Document Type : Article

**Authors**

Department of Electronics and Communication Engineering, NIT Durgapur, West Bengal, India, 713209

**Abstract**

Abstract – This paper proposes a fundamental approach for radiation pattern correction of the mutually coupled circular dipole antenna array (CDAA) using parametric assimilation technique. The effect of mutual coupling is an indispensable part of any practical design issue of the antenna array. Many analytical and numerical techniques have been put forward in the past few decades for the calculation, compensation and reduction of mutual coupling effect. This paper shows an accurate method for mutual coupling correction by using a recently proposed technique called parametric assimilation technique, where the values of mutual impedance are calculated and assimilated with the values of the desired radiation pattern. The proposed technique is cost-effective, less complicated and easy to implement while achieves better performance for mutually coupled circular dipole antenna array synthesis. Grey Wolf Optimization (GWO) algorithm is a state-of-the-art stochastic algorithm applied here to find the optimal values of the current excitation weights and the inter-element spacing between each element of the CDAA for the desired, uncorrected and corrected far-field radiation pattern synthesis. PSO and DE optimization-based statistical results are also reported to compare the results obtained by using GWO algorithm to confirm the outstanding performance of GWO algorithm based design.

**Keywords**

References:

[1] Ballanis, C.A. “Antenna Theory Analysis and Design”, 2nd Edition, John Willey and Son’s Inc, New York (1997).

[2] Elliott, R. S. “Antenna Theory and Design”, Revised Edition, John Willey, NJ (2003).

[3] Collin, R. E. “Antenna and radio wave propagation”, McGraw-Hill, New York (1985).

[4] Sharaqa, A. and Dib, N. “Circular Antenna Array Synthesis Using Firefly Algorithm”, International Journal of RF and Microwave Computer-Aided Engineering, 24(2), pp. 139-146 (2014).

[5] Das, A., Mandal, D. and Ghoshal, S. P., et. al. “Moth flame optimization-based design of linear and circular antenna array for sidelobe reduction”, International Journal of Numerical Modelling, 32(1), pp. 1-15 (2018).

[6] Das, A., Mandal, D. and Ghoshal, S. P., et. al. “A Heuristic Approach to Design Linear and Circular Antenna Array for Side Lobe Reduction”, Iranian Journal of Science and Technology Transaction of Electrical Engineering, 43(1), pp. 67-76 (2018).

[7] Singh, U. and Kamal, T. S. “Design of non-uniform circular antenna arrays using biogeography-based optimization”, IET Microwaves Antennas and Propagation, 5(11), pp. 1365-1370 (2011).

[8] Guney, K. and Basbug, S. “A parallel implementation of seeker optimization algorithm for designing circular and concentric circular antenna arrays”, Applied Soft Computing, 22, pp. 287–296 (2014).

[9] Rattan, M., Patterh, M. S. and Sohi, B. S. “Optimization of circular antenna arrays of isotropic radiators using simulated annealing”, International Journal of Microwave and Wireless Technologies, 1(5), pp. 441-446 (2009).

[10] Shihab, M., Najjar, Y. and Khodier, NDM. “Design of non-uniform circular antenna arrays using particle swarm optimization”, Journal of Electrical Engineering, 59(4), pp. 216–220 (2008).

[11] Chakravorty, P. and Mandal, D. “Radiation Pattern Correction in Mutually Coupled Antenna Arrays Using Parametric Assimilation Technique”, IEEE Transactions On Antennas And Propagation, 64(9), pp. 4092-4095 (2016).

[12] Das, A., Mandal, D. and Ghoshal, S. P., et. al. “An efficient side lobe reduction technique considering mutual coupling effect in linear array antenna using BAT algorithm”, Swarm and Evolutionary Computation, 35, pp. 26–40 (2017).

[13] Singh, H., Sneha, H. L. and Jha, R. M. “Mutual Coupling in Phased Arrays: A Review”, International Journal of Antennas and Propagation, 2013, pp.1-23 (2013).

[14] Gupta, I. J. and Ksienski, A. A. “Effect of Mutual Coupling on the Performance of Adaptive Arrays”, IEEE Transactions On Antennas And Propagation, 31(5), pp. 785-791 (1983).

[15] Salonen, I., Toropainen, A. and Vainikainen, P. “Linear pattern correction in a small microstrip antenna array”, IEEE Transactions on Antennas Propagation, 52, pp. 578 – 586 (2004).

[16] Kang, Y. W. and Pozar, D. M. “Correction of Error in Reduced Sidelobe Synthesis due to Mutual Coupling” IEEE Transaction On Antennas and Propagation, 33(9), pp.1025-1028 (1985).

[17] Kelley, D. F. and Stutzman, W. L. “Array Antenna Pattern Modeling Methods that Include Mutual Coupling Effects”, IEEE Transactions on Antennas And Propagation, 41(12), pp. 1625-1632 (1993).

[18] Kennedy, J. and Eberhart, R. “Particle swarm optimization”, Proceeding of IEEE International Conference On Neural Network, 4, pp. 1942-1948 (1995).

[19] Eberhart, R. and Shi, Y. “Comparison between genetic algorithm and particle swarm optimization”, in Evolutionary Programming VII, Springer, pp. 611-616 (1998).

[20] Robinson, J. and Rahmat-Samii, Y. “Particle Swarm Optimization in Electromagnetics”, IEEE Transaction on Antenna Propagation, 52 (2) pp. 397-407 (2004).

[21] Storn, R. and Price, K. “Differential evolution- a simple and efficient adaptive scheme for global optimization over continuous spaces”, Technical Report, International Computer science Institute, Berkley (1995).

[22] Karaboga, N. “Digital IIR filter design using differential evolution algorithm”, EURASIP Journal on Applied Signal Processing, 2005, Article ID. 8, pp.1269-1276 (2005).

[23] Mirjalili, S., Mirjalili, S.M., Lewis, A. “Grey Wolf Optimizer”, Advances in Engineering Software, 69, pp. 46-61 (2014).

[24] Saxena, P. and Kothari, A. “Optimal Pattern Synthesis of Linear Antenna Array Using Grey Wolf Optimization Algorithm”, International Journal of Antennas and Propagation, 2016, Article ID 1205970 (2016).

[25] Das, A., Mandal, D. and Ghoshal, S.P., et. al., “Concentric circular antenna array synthesis for sidelobe suppression using moth flame optimization”, International Journal of Electronics and Communication (AEU), 86, pp. 177-184 (2018).

[26] Das, A., Mandal, D. and Kar, R. “An Optimal Far-Field Radiation Pattern Synthesis of Time Modulated Linear and Concentric Circular Antenna Array”, International Journal of Numerical Modelling-Electronic Networks, Devices and Fields, 32(6), pp.1-20, (2019).

[27] Das, A., Mandal, D. and Ghoshal, S.P. et. al., “An Optimal Mutually Coupled Concentric Circular Antenna Array Synthesis Using Ant Lion Optimization”, Annals of Telecommunication, 74(11-12), pp. 687-696, (2019).

[28] Ram, G., Mandal, D. and Kar, R., et. al., “Circular and concentric circular antenna array synthesis using cat swarm optimization”, IETE Technical Review, 32(3), pp. 204–217, (2015).

[29] Babayigit, B. and Senyigit, E. “Design optimization of circular antenna arrays using Taguchi method”, Neural Computing and Application, 28(6), pp. 1443-1452, (2017).

[30] Ram, G., Mandal, D. and Kar, R., et. al. “Opposition-based gravitational search algorithm for synthesis circular and concentric circular antenna array”, Scientia Iranica D, 22(6), pp. 2457-2471, (2015).

[31] Ram, G., Mandal, D. and Kar, R., et. al. “Improvement in various radiation characteristics of time modulated linear antenna arrays using evolutionary algorithms” Journal of Experimental and Theoretical Artificial Intelligence, 28(1-2), pp. 151-180, (2016).

[32] Ram, G., Mandal, D. and Kar, R., et. al. “Pencil beam pattern synthesis of time-modulated concentric circular antenna array using PSO with Aging Leader and Challenger” Journal of Electromagnetic Waves and Applications, 29(12), pp. 1610-1629, (2015).

[33] Ram,G., Mandal, D. and Ghoshal, S.P., et. al. “Optimization of radiation characteristics of time modulated circular geometry using DEWM”, Scientia Iranica D, 25(3), pp. 1571-1581, (2018).

[34] Mahata, S., Saha, S.K. and Kar, R., et. al. “Optimal design of fractional-order digital integrators: An evolutionary approach”, Scientia Iranica D, 25(6), pp. 3604-3627, (2018).

[35] Walpole, R.E. and Myer, R.H. “Probability and statistics for engineers and scientists”, New York, Macmillan (1978).

[2] Elliott, R. S. “Antenna Theory and Design”, Revised Edition, John Willey, NJ (2003).

[3] Collin, R. E. “Antenna and radio wave propagation”, McGraw-Hill, New York (1985).

[4] Sharaqa, A. and Dib, N. “Circular Antenna Array Synthesis Using Firefly Algorithm”, International Journal of RF and Microwave Computer-Aided Engineering, 24(2), pp. 139-146 (2014).

[5] Das, A., Mandal, D. and Ghoshal, S. P., et. al. “Moth flame optimization-based design of linear and circular antenna array for sidelobe reduction”, International Journal of Numerical Modelling, 32(1), pp. 1-15 (2018).

[6] Das, A., Mandal, D. and Ghoshal, S. P., et. al. “A Heuristic Approach to Design Linear and Circular Antenna Array for Side Lobe Reduction”, Iranian Journal of Science and Technology Transaction of Electrical Engineering, 43(1), pp. 67-76 (2018).

[7] Singh, U. and Kamal, T. S. “Design of non-uniform circular antenna arrays using biogeography-based optimization”, IET Microwaves Antennas and Propagation, 5(11), pp. 1365-1370 (2011).

[8] Guney, K. and Basbug, S. “A parallel implementation of seeker optimization algorithm for designing circular and concentric circular antenna arrays”, Applied Soft Computing, 22, pp. 287–296 (2014).

[9] Rattan, M., Patterh, M. S. and Sohi, B. S. “Optimization of circular antenna arrays of isotropic radiators using simulated annealing”, International Journal of Microwave and Wireless Technologies, 1(5), pp. 441-446 (2009).

[10] Shihab, M., Najjar, Y. and Khodier, NDM. “Design of non-uniform circular antenna arrays using particle swarm optimization”, Journal of Electrical Engineering, 59(4), pp. 216–220 (2008).

[11] Chakravorty, P. and Mandal, D. “Radiation Pattern Correction in Mutually Coupled Antenna Arrays Using Parametric Assimilation Technique”, IEEE Transactions On Antennas And Propagation, 64(9), pp. 4092-4095 (2016).

[12] Das, A., Mandal, D. and Ghoshal, S. P., et. al. “An efficient side lobe reduction technique considering mutual coupling effect in linear array antenna using BAT algorithm”, Swarm and Evolutionary Computation, 35, pp. 26–40 (2017).

[13] Singh, H., Sneha, H. L. and Jha, R. M. “Mutual Coupling in Phased Arrays: A Review”, International Journal of Antennas and Propagation, 2013, pp.1-23 (2013).

[14] Gupta, I. J. and Ksienski, A. A. “Effect of Mutual Coupling on the Performance of Adaptive Arrays”, IEEE Transactions On Antennas And Propagation, 31(5), pp. 785-791 (1983).

[15] Salonen, I., Toropainen, A. and Vainikainen, P. “Linear pattern correction in a small microstrip antenna array”, IEEE Transactions on Antennas Propagation, 52, pp. 578 – 586 (2004).

[16] Kang, Y. W. and Pozar, D. M. “Correction of Error in Reduced Sidelobe Synthesis due to Mutual Coupling” IEEE Transaction On Antennas and Propagation, 33(9), pp.1025-1028 (1985).

[17] Kelley, D. F. and Stutzman, W. L. “Array Antenna Pattern Modeling Methods that Include Mutual Coupling Effects”, IEEE Transactions on Antennas And Propagation, 41(12), pp. 1625-1632 (1993).

[18] Kennedy, J. and Eberhart, R. “Particle swarm optimization”, Proceeding of IEEE International Conference On Neural Network, 4, pp. 1942-1948 (1995).

[19] Eberhart, R. and Shi, Y. “Comparison between genetic algorithm and particle swarm optimization”, in Evolutionary Programming VII, Springer, pp. 611-616 (1998).

[20] Robinson, J. and Rahmat-Samii, Y. “Particle Swarm Optimization in Electromagnetics”, IEEE Transaction on Antenna Propagation, 52 (2) pp. 397-407 (2004).

[21] Storn, R. and Price, K. “Differential evolution- a simple and efficient adaptive scheme for global optimization over continuous spaces”, Technical Report, International Computer science Institute, Berkley (1995).

[22] Karaboga, N. “Digital IIR filter design using differential evolution algorithm”, EURASIP Journal on Applied Signal Processing, 2005, Article ID. 8, pp.1269-1276 (2005).

[23] Mirjalili, S., Mirjalili, S.M., Lewis, A. “Grey Wolf Optimizer”, Advances in Engineering Software, 69, pp. 46-61 (2014).

[24] Saxena, P. and Kothari, A. “Optimal Pattern Synthesis of Linear Antenna Array Using Grey Wolf Optimization Algorithm”, International Journal of Antennas and Propagation, 2016, Article ID 1205970 (2016).

[25] Das, A., Mandal, D. and Ghoshal, S.P., et. al., “Concentric circular antenna array synthesis for sidelobe suppression using moth flame optimization”, International Journal of Electronics and Communication (AEU), 86, pp. 177-184 (2018).

[26] Das, A., Mandal, D. and Kar, R. “An Optimal Far-Field Radiation Pattern Synthesis of Time Modulated Linear and Concentric Circular Antenna Array”, International Journal of Numerical Modelling-Electronic Networks, Devices and Fields, 32(6), pp.1-20, (2019).

[27] Das, A., Mandal, D. and Ghoshal, S.P. et. al., “An Optimal Mutually Coupled Concentric Circular Antenna Array Synthesis Using Ant Lion Optimization”, Annals of Telecommunication, 74(11-12), pp. 687-696, (2019).

[28] Ram, G., Mandal, D. and Kar, R., et. al., “Circular and concentric circular antenna array synthesis using cat swarm optimization”, IETE Technical Review, 32(3), pp. 204–217, (2015).

[29] Babayigit, B. and Senyigit, E. “Design optimization of circular antenna arrays using Taguchi method”, Neural Computing and Application, 28(6), pp. 1443-1452, (2017).

[30] Ram, G., Mandal, D. and Kar, R., et. al. “Opposition-based gravitational search algorithm for synthesis circular and concentric circular antenna array”, Scientia Iranica D, 22(6), pp. 2457-2471, (2015).

[31] Ram, G., Mandal, D. and Kar, R., et. al. “Improvement in various radiation characteristics of time modulated linear antenna arrays using evolutionary algorithms” Journal of Experimental and Theoretical Artificial Intelligence, 28(1-2), pp. 151-180, (2016).

[32] Ram, G., Mandal, D. and Kar, R., et. al. “Pencil beam pattern synthesis of time-modulated concentric circular antenna array using PSO with Aging Leader and Challenger” Journal of Electromagnetic Waves and Applications, 29(12), pp. 1610-1629, (2015).

[33] Ram,G., Mandal, D. and Ghoshal, S.P., et. al. “Optimization of radiation characteristics of time modulated circular geometry using DEWM”, Scientia Iranica D, 25(3), pp. 1571-1581, (2018).

[34] Mahata, S., Saha, S.K. and Kar, R., et. al. “Optimal design of fractional-order digital integrators: An evolutionary approach”, Scientia Iranica D, 25(6), pp. 3604-3627, (2018).

[35] Walpole, R.E. and Myer, R.H. “Probability and statistics for engineers and scientists”, New York, Macmillan (1978).

Transactions on Computer Science & Engineering and Electrical Engineering (D)

May and June 2022Pages 1455-1474