On the Effects of Flat Fading Channels on the Steady-State Performance of Diffusion Adaptive Networks

Document Type : Original Article

Authors

1 Department of Electrical Engineering, University of Malayer

2 Faculty of Electrical and Computer Engineering, University of Tabriz

Abstract

Adaptive networks are known as powerful solution for distributed estimation problems. It is shown in available works that, under the ideal link condition, diffusion adaptive networks are efficient solutions for distributed estimation. However, ideal link is not a practical assumption for many applications. Thus, this paper aims to study the steady-state performance of diffusion adaptive networks with flat fading channels. Using the energy conservation argument, we derive closed-form expressions for EMSE and MSD metrics. We also derive the required bound (in terms of the step size parameter) for stability of diffusion adaptive network with fading links. Our analysis shows that in this condition, steady-state curves are not monotonic increasing functions of step size. We provide simulation results to support the analysis.

Keywords


[1]D. Estrin, G. Pottie, and M. Srivastava, “Intrumenting the world with wireless sensor setworks,” in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), Salt Lake City, UT, pp. 20332036, 2001.
[2]A. H. Sayed, Adaptive networks,”Proceedings of the IEEE, vol. 102, no. 4, pp. 460-497, 2014.
[3]J. Li and A. H. Sayed, Modeling bee swarming behavior through diffusion adaptation with asymmetric information sharing,”EURASIP Journal on Advances in Signal Processing, 2012:18, doi:10.1186/1687-6180-2012-18, 2012.
[4]F. Cattivelli and A. H. Sayed, Modeling bird flight formations using diffusion adaptation,”IEEE Transactions on Signal Processing, vol. 59, no. 5, pp. 2038-2051, 2011.
[5]J. Chen, X. Zhao, and A. H. Sayed, Bacterial motility via diffusion adaptation,”Proc. 44th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, pp. 1930-1934, 2010.
[6]K. Eftaxias, S. Sanei, and A. H. Sayed, Modeling brain cortical connectivity using diffusion adaptation,”' in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), pp. 959-962, 2013.
[7]A. Khalili, A. Rastegarnia, M. K. Islam, and Z. Yang, “A bio-inspired cooperative algorithm for distributedsource localization with mobile nodes,”in Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 35153518, 2013.
[8]P. Di Lorenzo, S. Barbarossa, and A. H. Sayed, Distributed spectrum estimation for small cell networks based on sparse diffusion adaptation,”IEEE Signal Processing Letters, vol. 20, no. 12, pp. 1261-1265, 2013.
[9]H.Nosrati,M.Taheri, M.Shamsi, MH.Sedaaghi,Adaptive power spectral estimation using distributed wireless sensor networks,”9th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP), Manchester, pp. 128 133, 2014.
[10]C. G. Lopes and A. H. Sayed, “Incremental adaptive strategies over distributed networks,” IEEE Transactions on Signal Processing, vol. 55, no. 8, pp. 40644077,2007.
[11]M. Saeed and A. U. H. Sheikh, “A new LMS strategy for sparse estimation in adaptive networks,” in Proc 23rd International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), pp. 17221733, 2012.
[12]M. S. E. Abadi and A.-R. Danaee, “Low computational complexity family of affine projection algorithms over adaptive distributed incremental networks,” AEU -International Journal of Electronics and Communications, vol. 68, no. 2, pp. 97 110, 2014.
[13]A. Khalili, A. Rastegarnia, W. Bazzi, and Z. Yang, “Derivation and analysis of incremental augmented complex least mean square algorithm,” IET Signal Processing, vol. 9, no. 4, pp. 312319, 2015.
[14]C. G. Lopes and A. H. Sayed, “Diffusion least-mean squares over adaptivenetworks: Formulation and performance analysis,” IEEE Trans. on Signal Process., vol. 56, no. 7, pp. 31223136, 2008.
[15]O. Gharehshiran, V. Krishnamurthy, and G. Yin, “Distributed energy-aware diffusion least mean squares: Game-theoretic learning,” IEEE Journal of Selected Topics in Signal Processing, vol. 7, no. 5, pp. 821836, 2013.
[16]X. Zhao and A. H. Sayed, ``Distributed clustering and learning over networks,'' IEEE Trans. Signal Process.,”vol. 63, no. 13, pp. 3285-3300, 2015.
[17]P. Di Lorenzo and S. Barbarossa, “Distributed least mean squares strategies for sparsity-aware estimation over gaussian markov random fields,” in Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on, pp. 54725476, 2014.
[18]R. Arablouei, S. Werner, Y.-F. Huang, and K. Dogancay, Distributed least mean-square estimation with partial diffusion,”IEEE Transactions on Signal Processing, vol. 62, pp. 472-42014.
[19]M. O. Sayin and S. S. Kozat, Single bit and reduced dimension diffusion strategies over distributed networks,”IEEE Signal Processing Letters, vol. 20, pp. 976-979, 2013.
[20]J. Chen, C. Richard, and A. H. Sayed, Diffusion LMS over multitask networks,”IEEE Transactions on Signal Processing, vol. 63, no. 11, pp. 2733-2748, 2015.
[21]A. Khalili, M.A.Tinati, A. Rastegarnia, Performance analysis of distributed incremental LMS algorithm with noisy links,”InternationalJournal of DistributedSensorNetworks, vol. 2011, pp. 110, 2011.
[22]A. Khalili, M.A., Tinati, A.Rastegarnia, Steady-state analysis of incremental LMS adaptive networks with noisy links,”IEEE Transactions on Signal Processing, vol. 59, no.5, pp. 24162421, 2011.
[23]A. Khalili, M.A.Tinati, A. Rastegarnia, J.A. ChambersTransient analysis of diffusion least-mean squares adaptive networks with noisy channels,”InternationalJournal of Adaptive Control and Signal Processing, vol. 26, no. 2, pp. 171180, 2011.
[24]A. Khalili, M.A. Tinati, A. Rastegarnia, J.A. Chambers,Steady-state analysis of diffusion LMS adaptive networks with noisy links,”IEEE Transactions on Signal Processing, vol. 60, no. 2, pp. 974979, 2012.
[25]X. Zhao, S. Tu, A. H.Sayed, Diffusion adaptation over networks under imperfect information exchange and non-stationary data,”IEEE Transactions on Signal Processing, vol. 60, no. 7, pp. 34603475, 2012.
[26]A Khalili, A Rastegarnia, WM Bazzi, Z Yang, Diffusion adaptive networks with imperfect communications: link failure and channel noise,”IET Signal Processing, vol. 8, no. 1, pp. 5966, 2014.
[27]R. Abdolee and B. Champagne, Diffusion LMS algorithms for sensor networksover non-ideal inter-sensor wireless channels,” in Proc. Int. Conf. Distributed Comput. Sens. Syst. Workshops, pp. 1-6, 2011
[28]M. K. Banavar, C. Tepedelenlioglu, and A. Spanias, Performance of distributed estimation over multiple access fading channels with partial feedback,” in Proc. Int. Conf. Acoust., Speech Signal Process. (ICASSP), pp. 22532256, 2008.
[29]S. Cui, J. Xiao, A. Goldsmith, Z.-Q. Luo, and H. V. Poor, Estimation diversity and energy efficiency in distributed sensing,” IEEE Transactions on Signal Processing, vol. 55, no. 9, pp. 46834695, 2007.
[30]A. Ribeiro and G. B. Giannakis, “Bandwidth-constrained distributed estimation for wireless sensor networksPart I: Gaussian case,” IEEE Transactions on Signal Processing, vol. 54, no. 3, pp. 11311143, 2006.
[31]C. Tepedelenlioglu, M. K. Banavar, and A. Spanias, “Asymptotic analysis of distributed estimation over fading multilple access channels,” in Proc. 41st Asilomar Conf. Signals, Syst. Comput., pp. 21402144, 2007.
[32]A. Khalili, A. Rastegarnia, and S. Sanei, “Performance analysis of incremental LMS over flat fading channels”, to be published in IEEE Transactions on Control of Network Systems, D2016, OI. 10.1109/TCNS.2016.2516826.