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A Beamformer Design Based on Fibonacci Branch Search

By Tianbao Dong, Haichuan Zhang, and Fangling Zeng
Progress In Electromagnetics Research B, Vol. 88, 73-95, 2020


An approach towards beamforming for a uniform linear array (ULA) based on a novel optimization algorithm, designated as Fibonacci branch search (FBS) is presented in this paper. The proposed FBS search strategy was inspired from Fibonacci sequence principle and uses a fundamental branch structure and interactive searching rules to obtain the global optimal solution in the search space. The structure of FBS is established by two types of multidimensional points on the basis of shortening fraction formed by the Fibonacci sequence, and in this mode, interactive global searching and local optimization rules are implemented alternately to reach global optima, avoiding stagnating in local optimum. At the same time, the rigorous mathematical proof for the accessibility and convergence of FBS towards the global optimum is presented to further verify the validity of our theory and support our claim.Taking advantage of the global search ability and high convergence rate of this technique, a robust adaptive beamformer technique is also constructed here by FBS as a real time implementation to improve the beamforming performance by preventing the loss of optimal trajectory. The performance of the FBS is compared with five typical heuristic optimization algorithms, and the reported simulation results demonstrate the superiority of the proposed FBS algorithm in locating the optimal solution with higher precision and reveal the further improvement in adaptive beamforming performance.


Tianbao Dong, Haichuan Zhang, and Fangling Zeng, "A Beamformer Design Based on Fibonacci Branch Search," Progress In Electromagnetics Research B, Vol. 88, 73-95, 2020.


    1. Huang, X., L. Bai, I. Vinogradov, and E. Peers, "Adaptive beamforming for array signal processing in aeroacoustic measurements," Journal of the Acoustical Society of America, Vol. 131, No. 3, 2152-2161, 2012.

    2. Daneshmand, S., N. Sokhandan, M. Zaeriamirani, and G. Lachapelle, "Precise calibration of a GNSS antenna array for adaptive beamforming applications," Sensors, Vol. 14, No. 6, 9669, 2014.

    3. Leight, J. and B. Toland, "Photonic beamforming technologies for advanced military and commercial SATCOM antennas," Aerospace Conference, 1999.

    4. Zhao, H., B. Lian, and J. Feng, "Space-time adaptive processing for GPS anti-jamming receiver," Physics Procedia, Vol. 33, No. 1, 1060-1067, 2012.

    5. Synnevag, J. F., A. Austeng, and S. Holm, "Adaptive beamforming applied to medical ultrasound imaging," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, Vol. 54, No. 8, 1606-1613, 2007.

    6. Khamy, S. E. E. and A. M. Gaballa, "Adaptive arrays for MC-CDMA using the MSINR guided multimodulus algorithm," 2008 National Radio Science Conference, 2008.

    7. Chen, H. W. and J. W. Zhao, "Wideband MVDR beamforming for acoustic vector sensor linear array," IEE Proceedings — Radar, Sonar and Navigation, Vol. 151, No. 3, 158-162, 2004.

    8. Mu, P., L. Dan, and Q. Yin, "A robust MVDR beamforming based on covariance matrix reconstruction," International Conference on Graphic & Image Processing, 2011.

    9. Sinha, P., A. D. George, and K. Kim, "Parallel algorithms for robust broadband MVDR beamforming," Journal of Computational Acoustics, Vol. 10, No. 1, 69-96, 2002.

    10. Shahbazpanahi, S., A. B. Gershman, and Z.-Q. Luo, "Robust adaptive beamforming using worst-case SINR optimization: A new diagonal loading-type solution for general-rank signal models," Proceedings, IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003.

    11. Mozaffarzadeh, M., A. Mahloojifar, M. Orooji, K. Kratkiewicz, S. Adabi, and M. Nasiriavanaki, "Linear-array photoacoustic imaging using minimum variance-based delay multiply and sum adaptive beamforming algorithm," Journal of Biomedical Optics, Vol. 23, No. 2, 026002, 2018.

    12. Shahab, S. N., A. R. Zainun, H. A. Ali, M. Hojabri, and H. Nurul, "MVDR algorithm based linear antenna array performance assessment for adaptive beamforming application," Journal of Engineering Science and Technology, Vol. 12, No. 5, 1366-1385, 2017.

    13. Wei, C. and Y. Lu, "Adaptive beamforming for arbitrary array by particle swarm optimization," IEEE International Conference on Computational Electromagnetics, 2015.

    14. Vitale, M., G. Vesentini, N. N. Ahmad, and L. Hanzo, "Genetic algorithm assisted adaptive beamforming," Proceedings IEEE 56th Vehicular Technology Conference, 2002.

    15. He, L. and S. Huang, "Modified firefly algorithm based multilevel thresholding for color image segmentation," Neurocomputing, Vol. 240, 152-174, 2017.

    16. Sun, K., S. Mou, J. Qiu, T. Wang, and H. Gao, "Adaptive fuzzy control for non-triangular structural stochastic switched nonlinear systems with full state constraints," IEEE Transactions on Fuzzy Systems, Vol. 27, No. 8, 1587-1601, 2018.

    17. Qiu, J., K. Sun, T. Wang, and H. Gao, "Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance," IEEE Transactions on Fuzzy Systems, Vol. 27, No. 11, 2152-2162, 2019.

    18. Liao, B. and S. C. Chan, "Adaptive beamforming for uniform linear arrays with unknown mutual coupling," IEEE Antennas and Wireless Propagation Letters, Vol. 11, 464-467, 2012.

    19. Etminaniesfahani, A., A. Ghanbarzadeh, and Z. Marashi, "Fibonacci indicator algorithm: A novel tool for complex optimization problems," Engineering Applications of Artificial Intelligence, Vol. 74, 1-9, 2018.

    20. Subasi, M., N. Yildirim, and B. Yildiz, "An improvement on Fibonacci search method in optimization theory," Applied Mathematics and Computation, Vol. 147, 893-901, 2004.

    21. Yildiz, B. and E. Karaduman, "On Fibonacci search method with k-Lucas numbers," Applied Mathematics and Computation, Vol. 143, 523-531, 2003.

    22. Omolehin, J. O., M. A. Ibiejugba, A. E. Onachi, and D. J. Evans, "A Fibonacci Search technique for a class of multivariable functions and ODEs," International Journal of Computer Mathematics, Vol. 82, 1505-1524, 2005.

    23. Ramaprabha, R., M. Balaji, and B. L. Mathur, "Maximum power point tracking of partially shaded solar PV system using modified Fibonacci search method with fuzzy controller," InternationaJournal of Electrical Power & Energy Systems, Vol. 43, 754-765, 2012.

    24. Wang, X., et al., "Cutting parameters multi-scheme optimization based on Fibonacci tree optimization algorithm," Control and Decision, Vol. 33, 1373-1381, 2018.

    25. Kaid Omar, O., F. Debbat, and A. Boudghene Stambouli, "Null steering beamformer using hybrid algorithm based on Honey Bees Mating Optimisation and Tabu Search in adaptive antenna array," Progress In Electromagnetics Research C, Vol. 32, 65-80, 2012.

    26. Ng, C. K. and D. Li, "Test problem generator for unconstrained global optimization," Computers & Operations Research, Vol. 51, No. 51, 338-349, 2014.

    27. Yang, Y. and Y. Shang, "A new filled function method for unconstrained global optimization," Mathematical Problems in Engineering, Vol. 8, No. 1, 501-512, 2010.

    28. Saeed, S., H. C. Ong, and S. Sathasivam, "Self-adaptive single objective hybrid algorithm for unconstrained and constrained test functions: An application of optimization algorithm," Arabian Journal for Science and Engineering, Vol. 44, No. 4, 3497-3513, 2019.

    29. Mallipeddi, R., J. P. Lie, P. N. Suganthan, S. G. Razul, and C. M. S. See, "A differential evolution approach for robust adaptive beamforming based on joint estimation of look direction and array geometry," Progress In Electromagnetics Research, Vol. 119, 381-394, 2011.

    30. Banerjee, S. and V. V. Dwivedi, "Performance analysis of adaptive beamforming using particle swarm optimization," 11th International Conference on Industrial and Information Systems (ICIIS), 242-246, IEEE, 2016.

    31. Ismaiel, A. M., E. Elsaidy, and Y. Albagory, "Performance improvement of high altitude platform using concentric circular antenna array based on particle swarm optimization," AEU --- International Journal of Electronics and Communications, Vol. 91, 85-90, 2018.

    32. Ruchi, R., A. Nandi, and B. Basu, "Design of beam forming network for time-modulated linear array with artificial bees colony algorithm," International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 28, No. 5, 508-521, 2015.

    33. Yeo, B. K. and Y. Lu, "Adaptive array digital beamforming using complex-coded particle swarm optimization-genetic algorithm," Microwave Conference, 2006.