Document Type : Article

**Author**

School of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran

**Abstract**

An analytic method is proposed to reduce the number of elements of a Uniformly Spaced Antenna Arrays (USAAs). To this end, both excitations and positions of a Nonuniformly Spaced Antenna Array (NSAA) are obtained by equating the Fourier's coefficients of array factors of NSAA to those of predesigned USAA, in two steps. At first step, the array is considered USAA and excitations of elements are determined. At the second step, the position of elements are determined for the excitations obtained in the first step. These two steps are repeated several times to increase the accuracy. In fact, this method is the extension of Fourier's Coefficients Equating (FCE) method previously introduced to design NSAAs. The effectiveness of the presented method for both pencil beam and shaped beam patterns is verified by some comprehensive examples.

**Keywords**

References:

1. Balanis, C. A., Antenna Theory: Analysis and Design, New York: John Wiley & Sons (2005).

2. Khalaj-Amirhosseini, M. "Synthesis of linear and planar arrays with sidelobes of individually arbitrary levels", Int. J. of RF and Microwave Computer Aided Design, 29(3), mmce. 21637, pp. 1-9 (2018).

3. Kurup, D.G., Himdi, M., and Rydberg, A. "Synthesisv of uniform amplitude unequally spaced arrays using the differential evolution algorithm", IEEE Trans. Antenna Propag., 51(9), pp. 2210-2217 (2003).

4. Lin, C., Qing, A., and Feng, Q. "Synthesis of unequally spaced antenna arrays by using differential evolution", IEEE Trans. Antennas Propag., 58(8), pp. 2553-2558 (2010).

5. Mahmoud, K.R. "Synthesis of unequally-spaced linear array using modified central force optimization algorithm", IET Microwaves, Antennas & Propagation, 10(10), pp. 1011-1021 (2016).

6. Schjaer-Jacobsen, H. and Madsen, K. "Synthesis of nonuniformly spaced arrays using a general nonlinear minimax optimization method", IEEE Trans. Antennas Propag., 24(4), pp. 501-506 (1976).

7. Oraizi, H. and Fallahpour, M. "Nonuniformly spaced linear array design for the specified beamwidth/ sidelobe level or specified irectivity/sidelobe level with coupling considerations", Progress in Electromagnetic Research M, 4, pp. 185-209 (2008).

8. Asif Zaman, M. and Abdul-Matin, Md. "Nonuniformly spaced linear antenna array design using fire y algorithm", Int. Journal of Microwave Science and Technology, Article ID 256759, 2012, pp. 1-8 (2012).

9. Bae, J.-H., Kim, K.-T., Lee, J.-H., et al. "Design of steerable non-uniform linear array geometry for sidelobe reduction" Microwave and Optical Technology Lett., 36(5), pp. 363-367 (2003).

10. Yuan, P., Guo, C., Ding, J., et al. "Synthesis of nonuniform sparse linear array antenna using whale optimization algorithm", Asia-Pacific Conference on Antennas and Propagation (APCAP), China (2017).

11. Gangwar, V.S., Singh, A.K., and Singh, S.P. "An effective approach for the synthesis of unequally spaced antenna array by estimating optimum elements density on the aperture", IEEE Antennas and Wireless Propagation Letters, 16, pp. 2278-2282 (2017).

12. Harrington, R.F. "Sidelobe reduction by nonuniform element spacing", IRE Trans. Antennas Propagation, 9(2), pp. 187-192 (1961).

13. Ishimaru, A. "Theory of unequally spaced arrays", IEEE Trans. Antennas Propagat., 10(6), pp. 691-702 (1962).

14. Redlich, R.W. "Iterative least squares synthesis of nonuniformly spaced linear array", IEEE Trans. Antennas Propagation, 21(1), pp. 106-108 (1973).

15. Hodjat F. and Hovanessian, S.A. "Nonuniformly spaced linear and planar array antennas for sidelobe reduction", IEEE Trans. Antennas Propagation, 26(2), pp. 198-204 (1978).

16. Yu, C.-C. "Sidelobe reduction of asymmetric linear array by spacing perturbation", Electronics Letters, 33(9), pp. 730-732 (1997).

17. Ren, X.F., Azevedo, J.A., and Casimiro, A.M. "Synthesis of non-uniformly spaced arrays using the Fourier transform and window techniques", IET Microwaves, Antennas & Propagation, 3(8), pp. 1245-1253 (2009).

18. Ishimaru, A. "Unequally spaced arrays based on the Poisson sum formula", IEEE Trans. Antennas Propagation, 62(4), pp. 1549-1554 (2014).

19. You, B.Q., Cai, L.R., Zhou, J.H., et al. "Hybrid approach for the synthesis of unequally spaced array antennas with sidelobes reduction", IEEE Antennas and Wireless Propagation Letters, 14, pp. 1569-1572 (2015).

20. Khalaj-Amirhosseini, M., Vecchi, G., and Pirinoli, P. "Near-Chebyshev pattern for nonuniformly spaced arrays using zeros matching method", IEEE Trans. Antennas and Propagation, 65(10), pp. 5155-5161 (2017).

21. Khalaj-Amirhosseini, M. "Design of nonuniformly spaced arrays using zeros matching method", Int. Journal of RF and Microwave Computer-Aided Engineering, 28(9), mmce.21490, pp. 1-5 (2018).

22. Khalaj-Amirhosseini, M. "Design of nonuniformly spaced antenna arrays using Fourier's coefficients equating method", IEEE Trans. Antennas and Propagation, 66(10), pp. 5326-5332 (2018).

23. Yang, K., Zhao, Z.Q., and Liu, Q. H. "Fast pencil beam pattern synthesis of large unequally spaced antenna arrays", IEEE Trans. Antennas and Propagation, 61(2), pp. 627-634 (2013).

24. Liu, Y., Nie, Z., and Liu, Q.H. "Reducing the number of elements in a linear antenna array by the matrix pencil method", IEEE Trans. Antennas Propag., 56(9), pp. 2955-2962 (2008).

25. Liu, Y., Liu, Q.H., and Nie, Z. "Reducing the number of elements in the synthesis of shaped-beam patterns by the forward-backward matrix pencil method", IEEE Trans. Antennas Propag., 58(2), pp. 604-608 (2010).

26. Alijani, M. and Neshati, M.H. "A new noniterative method for pattern synthesis of unequally spaced linear arrays", Int. Journal of RF and Microwave Computer- Aided Engineering, 29(11), e21921 (2019).

27. Goudos, S.K., Boursianis, A., Siakavara, K., et al. "Novel methodology for designing antenna arrays with reduced number of elements based on differential evolution with ranking-based mutation operators", Int. Applied Computational Electromagnetics Society Symposium (ACES), China (2018).

28. You, P., Liu, Y., Chen, S.-L., et al. "Synthesis of unequally spaced linear antenna arrays with minimum element spacing constraint by alternating convex optimization", IEEE Antennas and Wireless Propagation Letters, 16, pp. 3126-3130 (2017).

29. Shen, H. and Wang, B. "An effective method for synthesizing multiple-pattern linear arrays with a reduced number of antenna elements", IEEE Trans. Antennas Propagation, 65(5), pp. 2358-2366 (2017).

30. Sokolnikoff, I.S. and Sokolnikoff, E.S. Higher Mathematics for Engineers and Physicists, McGraw-Hill (1941).

2. Khalaj-Amirhosseini, M. "Synthesis of linear and planar arrays with sidelobes of individually arbitrary levels", Int. J. of RF and Microwave Computer Aided Design, 29(3), mmce. 21637, pp. 1-9 (2018).

3. Kurup, D.G., Himdi, M., and Rydberg, A. "Synthesisv of uniform amplitude unequally spaced arrays using the differential evolution algorithm", IEEE Trans. Antenna Propag., 51(9), pp. 2210-2217 (2003).

4. Lin, C., Qing, A., and Feng, Q. "Synthesis of unequally spaced antenna arrays by using differential evolution", IEEE Trans. Antennas Propag., 58(8), pp. 2553-2558 (2010).

5. Mahmoud, K.R. "Synthesis of unequally-spaced linear array using modified central force optimization algorithm", IET Microwaves, Antennas & Propagation, 10(10), pp. 1011-1021 (2016).

6. Schjaer-Jacobsen, H. and Madsen, K. "Synthesis of nonuniformly spaced arrays using a general nonlinear minimax optimization method", IEEE Trans. Antennas Propag., 24(4), pp. 501-506 (1976).

7. Oraizi, H. and Fallahpour, M. "Nonuniformly spaced linear array design for the specified beamwidth/ sidelobe level or specified irectivity/sidelobe level with coupling considerations", Progress in Electromagnetic Research M, 4, pp. 185-209 (2008).

8. Asif Zaman, M. and Abdul-Matin, Md. "Nonuniformly spaced linear antenna array design using fire y algorithm", Int. Journal of Microwave Science and Technology, Article ID 256759, 2012, pp. 1-8 (2012).

9. Bae, J.-H., Kim, K.-T., Lee, J.-H., et al. "Design of steerable non-uniform linear array geometry for sidelobe reduction" Microwave and Optical Technology Lett., 36(5), pp. 363-367 (2003).

10. Yuan, P., Guo, C., Ding, J., et al. "Synthesis of nonuniform sparse linear array antenna using whale optimization algorithm", Asia-Pacific Conference on Antennas and Propagation (APCAP), China (2017).

11. Gangwar, V.S., Singh, A.K., and Singh, S.P. "An effective approach for the synthesis of unequally spaced antenna array by estimating optimum elements density on the aperture", IEEE Antennas and Wireless Propagation Letters, 16, pp. 2278-2282 (2017).

12. Harrington, R.F. "Sidelobe reduction by nonuniform element spacing", IRE Trans. Antennas Propagation, 9(2), pp. 187-192 (1961).

13. Ishimaru, A. "Theory of unequally spaced arrays", IEEE Trans. Antennas Propagat., 10(6), pp. 691-702 (1962).

14. Redlich, R.W. "Iterative least squares synthesis of nonuniformly spaced linear array", IEEE Trans. Antennas Propagation, 21(1), pp. 106-108 (1973).

15. Hodjat F. and Hovanessian, S.A. "Nonuniformly spaced linear and planar array antennas for sidelobe reduction", IEEE Trans. Antennas Propagation, 26(2), pp. 198-204 (1978).

16. Yu, C.-C. "Sidelobe reduction of asymmetric linear array by spacing perturbation", Electronics Letters, 33(9), pp. 730-732 (1997).

17. Ren, X.F., Azevedo, J.A., and Casimiro, A.M. "Synthesis of non-uniformly spaced arrays using the Fourier transform and window techniques", IET Microwaves, Antennas & Propagation, 3(8), pp. 1245-1253 (2009).

18. Ishimaru, A. "Unequally spaced arrays based on the Poisson sum formula", IEEE Trans. Antennas Propagation, 62(4), pp. 1549-1554 (2014).

19. You, B.Q., Cai, L.R., Zhou, J.H., et al. "Hybrid approach for the synthesis of unequally spaced array antennas with sidelobes reduction", IEEE Antennas and Wireless Propagation Letters, 14, pp. 1569-1572 (2015).

20. Khalaj-Amirhosseini, M., Vecchi, G., and Pirinoli, P. "Near-Chebyshev pattern for nonuniformly spaced arrays using zeros matching method", IEEE Trans. Antennas and Propagation, 65(10), pp. 5155-5161 (2017).

21. Khalaj-Amirhosseini, M. "Design of nonuniformly spaced arrays using zeros matching method", Int. Journal of RF and Microwave Computer-Aided Engineering, 28(9), mmce.21490, pp. 1-5 (2018).

22. Khalaj-Amirhosseini, M. "Design of nonuniformly spaced antenna arrays using Fourier's coefficients equating method", IEEE Trans. Antennas and Propagation, 66(10), pp. 5326-5332 (2018).

23. Yang, K., Zhao, Z.Q., and Liu, Q. H. "Fast pencil beam pattern synthesis of large unequally spaced antenna arrays", IEEE Trans. Antennas and Propagation, 61(2), pp. 627-634 (2013).

24. Liu, Y., Nie, Z., and Liu, Q.H. "Reducing the number of elements in a linear antenna array by the matrix pencil method", IEEE Trans. Antennas Propag., 56(9), pp. 2955-2962 (2008).

25. Liu, Y., Liu, Q.H., and Nie, Z. "Reducing the number of elements in the synthesis of shaped-beam patterns by the forward-backward matrix pencil method", IEEE Trans. Antennas Propag., 58(2), pp. 604-608 (2010).

26. Alijani, M. and Neshati, M.H. "A new noniterative method for pattern synthesis of unequally spaced linear arrays", Int. Journal of RF and Microwave Computer- Aided Engineering, 29(11), e21921 (2019).

27. Goudos, S.K., Boursianis, A., Siakavara, K., et al. "Novel methodology for designing antenna arrays with reduced number of elements based on differential evolution with ranking-based mutation operators", Int. Applied Computational Electromagnetics Society Symposium (ACES), China (2018).

28. You, P., Liu, Y., Chen, S.-L., et al. "Synthesis of unequally spaced linear antenna arrays with minimum element spacing constraint by alternating convex optimization", IEEE Antennas and Wireless Propagation Letters, 16, pp. 3126-3130 (2017).

29. Shen, H. and Wang, B. "An effective method for synthesizing multiple-pattern linear arrays with a reduced number of antenna elements", IEEE Trans. Antennas Propagation, 65(5), pp. 2358-2366 (2017).

30. Sokolnikoff, I.S. and Sokolnikoff, E.S. Higher Mathematics for Engineers and Physicists, McGraw-Hill (1941).

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

January and February 2023Pages 228-236