Abstract
This chapter studies the performance of a wireless sensor network in the context of binary detection of a deterministic signal. The work considers a decentralized organization of spatially distributed sensor nodes, deployed close to the phenomena under monitoring. Each sensor receives a sequence of observations and transmits a summary of its information, over fading channel, to a data gathering node, called fusion center, where a global decision is made. Because of hard energy limitations, the objective is to develop optimal power allocation schemes that minimize the total power spent by the whole sensor network under a desired performance criterion, specified as the detection error probability. The fusion of binary decisions is studied in this chapter by considering two scenarios depending on whether the observations are independent and identically distributed (i.i.d.) or correlated. The present work aims at developing a numerical solution for the optimal power allocation scheme via variations of the biogeography-based optimization algorithm. The proposed algorithms have been tested for several case studies, and their performances are compared with constrained versions of the differential evolution algorithm, the genetic algorithm, and the particle swarm optimization algorithm.
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
Notes
- 1.
The number of sensor nodes and the number of distinct messages are fixed beforehand. This implicitly limits the amount of data available at the fusion center. The quantity of information provided to the fusion center by a network of L sensors, each sending one of D ℓ possible messages, does not exceed \(\sum_{\ell=1}^{L} \lceil\log_{2}(D_{\ell}) \rceil\) bits per channel use [23].
- 2.
In general, Σ v is not a diagonal matrix unless the observation noise is independent and identically distributed (i.i.d.).
- 3.
The assumption that the transmission is idealized, i.e., the information sent from local sensors is assumed to be received intact at the fusion center may be reasonable for some applications, but it may not be realistic for many WSNs where the transmitted information has to endure both channel fading and noise/interference. Acquiring channel state information may be too costly for a resource-constrained sensor network. It may also be impossible to accurately estimate the quality of a fast-changing channel. Hence, it can be argued to be reasonable to assume that this information is available at the fusion center.
- 4.
Correlation degree ρ=1 means that two observations are perfectly correlated. Correlation degree 0<ρ<1 indicates that two observations are partially correlated (i.e., spatial correlation), while ρ=0 implies that two observations are independent of each other.
- 5.
References
Abadir, K., Magnus, J.: Matrix Algebra. Econometric Exercises 1. Cambridge University Press, Cambridge (2005)
Akyildiz, I.F., Su, W., Sankasubramaniam, Y., Cayirci, E.: Wireless sensor networks: a survey. Comput. Netw. 38, 393–422 (2002)
Back, T.: Evolutionary Algorithms in Theory and Practice. Oxford Univ. Press, Oxford (1996)
Boussaïd, I., Chatterjee, A., Siarry, P., Ahmed-Nacer, M.: Hybridizing biogeography-based optimization with differential evolution for optimal power allocation in wireless sensor networks. IEEE Trans. Veh. Technol. 60(5), 28–39 (2011). doi:10.1109/TVT.2011.2151215
Boussaïd, I., Chatterjee, A., Siarry, P., Ahmed-Nacer, M.: Two-stage update biogeography-based optimization using differential evolution algorithm (DBBO). Comput. Oper. Res. 38, 1188–1198 (2011)
Boussaïd, I., Chatterjee, A., Siarry, P., Ahmed-Nacer, M.: Biogeography-based optimization for constrained optimization problems. Comput. Oper. Res. 39, 3293–3304 (2012)
Chamberland, J.F., Veeravalli, V.V.: Decentralized detection in wireless sensor systems with dependent observations. In: International Conference on Computing, Communications and Control Technologies, Austin, TX (2004)
Coello, C.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191(11–12), 1245–1287 (2002)
Deb, K.: An efficient constraint handling method for genetic algorithm. Comput. Methods Appl. Mech. Eng. 186, 311–338 (2000)
Deb, K., Agrawal, R.: Simulated binary crossover for continuous search space. Complex Syst. 9, 115–148 (1995)
Dow, M.: Explicit inverses of Toeplitz and associated matrices. ANZIAM J. 44(E), E185–E215 (2003)
Kay, S.: Fundamentals of Statistical Signal Processing, Vol. 2: Detection Theory. Prentice Hall Signal Processing Series. Prentice Hall, Englewood Cliffs (1998)
Kuhn, H.W.: Nonlinear programming: a historical view. SIGMAP Bull. 31, 6–18 (1982). doi:10.1145/1111278.1111279
Levy, B.C.: Principles of Signal Detection and Parameter Estimation. Springer, Berlin (2008)
MacArthur, R., Wilson, E.: The Theory of Biogeography. Princeton University Press, Princeton (1967)
Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. Evol. Comput. 4(1), 1–32 (1996)
Neyman, J., Pearson, E.S.: On the problem of the most efficient tests of statistical hypotheses. Philos. Trans. R. Soc. Lond. Ser. A 231, 289–337 (1933)
Poor, H.: An Introduction to Signal Detection and Estimation, 2nd edn. Springer Texts in Electrical Engineering. Springer, New York (1998)
Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Natural Computing Series. Springer, Berlin (2005)
Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput. 4, 284–294 (2000)
Simon, D.: Biogeography-based optimization. IEEE Trans. Evol. Comput. 12, 702–713 (2008)
Storn, R.M., Price, K.V.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997)
Swami, A., Zhao, Q., Hong, Y.: Wireless Sensor Networks: Signal Processing and Communications. Wiley, New York (2007)
Tenny, R.R., Sandell, N.R.: Detection with distributed sensors. IEEE Trans. Aerosp. Electron. Syst. 17, 501–510 (1981)
Trees, H.: Detection, Estimation, and Modulation Theory. Wiley-Interscience, New York (1998)
Tsitsiklis, J.: Decentralized detection. Adv. Stat. Signal Process. 2, 297–344 (1993)
Wimalajeewa, T., Jayaweera, S.K.: Optimal power scheduling for correlated data fusion in wireless sensor networks via constrained PSO. Trans. Wirel. Commun. 7(9), 3608–3618 (2008). doi:10.1109/TWC.2008.070386
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Boussaïd, I., Chatterjee, A., Siarry, P., Ahmed-Nacer, M. (2013). A Comparative Study of Modified BBO Variants and Other Metaheuristics for Optimal Power Allocation in Wireless Sensor Networks. In: Chatterjee, A., Nobahari, H., Siarry, P. (eds) Advances in Heuristic Signal Processing and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37880-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-37880-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37879-9
Online ISBN: 978-3-642-37880-5
eBook Packages: Computer ScienceComputer Science (R0)