Progress In Electromagnetics Research B
ISSN: 1937-6472
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By G. Buonanno and R. Solimene

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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.

G. Buonanno and R. Solimene, "Comparing Different Schemes for Random Arrays," Progress In Electromagnetics Research B, Vol. 71, 107-118, 2016.

1. Bilinskis, I., Digital Alias-free Signal Processing, John Wiley & Sons, Inc., 2007.

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.

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.

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.

5. Andreasen, M. G., "Linear arrays with variable in-terelement spacing," IRE Trans. Antennas Propagat., Vol. 10, 137-143, 1962.

6. Steinberg, B. D., "The peak sidelobe of the phased array having randomly located elements," IEEE Trans. Antennas Propagat., Vol. 20, 129-136, 1972.

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.

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

9. Unz, H., "Linear arrays with arbitrarily distributed elements," IRE Trans. Antennas Propagat., Vol. 8, 222-223, 1960.

10. Ishimaru, A., "Theory of unequally-spaced arrays," IRE Trans. Antennas Propagat., Vol. 10, 691-702, 1962.

11. Willey, R. E., "Space tapering of linear and planar arrays," IEEE Trans. Antennas Propag., Vol. 10, No. 4, 369-377, 1962.

12. Sandler, S., "Some equivalences between equally and unequally spaced arrays," IRE Trans. Antennas Propagat., Vol. 8, 496-500, September 1960.

13. Maffett, A. L., "Array factors with non uniform spacing parameters," IRE Trans. Antennas Propagat., Vol. 10, 131-146, 1962.

14. Skolnik, M., G. Nemhauser, and J. Sherman, "Dynamic programming applied to unequally spaced arrays," IEEE Trans. Antennas Propag., 35-43, January 1964.

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.

16. Haupt, R. L., "Thinned arrays using genetic algorithms," IEEE Trans. Antennas Propag., Vol. 42, No. 7, 993-999, 1994.

17. Haupt, R. L., "Unit circle representation of aperiodic arrays," IEEE Trans. Antennas Propag., Vol. 43, No. 10, 1152-1155, 1995.

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.

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.

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.

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.

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.

23. Razavi, A. and K. Forooraghi, "Thinned arrays using pattern search algorithms," Progress In Electromagnetics Research, Vol. 78, 61-71, 2008.

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.

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.

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

27. Agrawal, V. and Y. Lo, "Distribution of sidelobe level in random arrays," Proc. IEEE, Vol. 57, No. 10, 1764-1765, 1969.

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.

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.

30. Hendricks, W. J., "The totally random versus the bin approach for random arrays," IEEE Trans. Antennas Propag., Vol. 39, 1757-1762, 1991.

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.

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.

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.

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.

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

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