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

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.

[1]  Martin Haardt,et al.  Robust adaptive beamforming algorithms using the constrained constant modulus criterion , 2014, IET Signal Process..

[2]  Henry Cox,et al.  Robust adaptive beamforming , 2005, IEEE Trans. Acoust. Speech Signal Process..

[3]  Yangquan Chen,et al.  Single image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction , 2017, ISA transactions.

[4]  YangQuan Chen,et al.  Fractional-order exponential switching technique to enhance sliding mode control , 2017 .

[5]  Syed Zubair,et al.  A new computing approach for power signal modeling using fractional adaptive algorithms. , 2017, ISA transactions.

[6]  Shibo He,et al.  A Robust and Efficient Algorithm for Coprime Array Adaptive Beamforming , 2017, IEEE Transactions on Vehicular Technology.

[7]  A. Atangana,et al.  Analysis of Lassa hemorrhagic fever model with non-local and non-singular fractional derivatives , 2018, International Journal of Biomathematics.

[8]  Yan Wang,et al.  Dynamic analysis and synchronization of conformable fractional-order chaotic systems , 2018, The European Physical Journal Plus.

[9]  Raja Muhammad Asif Zahoor,et al.  Modified Volterra LMS algorithm to fractional order for identification of Hammerstein non-linear system , 2017, IET Signal Process..

[10]  Raja Muhammad Asif Zahoor,et al.  Fractional Volterra LMS algorithm with application to Hammerstein control autoregressive model identification , 2019, Neural Computing and Applications.

[11]  Syed Muslim Shah,et al.  Fractional-order adaptive signal processing strategies for active noise control systems , 2016 .

[12]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .

[13]  Haci Mehmet Baskonus,et al.  Solutions of partial differential equations using the fractional operator involving Mittag-Leffler kernel , 2018, The European Physical Journal Plus.

[14]  Raja Muhammad Asif Zahoor,et al.  Novel generalization of Volterra LMS algorithm to fractional order with application to system identification , 2018, Neural Computing and Applications.

[15]  Ashwin Kothari,et al.  Performance Analysis of Adaptive Beamforming Algorithms for Smart Antennas , 2014 .

[16]  Yuquan Chen,et al.  Study on fractional order gradient methods , 2017, Appl. Math. Comput..

[17]  Andrea M. Tonello,et al.  Training symbol exploitation in CP-OFDM for DoA estimation in multipath channels , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[18]  Muhammad Saeed Aslam,et al.  A sliding-window approximation-based fractional adaptive strategy for Hammerstein nonlinear ARMAX systems , 2017 .

[19]  Anupama Senapati,et al.  A Comparative Study of Adaptive Beamforming Techniques in Smart Antenna Using LMS Algorithm and Its Variants , 2015, 2015 International Conference on Computational Intelligence and Networks.

[20]  Xiaojian Li,et al.  A Novel Fractional Order Normalized LMS Algorithm with Direction Optimization , 2016 .

[21]  Yikun Yang,et al.  Spline adaptive filter with fractional-order adaptive strategy for nonlinear model identification of magnetostrictive actuator , 2017 .

[22]  Sreeraman Rajan,et al.  Direction of Arrival Estimation Using Directive Antennas in Uniform Circular Arrays , 2015, IEEE Transactions on Antennas and Propagation.

[23]  Omar Abu Arqub,et al.  Solutions of Bagley–Torvik and Painlevé equations of fractional order using iterative reproducing kernel algorithm with error estimates , 2018, Neural Computing and Applications.

[24]  Saeid R. Seydnejad,et al.  Broadband Adaptive Beamforming of Conformal Arrays for Wireless Communications Based on Generalized Sidelobe Canceller , 2017, Wirel. Pers. Commun..

[25]  Muhammad Aslam Uqaili,et al.  A comparative mathematical analysis of RL and RC electrical circuits via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives , 2018 .

[26]  J. F. Gómez-Aguilar,et al.  Analytical solutions of the Keller-Segel chemotaxis model involving fractional operators without singular kernel , 2018 .

[27]  Taza Gul,et al.  Fractional-order three-dimensional thin-film nanofluid flow on an inclined rotating disk , 2018, The European Physical Journal Plus.

[28]  Paulo Moura Oliveira,et al.  Particle swarm optimization with fractional-order velocity , 2010 .

[29]  Yan Li,et al.  An innovative fractional order LMS based on variable initial value and gradient order , 2017, Signal Process..

[30]  Nuno M. Fonseca Ferreira,et al.  Introducing the fractional-order Darwinian PSO , 2012, Signal Image Video Process..

[31]  Raja Muhammad Asif Zahoor,et al.  Two-stage fractional least mean square identification algorithm for parameter estimation of CARMA systems , 2015, Signal Process..

[32]  Lu Liu,et al.  A review and evaluation of numerical tools for fractional calculus and fractional order controls , 2015, Int. J. Control.

[33]  Fawad Zaman,et al.  Sidelobe Suppression with Null Steering by Independent Weight Control , 2015 .

[34]  Ilknur Koca,et al.  Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order , 2016 .

[35]  V. M. Alvarado-Martínez,et al.  Analysis of projectile motion: A comparative study using fractional operators with power law, exponential decay and Mittag-Leffler kernel , 2018 .

[36]  Syed Zubair,et al.  Fractional stochastic gradient descent for recommender systems , 2018, Electronic Markets.

[37]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[38]  A. Atangana,et al.  New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model , 2016, 1602.03408.

[39]  Naveed Ishtiaq Chaudhary,et al.  Identification of Hammerstein nonlinear ARMAX systems using nonlinear adaptive algorithms , 2015 .

[40]  Songsong Cheng,et al.  A universal modified LMS algorithm with iteration order hybrid switching. , 2017, ISA transactions.

[41]  Ijaz Mansoor Qureshi,et al.  Robust LCMV Beamformer for Direction of Arrival Mismatch Without Beam Broadening , 2018, Wirel. Pers. Commun..

[42]  Abdon Atangana,et al.  Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus , 2016 .

[43]  Saif Ullah,et al.  A new fractional model for the dynamics of the hepatitis B virus using the Caputo-Fabrizio derivative , 2018, The European Physical Journal Plus.

[44]  Reza Roohi,et al.  A comprehensive numerical study of space-time fractional bioheat equation using fractional-order Legendre functions , 2018, The European Physical Journal Plus.

[45]  Syed Zubair,et al.  Normalized fractional adaptive methods for nonlinear control autoregressive systems , 2019, Applied Mathematical Modelling.

[46]  J. F. Gómez-Aguilar,et al.  Fundamental solutions to electrical circuits of non-integer order via fractional derivatives with and without singular kernels , 2018 .

[47]  Wei Jin,et al.  A User Parameter-Free Robust Adaptive Beamformer Based on General Linear Combination in Tandem with Steering Vector Estimation , 2014, Wirel. Pers. Commun..

[48]  Alireza Alfi,et al.  Fractional calculus-based firefly algorithm applied to parameter estimation of chaotic systems , 2018, Chaos, Solitons & Fractals.

[49]  Dumitru Baleanu,et al.  Caputo-Fabrizio Derivative Applied to Groundwater Flow within Confined Aquifer , 2017 .

[50]  Ijaz Mansoor Qureshi,et al.  Independent null steering by decoupling complex weights , 2011, IEICE Electron. Express.

[51]  Ahmed S. Elwakil,et al.  Guest Editorial: Fractional-Order Circuits and Systems: Theory, Design, and Applications , 2016, Circuits Syst. Signal Process..

[52]  Naveed Ishtiaq Chaudhary,et al.  Momentum fractional LMS for power signal parameter estimation , 2018, Signal Process..

[53]  Feng Gao,et al.  On a fractal LC-electric circuit modeled by local fractional calculus , 2017, Commun. Nonlinear Sci. Numer. Simul..

[54]  Raja Muhammad Asif Zahoor,et al.  Design of fractional adaptive strategy for input nonlinear Box-Jenkins systems , 2015, Signal Process..

[55]  Han Li,et al.  Power-pattern synthesis for energy beamforming in wireless power transmission , 2017, Neural Computing and Applications.

[56]  Amir Anees,et al.  Analysis of optimized signal processing algorithms for smart antenna system , 2012, Neural Computing and Applications.

[57]  Lu Liu,et al.  A review and evaluation of numerical tools for fractional calculus and fractional order control , 2015, ArXiv.

[58]  J. F. Gómez‐Aguilar,et al.  Application of fractional derivative with exponential law to bi-fractional-order wave equation with frictional memory kernel , 2017 .

[59]  Petre Stoica,et al.  Robust Adaptive Beamforming: Li/Robust Adaptive Beamforming , 2005 .

[60]  A. Luo,et al.  Fractional Dynamics and Control , 2011 .

[61]  Qun Wan,et al.  Adaptive beamforming algorithms with robustness against steering vector mismatch of signals , 2017 .

[62]  Naveed Ishtiaq Chaudhary,et al.  Design of normalized fractional adaptive algorithms for parameter estimation of control autoregressive autoregressive systems , 2018 .

[63]  Junaid Ali Khan,et al.  An Application of Artificial Intelligence for the Joint Estimation of Amplitude and Two-Dimensional Direction of Arrival of Far Field Sources Using 2-L-Shape Array , 2013 .

[64]  Naveed Ishtiaq Chaudhary,et al.  Design of modified fractional adaptive strategies for Hammerstein nonlinear control autoregressive systems , 2015 .

[65]  Caijun Zhong,et al.  Application of smart antenna technologies in simultaneous wireless information and power transfer , 2014, IEEE Communications Magazine.

[66]  Dumitru Baleanu,et al.  Artificial neural network approach for a class of fractional ordinary differential equation , 2016, Neural Computing and Applications.

[67]  Clara-Mihaela Ionescu,et al.  The role of fractional calculus in modeling biological phenomena: A review , 2017, Commun. Nonlinear Sci. Numer. Simul..

[68]  J. A. Tenreiro Machado,et al.  New Trends in Nanotechnology and Fractional Calculus Applications , 2010 .

[69]  Abdon Atangana,et al.  On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation , 2016, Appl. Math. Comput..

[70]  Raza Samar,et al.  Fractional-order algorithms for tracking Rayleigh fading channels , 2018 .

[71]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .