Efficient combination policies for diffusion adaptive networks

  • Jie Wang
  • Fei Dai
  • Jie Yang
  • Guan GuiEmail author


Diffusion adaptive networks (DANs) have many applications such as signal processing, mobile wireless sensor network and the internet of things (IoT). Unlike the classical centralized networks, a DAN uses the information exchange among local neighbors to solve global problems. The performance of the DAN highly depends on the combination matrix policies, which raises the issue of the optimal selection of the combination matrix. However, traditional combination policies focus on either the steady-state error or the convergence speed. Inspired by the solution of minimizing the mean square deviation (MSD) of the DAN, this paper proposes two efficient adaptive combination policies: 1) relative-instantaneous-error combination policy and 2) relative-deviation combination policy. These two policies are related to the inverse of noise by different metrics. Computer simulations verify that the proposed combination policies outperform the existing combination rules in either steady-state error or convergence rate in various noise environments. Finally, we apply the two combined rules to the collaborative target-tracking problem and achieve expected results.


Combination policy Collaborative target tracking Diffusion adaptive network Signal processing Internet of things (IoT) 



This work was funded by the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, National Natural Science Foundation of China Grants (No. 61701258, No. 61501223), Jiangsu Specially Appointed Professor Program (No. RK002STP16001), Summit of the Six Top Talents Program of Jiangsu (No. XYDXX-010), Program for High-Level Entrepreneurial and Innovative Talents Introduction (No. CZ0010617002), NJUPTSF (No. NY215026) and 1311 Talent Plan of NJUPT.


  1. 1.
    Tu S, Sayed AH (2011) Mobile adaptive networks. IEEE J Sel Top Signal Process 5(4):649–664Google Scholar
  2. 2.
    Cattivelli FS, Sayed AH (2011) Modeling bird flight formations using diffusion adaptation. IEEE Trans Signal Process 59(5):2038–2051MathSciNetzbMATHGoogle Scholar
  3. 3.
    Wan L, Han G, Zhang D, Li A, Feng N (2017) Distributed DOA estimation for arbitrary topology structure of mobile wireless sensor network using cognitive radio. Wirel Pers Commun 93(2):431–445Google Scholar
  4. 4.
    Wan L, Han G, Jiang J, Rodrigues J, Feng N, Zhu T (2017) DOA estimation for coherently distributed sources considering circular and noncircular signals in massive MIMO systems. IEEE Syst J 11(1):41–49Google Scholar
  5. 5.
    Wan L, Han G, Shu L, Feng N, Zhu C, Lloret J (2015) Distributed parameter estimation for mobile wireless sensor network based on cloud computing in battlefield surveillance system. IEEE Access 3:1729–1739Google Scholar
  6. 6.
    Teng H, et al. (2018) Adaptive transmission range based topology control scheme for fast and reliable data collection. Wirel Commun Mob Comput 2018:1–21Google Scholar
  7. 7.
    Liu M, Song T, Gui G (2018) Deep cognitive perspective: resource allocation for NOMA based heterogeneous IoT with imperfect SIC. IEEE Internet Things J, 1–11.
  8. 8.
    Liu M, Yang J, Song T, Hu J, Gui G (2019) Deep learning-inspired message passing algorithm for efficient resource allocation in cognitive radio networks. IEEE Trans Veh Technol 68(1):641–653. Google Scholar
  9. 9.
    Lv S, Lu Y, Dong M, Wang X, Dou Y, Zhuang W (2017) Qualitative action recognition by wireless radio signals in human-machine systems. IEEE Trans Human-Machine Syst 47(6):789–800Google Scholar
  10. 10.
    Lu Y, Cheng C, Yang J, Gui G (2019) Improved hybrid precoding scheme for MmWave large-scale MIMO systems. IEEE Access 7(1):12027–12034. Google Scholar
  11. 11.
    Huang H, Xia W, Xiong J, Yang J, Zheng G, Zhu X (2019) Unsupervised learning based fast beamforming design for downlink MIMO. IEEE Access 7 (1):7599–7605. Google Scholar
  12. 12.
    Pan J, Yin Y, Xiong J, Wang L, Gui G, Sari H (2018) Deep learning-based unmanned surveillance systems for observing water levels. IEEE Access 6(1):73561–73571Google Scholar
  13. 13.
    Xiong J, Long X, Shi R, Wang M, Yang J, Gui G (2018) Background error propagation model based RDO in HEVC for surveillance and conference video coding. IEEE Access 6(1):67206–67216Google Scholar
  14. 14.
    Zhou T, Yang S, Wang L, Yao J, Gui G (2018) Improved cross-label suppression dictionary learning for face recognition. IEEE Access 6(1):48716–48725Google Scholar
  15. 15.
    Chen L, Ho Y, Lee H, Wu H, Liu H (2017) An open framework for participatory PM2. 5 monitoring in smart cities. IEEE Access 5:14441–14454Google Scholar
  16. 16.
    Tao M, Ota K, Dong M (2018) Locating compromised data sources in IoT-enabled smart cities: a great-alternative-region-based approach. IEEE Trans Ind Informatics 14(6):2579–2587Google Scholar
  17. 17.
    Tao M, Ota K, Dong M (2017) Ontology-based data semantic management and application in IoT- and cloud-enabled smart homes. Futur Gener Comput Syst 76:528–539Google Scholar
  18. 18.
    Li D, Dong M, Yuan Y, Chen J, Ota K, Tang Y (2018) SEER-MCache: a prefetchable memory object caching system for IoT real-time data processing. IEEE Internet Things J 5(5):3648–3660Google Scholar
  19. 19.
    Wang J, Fan S, Yang J, Xiong J, Gui G (2017) Reconsider the sparsity-induced least mean square algorithms on channel estimation. In: International wireless internet conference (WiCON), pp 85–102Google Scholar
  20. 20.
    Wang J, Yang J, Xiong J, Sari H, Gui G (2018) SHAFA: sparse hybrid adaptive filtering algorithm to estimate channels in various SNR environments. IET Commun 12(16):1963–1967Google Scholar
  21. 21.
    Nedic A, Ozdaglar A (2009) Distributed subgradient methods for multi-agent optimization. IEEE Trans Automat Contr 54(1):48–61MathSciNetzbMATHGoogle Scholar
  22. 22.
    Kar S, Moura JMF (2009) Distributed consensus algorithms in sensor networks with imperfect communication?: link failures and channel noise. IEEE Trans Signal Process 57(1):355–369MathSciNetzbMATHGoogle Scholar
  23. 23.
    Srivastava K, Nedic A (2011) Distributed asynchronous constrained stochastic optimization. IEEE J Sel Top Signal Process 5(4):772–790Google Scholar
  24. 24.
    Rabbat MG, Nowak RD (2005) Quantized incremental algorithms for distributed optimization. IEEE J Sel Areas Commun 23(4):798–808Google Scholar
  25. 25.
    Lopes CG, Sayed AH (2007) Incremental adaptive strategies over distributed networks. IEEE Trans Signal Process 55(8):4064–4077MathSciNetzbMATHGoogle Scholar
  26. 26.
    Chen J, Richard C, Hero AO, Sayed AH (2014) Diffusion LMS for multitask problems with overlapping hypothesis subspaces. In: IEEE international workshop on machine learning for signal processing, pp 1–6Google Scholar
  27. 27.
    Sayed AH (2014) Adaptive networks. Proc IEEE 102(4):460–497Google Scholar
  28. 28.
    Sayed AH, Tu S, Chen J, Zhao X, Towfic Z (2013) Diffusion strategies for adaptation and learning over networks: an examination of distributed strategies and network behavior. IEEE Signal Process Mag 30(3):155–171Google Scholar
  29. 29.
    Sayed AH (2013) Diffusion adaptation over networks. Acad Press Libr Signal Process 61:1419–1433zbMATHGoogle Scholar
  30. 30.
    Chen J, Sayed AH (2012) Diffusion adaptation strategies for distributed optimization and learning over networks. IEEE Trans Signal Process 60(8):4289–4305MathSciNetzbMATHGoogle Scholar
  31. 31.
    Sayed AH (2014) Adaptation, learning, and optimization over networks. Found Trends Mach Learn 7(4–5):1–501zbMATHGoogle Scholar
  32. 32.
    Tu S, Member S, Sayed AH (2012) Diffusion strategies outperform consensus strategies for distributed estimation over adaptive networks. IEEE Trans Signal Process 60(12):6217–6234MathSciNetzbMATHGoogle Scholar
  33. 33.
    Zhao X, Sayed AH (2012) Performance limits for distributed estimation over LMS adaptive networks. IEEE Trans Signal Process 60(10):5107–5124MathSciNetzbMATHGoogle Scholar
  34. 34.
    Blondel VD, Hendrickx JM, Olshevsky A, Tsitsiklis JN (2005) Convergence in multiagent coordination, consensus, and flocking. In: Proceedings of the 44th IEEE conference on decision and control, and the European control conference, pp 2996–3000Google Scholar
  35. 35.
    Xiao L, Boyd S (2003) Fast linear iterations for distributed averaging. In: IEEE conference on decision and control, pp 65–78Google Scholar
  36. 36.
    Scherber DS, Papadopoulos HC (2004) Locally constructed algorithms for distributed computations in ad-hoc networks. In: Information processing in sensor networks (IPSN), pp 11–19Google Scholar
  37. 37.
    Xiao L, Boyd S, Lall S (2005) A scheme for robust distributed sensor fusion based on average consensus. Inf Process Sensor Netw, 63–70Google Scholar
  38. 38.
    Cattivelli FS, Lopes CG, Sayed AH (2008) Diffusion recursive least-squares for distributed estimation over adaptive networks. IEEE Trans Signal Process 56(5):1865–1877MathSciNetzbMATHGoogle Scholar
  39. 39.
    Cattivelli FS, Sayed AH (2010) Diffusion LMS strategies for distributed estimation. IEEE Trans Signal Process 58(3):1035–1048MathSciNetzbMATHGoogle Scholar
  40. 40.
    Takahashi N, Yamada I, Sayed AH (2010) Diffusion least-mean squares with adaptive combiners: formulation and performance analysis. IEEE Trans Signal Process 58(7):4795–4810MathSciNetzbMATHGoogle Scholar
  41. 41.
    Tu S, Sayed AH (2011) Optimal combination rules for adaptation and learning over networks. In: IEEE international workshop on computational advances in multi-sensor adaptive processing (CAMSAP), pp 317–320Google Scholar
  42. 42.
    Yu C-K, Sayed AH (2013) A strategy for adjusting combination weights over adaptive networks. In: IEEE international conference on acoustics, speech and signal processing (ICASSP), pp 4579–4583Google Scholar
  43. 43.
    Wagner KT, Doroslovacki MI (2014) Combination coefficients for fastest convergence of distributed LMS estination. In: IEEE international conference on acoustic, speech and signal processing (ICASSP), pp 7218–7222Google Scholar
  44. 44.
    Fernandez-Bes J, Arenas-Garca J, Silva Magno TM, Azpicueta-Ruiz LA (2017) Adaptive diffusion schemes for heterogeneous networks. IEEE Trans Signal Proecessing 65(21):5661–5674MathSciNetGoogle Scholar
  45. 45.
    Chen J, Richard C, Sayed AH (2015) Diffusion LMS over multitask networks. IEEE Trans Signal Process 63(11):2733–2748MathSciNetzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information and Telecommunication EngineeringNanjing University of Posts and TelecommunicationsNanjingChina

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