Handbook of Optimization in Complex Networks pp 219-239 | Cite as
On Throughput Maximization Problem for UWB-Based Sensor Networks via Reformulation–Linearization Technique
Abstract
Nonlinear optimization problems (if not convex) are NP-hard in general. One effective approach to develop efficient solutions for these problems is to apply the branch-and-bound (BB) framework. A key step in BB is to obtain a tight linear relaxation for each nonlinear term. In this chapter, we show how to apply a powerful technique, called Reformulation–Linearization Technique (RLT), for this purpose. We consider a throughput maximization problem for an ultra-wideband (UWB)-based sensor network. Given a set of source sensor nodes in the network with each node generating a certain data rate, we want to determine whether or not it is possible to relay all these rates successfully to the base station. We formulate an optimization problem, with joint consideration of physical layer power control, link layer scheduling, and network layer routing. We show how to solve this nonlinear optimization problem by applying RLT and BB. We also use numerical results to demonstrate the efficacy of the proposed solution.
Preview
Unable to display preview. Download preview PDF.
References
- 1.P. Baldi, L. De Nardis, and M.-G. Di Benedetto, “Modeling and optimization of UWB communication networks through a flexible cost function,” IEEE Journal on Selected Areas in Communications, vol. 20, no. 9, pp. 1733–1744, December 2002.CrossRefGoogle Scholar
- 2.M.S. Bazaraa, H.D. Sherali, and C.M. Shetty, Nonlinear Programming: Theory and Algorithms, second edition, John Wiley & Sons, Inc., New York, NY, 1993.MATHGoogle Scholar
- 3.L.X. Cai, L. Cai, X. Shen, J.W. Mark, and Q. Zhang, “MAC protocol design and optimization for multi-hop ultra-wideband networks,” IEEE Transactions on Wireless Communications, vol. 8, no. 8, pp. 4056–4065, August 2009.CrossRefGoogle Scholar
- 4.F. Cuomo, C. Martello, A. Baiocchi, and F. Capriotti, “Radio resource sharing for ad hoc networking with UWB,” IEEE Journal on Selected Areas in Communications, vol. 20, no. 9, pp. 1722–1732, December 2002.CrossRefGoogle Scholar
- 5.M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness,W. H. Freeman and Company, pp. 245–248, New York, NY, 1979.Google Scholar
- 6.A. Goldsmith and S.B Wicker, “Design challenges for energy-constrained ad hoc wireless networks,” IEEE Wireless Communications, vol. 9, pp. 8–27, August 2002.Google Scholar
- 7.IEEE 802.15 WPAN High Rate Alternative PHY Task Group 3a, http://www.ieee802.org/15/pub/TG3a.html.
- 8.IEEE Journal on Selected Areas in Communications – Special Issue on Ultra-Wideband Radio in Multiaccess Wireless Communications, Guest Editors: N. Blefari-Melazzi, M.G. Di Benedettio, M. Geria, H. Luediger, M.Z. Win, and P. Withington, vol. 20, no. 9, December 2002.Google Scholar
- 9.A. Rajeswaran and R. Negi, “Capacity of ultra wide band wireless ad hoc networks,” IEEE Transactions on Wireless Communications, vol. 6, no. 10, pp. 3816–3824, October 2007.CrossRefGoogle Scholar
- 10.A. Rajeswaran, G. Kim, and R. Negi, “Joint power adaptation, scheduling and routing for ultra wide band networks,” IEEE Transactions on Wireless Communications, vol. 6, no. 5, pp. 1964–1972, May 2007.CrossRefGoogle Scholar
- 11.G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization, John Wiley & Sons, pp. 354–367, New York, NY, 1999.Google Scholar
- 12.R. Pilakkat and L. Jacob, “Scheduling and power control for MAC layer design in multihop IR-UWB networks,” International Journal of Network Management, vol. 20, issue 1, pp. 1–19, January 2010.Google Scholar
- 13.D. Porcino, “Ultra-wideband radio technology: potential and challenges ahead,” IEEE Communications Magazine, pp. 66–74, July 2003.Google Scholar
- 14.R.C. Qiu, H. Liu, and X. Shen, “Ultra-wideband for multiple access communications,” IEEE Communications Magazine, pp. 80–87, February 2005.Google Scholar
- 15.B. Radunovic and J.-Y. Le Boudec, “Optimal power control, scheduling, and routing in UWB networks,” IEEE Journal on Selected Areas in Communications, vol. 22, no. 7, pp. 1252–1270, September 2004.CrossRefGoogle Scholar
- 16.A. Rajeswaran, G. Kim, and R. Negi, “A scheduling framework for UWB & cellular networks,” Springer Mobile Networks and Applications (MONET), vol. 11, no. 1, pp. 9–20, 2006.Google Scholar
- 17.J.H. Reed, An Introduction to Ultra Wideband Communication Systems, Prentice Hall, 2005.Google Scholar
- 18.A. Rubinov and X. Yang, Lagrange-type Functions in Constrained Non-convex Optimization, Kluwer Academic Publishers, Norwell, MA, 2003.MATHGoogle Scholar
- 19.H.D. Sherali and W.P. Adams, A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems, Kluwer Academic Publishers, Dordrecht/Boston/London, Chapter 8, 1999.Google Scholar
- 20.H.D. Sherali, “Tight relaxations for nonconvex optimization problems using the reformulation-linearization/convexification technique (RLT),” Handbook of Global Optimization, Volume 2: Heuristic Approaches, eds. P.M. Pardalos and H.E. Romeijn, Kluwer Academic Publishers, Dordrecht/London/Boston, pp. 1–63, 2002.Google Scholar
- 21.Y. Shi and Y.T. Hou, “On the capacity of UWB-based wireless sensor network,” Elsevier Computer Networks Journal, vol. 52, issue 14, pp. 2797–2804, October 2008.MATHCrossRefGoogle Scholar
- 22.M. Win and R. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications,” IEEE Transactions on Communications, vol. 48, pp. 679–691, April 2000.CrossRefGoogle Scholar