volume | PIER Journals

Abstract

In this work, four types of random arrays are compared. In particular, the mean and variance of the array factor are derived. This provides a partial statistical characterisation that allows pointing out some important aspects of random arrays and link them to the number of elements and array aperture. In the absence of a simple and effective analytical apparatus, here great importance is also given to the experimental aspect, especially as far as the side-lobe level is concerned. To this end, Monte Carlo simulations are run to experimentally build the side-lobe distribution as a function of the number of radiators and the average spacing between two adjacent radiators. The obtained results show that random arrays where one is free to impose constraints on the minimum spacing between adjacent elements can obtain performance analogous to those achievable by other schemes which do not put such constraints. However, the former are preferable because they are able to zero the probability that adjacent radiators are separated with less than a certain minimum distance and this allows the mitigation of mutual coupling effects.

1. Bilinskis, I., Digital Alias-free Signal Processing, John Wiley & Sons, Inc., 2007.
doi:10.1002/9780470511633

2. Holm, S., A. Austeng, K. Iranpour, and J. F. Hopperstad, "Nonuniform sampling: Theory and practice," F. Marvasti Nonuniform Sampling: Theory and Practice, Chapter 19, 2001. Google Scholar

3. King, D. D., R. F. Packard, and R. K. Thomas, "Unequally-spaced, broad-band antenna arrays," IRE Trans. Antennas Propagat., Vol. 8, 380-384, 1960.
doi:10.1109/TAP.1960.1144876 Google Scholar

4. Ishimaru, A. and Y. S. Chen, "Thinning and broadbanding antenna arrays by unequal spacings," IEEE Trans. Antennas Propagat., Vol. 13, 34-42, January 1965.
doi:10.1109/TAP.1965.1138378 Google Scholar

5. Andreasen, M. G., "Linear arrays with variable in-terelement spacing," IRE Trans. Antennas Propagat., Vol. 10, 137-143, 1962.
doi:10.1109/TAP.1962.1137832 Google Scholar

6. Steinberg, B. D., "The peak sidelobe of the phased array having randomly located elements," IEEE Trans. Antennas Propagat., Vol. 20, 129-136, 1972.
doi:10.1109/TAP.1972.1140162 Google Scholar

7. Leahy, B. D. and B. D. Jeffs, "On the design of maximally sparse beamforming arrays," IEEE Trans. Antennas Propagat., Vol. 39, No. 8, 1178-1187, 1991.
doi:10.1109/8.97353 Google Scholar

8. Lo, Y. T., "A mathematical theory of antenna arrays with randomly spaced elements," IEEE Trans. Antennas Propagat., Vol. 12, 257268, 1964. Google Scholar

9. Unz, H., "Linear arrays with arbitrarily distributed elements," IRE Trans. Antennas Propagat., Vol. 8, 222-223, 1960.
doi:10.1109/TAP.1960.1144829 Google Scholar

10. Ishimaru, A., "Theory of unequally-spaced arrays," IRE Trans. Antennas Propagat., Vol. 10, 691-702, 1962.
doi:10.1109/TAP.1962.1137952 Google Scholar

11. Willey, R. E., "Space tapering of linear and planar arrays," IEEE Trans. Antennas Propag., Vol. 10, No. 4, 369-377, 1962.
doi:10.1109/TAP.1962.1137887 Google Scholar

12. Sandler, S., "Some equivalences between equally and unequally spaced arrays," IRE Trans. Antennas Propagat., Vol. 8, 496-500, September 1960.
doi:10.1109/TAP.1960.1144882 Google Scholar

13. Maffett, A. L., "Array factors with non uniform spacing parameters," IRE Trans. Antennas Propagat., Vol. 10, 131-146, 1962.
doi:10.1109/TAP.1962.1137831 Google Scholar

14. Skolnik, M., G. Nemhauser, and J. Sherman, "Dynamic programming applied to unequally spaced arrays," IEEE Trans. Antennas Propag., 35-43, January 1964.
doi:10.1109/TAP.1964.1138163 Google Scholar

15. Skolnik, M. I., J. W. Sherman, III, and F. C. Ogg, Jr., "Statistically designed density-tapered arrays," IEEE Trans. Antennas Propag., Vol. 12, 408-417, July 1964.
doi:10.1109/TAP.1964.1138239 Google Scholar

16. Haupt, R. L., "Thinned arrays using genetic algorithms," IEEE Trans. Antennas Propag., Vol. 42, No. 7, 993-999, 1994.
doi:10.1109/8.299602 Google Scholar

17. Haupt, R. L., "Unit circle representation of aperiodic arrays," IEEE Trans. Antennas Propag., Vol. 43, No. 10, 1152-1155, 1995.
doi:10.1109/8.467654 Google Scholar

18. Kerby, K. C. and J. T. Bernhard, "Sidelobe level and wideband behavior of arrays of random subarrays," IEEE Trans. Antennas Propag., Vol. 54, No. 8, 2253-2262, 2006.
doi:10.1109/TAP.2006.879195 Google Scholar

19. Liu, Y., Z.-P. Nie, and Q. H. Liu, "A new method for the synthesis of non-uniform linear arrays with shaped power patterns," Progress In Electromagnetics Research, Vol. 107, 349-363, 2010.
doi:10.2528/PIER10060912 Google Scholar

20. Zhao, X., Q. Yang, and Y. Zhang, "Compressed sensing approach for pattern synthesis of maximally sparse non-uniform linear array," IET Microw., Antennas Propag., Vol. 8, No. 5, 301-307, 2013.
doi:10.1049/iet-map.2013.0492 Google Scholar

21. Gregory, M. and D. Werner, "Ultrawideband aperiodic antenna arrays based on optimized raised power series representations," IEEE Trans. Antennas Propag., Vol. 58, No. 3, 756-764 , 2010.
doi:10.1109/TAP.2009.2039315 Google Scholar

22. Tokan, F. and F. Gunes, "The multi-objective optimization of non-uniform linear phased arrays using the genetic algorithm," Progress In Electromagnetics Research B, Vol. 17, 135-151, 2009.
doi:10.2528/PIERB09072309 Google Scholar

23. Razavi, A. and K. Forooraghi, "Thinned arrays using pattern search algorithms," Progress In Electromagnetics Research, Vol. 78, 61-71, 2008.
doi:10.2528/PIER07081501 Google Scholar

24. Kumar, B. P. and G. R. Branner, "Synthesis of unequally spaced arrays using Legendre series expansion," Proc. IEEE Antennas Propag. Int. Symp., Vol. 4, 2236-2239, 1997. Google Scholar

25. Kurup, D. G., M. Himdi, and A. Rydberg, "Synthesis of uniform amplitude unequally spaced antenna arrays using the differential evolution algorithm," IEEE Trans. Antennas Propag., Vol. 51, 2210-2217, 2003.
doi:10.1109/TAP.2003.816361 Google Scholar

26. Lo, Y. T. and S. W. Lee, "Aperiod arrays," Antenna Handbook: Antenna Theory, Vol. 2, Chapter 14, Chapman and Hall, 1993. Google Scholar

27. Agrawal, V. and Y. Lo, "Distribution of sidelobe level in random arrays," Proc. IEEE, Vol. 57, No. 10, 1764-1765, 1969.
doi:10.1109/PROC.1969.7392 Google Scholar

28. Donvito, M. B. and S. A. Kassam, "Characterization of the random array peak sidelobe," IEEE Trans. Antennas Propagat., Vol. 27, 379-385, May 1979.
doi:10.1109/TAP.1979.1142097 Google Scholar

29. Krishnamurthy, S., D. Bliss, C. Richmond, and V. Tarokh, "Peak sidelobe level gumbel distribution for arrays of randomly placed antennas," 2015 IEEE National Radar Conference --- Proceedings, 1671-1676, 2015.
doi:10.1109/RADAR.2015.7131267 Google Scholar

30. Hendricks, W. J., "The totally random versus the bin approach for random arrays," IEEE Trans. Antennas Propag., Vol. 39, 1757-1762, 1991.
doi:10.1109/8.121597 Google Scholar

31. Shinohara, N., B. Shishkov, H. Matsumoto, K. Hashimoto, and A. K. M. Baki, "New stochastic algorithm for optimization of both side lobes and grating lobes in large antenna arrays for MPT," Ieice Transactions --- IEICE, Vol. 91-B, No. 1, 286-296, 2008.
doi:10.1093/ietcom/e91-b.1.286 Google Scholar

32. Kolghi, H. and S. B. Kesler, "Comparison of two methods of generating sensor locations in random array," Antennas and Propagation Society International Symposium, Vol. 24, 1986. Google Scholar

33. Papoulis, A. and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th Ed., McGraw Hill, 2002.

34. Baglivo, J. A., Mathematica Laboratories for Mathematical Statistics, Emphasizing Simulation and Computer Intensive Methods, ASA-SIAM, Chapter 9, 120, 2005.
doi:10.1137/1.9780898718416

35. Agrawal, V. D. and Y. T. Lo, "Mutual coupling in phased arrays of randomly spaced antennas," IEEE Trans. on Antennas and Propagat., Vol. 20, 288-295, 1972.
doi:10.1109/TAP.1972.1140188 Google Scholar

36. Balanis, C. A., Antenna Theory: Analysis and Design, 2nd Ed., John Wiley and Sons, Inc., 1996.

Dr. Giovanni Buonanno

Dr. Raffaele Solimene