6 (2004)
Yaghoobi, H.: Scalable OFDMA physical layer in IEEE 802.16 WirelessMAN. Intel Technology Journal 8, 201–212 (2004)
Zhaorong, Z., Jianyao, Z., Jingjing, L., Weijiang, L., Yunjie, R.: Resource allocation based on immune algorithm in multi-cell cognitive radio networks with OFDMA. In: Fifth International Conference on Computational and Information Sciences (ICCIS), pp. 1644–1647 (2013)
Zukang, S., Jeffrey, G., Evans, B.: Short range wireless channel prediction using local information, signals, systems and computers. In: Conference Record of the Thirty-Seventh Asilomar Conference, vol. 1, pp. 1147–1151 (2003)
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Adasme, P., Lisser, A. (2015). Piecewise Linear Formulations for Downlink Wireless OFDMA Networks. In: Younas, M., Awan, I., Mecella, M. (eds) Mobile Web and Intelligent Information Systems. MobiWIS 2015. Lecture Notes in Computer Science(), vol 9228. Springer, Cham. https://doi.org/10.1007/978-3-319-23144-0_10
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DOI: https://doi.org/10.1007/978-3-319-23144-0_10
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