Skip to main content
SpringerLink
Log in

A new computing paradigm for the optimization of parameters in adaptive beamforming using fractional processing

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

The use of fractional calculus based novel adaptive algorithms to solve various applied physics and engineering problems is an emerging area of research. In the present study, the parameter estimation problem in adaptive beamforming is explored through the fractional least mean square (FrLMS) adaptive algorithm. The FrLMS algorithm uses the concept of the fractional order gradient in addition to the standard integer order gradient calculation in the recursive parameter update mechanism of optimization. The unknown parameters of adaptive beamforming networks are effectively estimated using FrLMS for various scenarios based on the number of antenna elements in a uniform linear array, the number of interference signals, the signal to noise ratios (SNRs) as well as fractional orders. A comparative study of the proposed FrLMS with standard LMS for different scenarios of adaptive beamforming shows the quality of the design scheme in terms of accuracy, convergence, robustness and stability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Sun, Y. Liu, H. Li, J. Li, A. Wang, Y. Zhang, Neural Comput. Appl. 30, 2327 (2018)

    Article  Google Scholar 

  2. W. Jin, W. Jia, F. Zhang, M. Yao, Wirel. Pers. Commun. 75, 1447 (2014)

    Article  Google Scholar 

  3. P. Alinezhad, S.R. Seydnejad, Wirel. Pers. Commun. 96, 1131 (2017)

    Article  Google Scholar 

  4. D. Inserra, A.M. Tonello, Training symbol exploitation in CP-OFDM for DoA estimation in multipath channels, in Signal Processing Conference (EUSIPCO), 2013 (IEEE, 2013)

  5. S. Haykin, Array Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, Inc., 1985)

  6. M.A. Gondal, A. Anees, Neural Comput. Appl. 23, 1083 (2013)

    Article  Google Scholar 

  7. Z. Ding, C. Zhong, D.W.K. Ng, M. Peng, H.A. Suraweera, R. Schober, H.V. Poor, IEEE Commun. Mag. 53, 86 (2015)

    Article  Google Scholar 

  8. B.R. Jackson, S. Rajan, B.J. Liao, S. Wang, IEEE Trans. Antennas Propag. 63, 736 (2015)

    Article  ADS  Google Scholar 

  9. M.Z.U. Khan, A.N. Malik, F. Zaman, I.M. Qureshi, Wirel. Pers. Commun. 104, 21 (2018)

    Article  Google Scholar 

  10. A. Senapati, K. Ghatak, J.S. Roy, A Comparative study of adaptive beamforming techniques in smart antenna using LMS algorithm and its variants, in International Conference on Computational Intelligence and Networks (CINE), 2015 (IEEE, 2015) pp. 58--62

  11. F. Zaman, I.M. Qureshi, J.A. Khan, Z.U. Khan, Int. J. Antennas Propag. (2013)

  12. J. Li, P. Stoica, Robust adaptive beamforming, Vol. 88 (John Wiley & Sons, 2005)

  13. L. Landau, R.C. de Lamare, M. Haardt, IET Signal Process. 8, 447 (2014)

    Article  Google Scholar 

  14. P. Saxena, A.G. Kothari, IERI Proc. 10, 131 (2014)

    Article  Google Scholar 

  15. J. Liu, W. Xie, G. Gui, Q. Zhang, Y. Zou, Q. Wan, IET Radar, Sonar Navig. 11, 1831 (2017)

    Article  Google Scholar 

  16. C. Zhou, Y. Gu, S. He, Z. Shi, IEEE Trans. Veh. Technol. 67, 1099 (2018)

    Article  Google Scholar 

  17. Y. Yang, B. Yang, M. Niu, Nonlinear Dyn. 90, 1647 (2017)

    Article  Google Scholar 

  18. N.I. Chaudhary, M.A.Z. Raja, Nonlinear Dyn. 79, 1385 (2015)

    Article  Google Scholar 

  19. N.I. Chaudhary, M.A.Z. Raja, M.S. Aslam, N. Ahmed, Neural Comput. Appl. 29, 41 (2018)

    Article  Google Scholar 

  20. N.I. Chaudhary, M.A. Manzar, M.A.Z. Raja, Neural Comput. Appl. (2018) https://doi.org/10.1007/s00521-018-3362-z

  21. Y. Chen, Q. Gao, Y. Wei, Y. Wang, Appl. Math. Comput. 314, 310 (2017)

    MathSciNet  Google Scholar 

  22. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applications, Vol. 198 (Elsevier, 1998)

  23. J.A.T.M.J. Sabatier, O.P. Agrawal, J.T. Machado (Editors), Advances in Fractional Calculus (Springer, Netherlands, 2007)

  24. J.T. Machado, V. Kiryakova, F. Mainardi, Commun. Nonlinear Sci. Numer. Simul. 16, 1140 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  25. B. Cuahutenango-Barro, M.A. Taneco-Hernández, J.F. Gómez-Aguilar, Eur. Phys. J. Plus 132, 515 (2017)

    Article  Google Scholar 

  26. A. Atangana, Eur. Phys. J. Plus 131, 373 (2016)

    Article  Google Scholar 

  27. Y. Wang, Eur. Phys. J. Plus 133, 481 (2018)

    Article  Google Scholar 

  28. R. Roohi, M.H. Heydari, M. Aslami, M.R. Mahmoudi, Eur. Phys. J. Plus 133, 412 (2018)

    Article  Google Scholar 

  29. V.F. Morales-Delgado, J.F. Gómez-Aguilar, S. Kumar, M.A. Taneco-Hernández, Eur. Phys. J. Plus 133, 200 (2018)

    Article  Google Scholar 

  30. J.F. Gómez-Aguilar, R.F. Escobar-Jiménez, M.G. López-López, V.M. Alvarado-Martínez, Eur. Phys. J. Plus 133, 103 (2018)

    Article  Google Scholar 

  31. D. Baleanu, J.A.T. Machado, A.C. Luo (Editors), Fractional Dynamics and Control (Springer Science & Business Media, 2011)

  32. Z. Li, L. Liu, S. Dehghan, Y. Chen, D. Xue, Int. J. Control 90, 1165 (2017)

    Article  Google Scholar 

  33. C. Yin, X. Huang, Y. Chen, S. Dadras, S.M. Zhong, Y. Cheng, Appl. Math. Model. 44, 705 (2017)

    Article  MathSciNet  Google Scholar 

  34. Q. Yang, Y. Zhang, T. Zhao, Y. Chen, ISA Trans. 82, 163 (2018)

    Article  Google Scholar 

  35. D. Baleanu, Z.B. Güvenç, J.T. Machado (Editors), New Trends in Nanotechnology and Fractional Calculus Applications (Springer, New York, 2010) p. C397

  36. T. Gul, M.A. Khan, A. Khan, M. Shuaib, Eur. Phys. J. Plus 133, 500 (2018)

    Article  Google Scholar 

  37. X.J. Yang, J.T. Machado, C. Cattani, F. Gao, Commun. Nonlinear Sci. Numer. Simul. 47, 200 (2017)

    Article  ADS  Google Scholar 

  38. J.F. Gómez-Aguilar, Eur. Phys. J. Plus 133, 197 (2018)

    Article  Google Scholar 

  39. C. Psychalinos, A.S. Elwakil, A.G. Radwan, K. Biswas, Circuits Syst. Signal Process. 35, 1807 (2016)

    Article  Google Scholar 

  40. K.A. Abro, A.A. Memon, M.A. Uqaili, Eur. Phys. J. Plus 133, 113 (2018)

    Article  Google Scholar 

  41. S. Ullah, M.A. Khan, M. Farooq, Eur. Phys. J. Plus 133, 237 (2018)

    Article  Google Scholar 

  42. C. Ionescu, A. Lopes, D. Copot, J.T. Machado, J.H.T. Bates, Commun. Nonlinear Sci. Numer. Simul. 51, 141 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  43. O.A. Arqub, B. Maayah, Neural Comput. Appl. 29, 1465 (2018)

    Article  Google Scholar 

  44. M. Yavuz, N. Ozdemir, H.M. Baskonus, Eur. Phys. J. Plus 133, 215 (2018)

    Article  Google Scholar 

  45. A. Jafarian, M. Mokhtarpour, D. Baleanu, Neural Comput. Appl. 28, 765 (2017)

    Article  Google Scholar 

  46. M.A.Z. Raja, N.I. Chaudhary, Signal Process. 107, 327 (2015)

    Article  Google Scholar 

  47. N.I. Chaudhary, M.A.Z. Raja, Signal Process. 116, 141 (2015)

    Article  Google Scholar 

  48. S. Cheng, Y. Wei, Y. Chen, Y. Li, Y. Wang, Signal Process. 133, 260 (2017)

    Article  Google Scholar 

  49. S. Cheng, Y. Wei, Y. Chen, S. Liang, Y. Wang, ISA Trans. 67, 67 (2017)

    Article  Google Scholar 

  50. S. Cheng, Y. Wei, Y. Chen, L.I. Xiaojian, Y. Wang, IFAC-PapersOnLine 49, 180 (2016)

    Article  MathSciNet  Google Scholar 

  51. N.I. Chaudhary, M. Ahmed, Z.A. Khan, S. Zubair, M.A.Z. Raja, N. Dedovic, Appl. Math. Model. 55, 698 (2018)

    Article  MathSciNet  Google Scholar 

  52. Z.A. Khan, N.I. Chaudhary, S. Zubair, Electron. Mark. (2018) https://doi.org/10.1007/s12525-018-0297-2

  53. N.I. Chaudhary, M.A.Z. Raja, A.U.R. Khan, Nonlinear Dyn. 82, 1811 (2015)

    Article  Google Scholar 

  54. N.I. Chaudhary, M.S. Aslam, M.A.Z. Raja, IET Signal Process. 11, 975 (2017)

    Article  Google Scholar 

  55. M.S. Aslam, N.I. Chaudhary, M.A.Z. Raja, Nonlinear Dyn. 87, 519 (2017)

    Article  Google Scholar 

  56. N.I. Chaudhary, S. Zubair, M.A.Z. Raja, N. Dedovic, Appl. Math. Model. 66, 457 (2019)

    Article  MathSciNet  Google Scholar 

  57. S.M. Shah, R. Samar, M.A.Z. Raja, Nonlinear Dyn. 92, 1243 (2018)

    Article  Google Scholar 

  58. S.M. Shah, R. Samar, N.M. Khan, M.A.Z. Raja, Nonlinear Dyn. 85, 1363 (2016)

    Article  Google Scholar 

  59. N.I. Chaudhary, S. Zubair, M.A.Z. Raja, ISA Trans. 68, 189 (2017)

    Article  Google Scholar 

  60. S. Zubair, N.I. Chaudhary, Z.A. Khan, W. Wang, Signal Process. 142, 441 (2018)

    Article  Google Scholar 

  61. Z.U. Khan, A.N. Malik, F. Zaman, S.A. Hussain, A.R. Khan, Int. J. Antennas Propag. 2015, 136826 (2015)

    Article  Google Scholar 

  62. F. Zaman, I.M. Qureshi, J.A. Khan, Z.U. Khan, Int. J. Antennas Propag. 2013, 593247 (2013)

    Article  Google Scholar 

  63. Z.U. Khan, A. Naveed, I.M. Qureshi, F. Zaman, IEICE Electron. Express 8, 1008 (2011)

    Article  Google Scholar 

  64. A. Atangana, I. Koca, Chaos Solitons Fractals 89, 447 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  65. A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, arXiv preprint: 1602.03408 (2016)

  66. A. Atangana, Appl. Math. Comput. 273, 948 (2016)

    MathSciNet  Google Scholar 

  67. A. Atangana, D. Baleanu, J. Eng. Mech. 143, D4016005 (2017)

    Article  Google Scholar 

  68. S. Jain, A. Atangana, Int. J. Biomath. 11, 1850100 (2018)

    Article  MathSciNet  Google Scholar 

  69. E.S. Pires, J.T. Machado, P.B. de Moura Oliveira, J.B. Cunha, L. Mendes, Nonlinear Dyn. 61, 295 (2010)

    Article  Google Scholar 

  70. M.S. Couceiro, R.P. Rocha, N.F. Ferreira, J.T. Machado, Signal Image Video Process. 6, 343 (2012)

    Article  Google Scholar 

  71. Y. Mousavi, A. Alfi, Chaos Solitons Fractals 114, 202 (2018)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electronics and Communication, Jiangsu University of Science and Technology, Zhenjiang, China

    Muhammad Asif Zahoor Raja, Rizwan Akhtar & Zhu Zhiyu

  2. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, Pakistan

    Muhammad Asif Zahoor Raja, Qaiser Khan, Ata Ur Rehman & Fawad Zaman

  3. Department of Electrical Engineering, International Islamic University, Islamabad, Pakistan

    Naveed Ishtiaq Chaudhary

Authors
  1. Muhammad Asif Zahoor Raja
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rizwan Akhtar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Naveed Ishtiaq Chaudhary
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhu Zhiyu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Qaiser Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ata Ur Rehman
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Fawad Zaman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rizwan Akhtar.

Additional information

Publisher's Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Raja, M.A.Z., Akhtar, R., Chaudhary, N.I. et al. A new computing paradigm for the optimization of parameters in adaptive beamforming using fractional processing. Eur. Phys. J. Plus 134, 275 (2019). https://doi.org/10.1140/epjp/i2019-12654-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2019-12654-6

Search

Navigation