Mathematical Relationship of an Isotropic Point Source and the Spherically Distributed Antenna Array
Keywords:
Distributed beamformingAbstract
This work investigates beam pattern behavior of an isotropic point source and a collection of sources distributed amongst a spherical volume. Pattern behavior is compared to the tapering of a plane wave expansion of spherical waves demonstrating self-adjoint characteristics. Beampatterns of atomic like orbitals and Zernike polynomials are provided as connections to common applications.
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References
A. Panicali and L. Yuen, “A probabilistic approach to large circular and spherical arrays,” IEEE Trans. Antennas Propag., vol. 17, pp. 514-522, July 1969.
T. A. Dzekov and R. S. Berkowitz, “Parameters of a spherical random antenna array,” in Electron. Lett., vol. 14, no. 16, pp. 495-496, Aug. 1978.
H. Ochiai, “Collaborative beamforming for distributed wireless ad hoc sensor networks,” IEEE Trans. Signal Process., vol. 53, pp. 4110, Nov. 2005.
M. F. A. Ahmed and S. A. Vorobyov, “Collaborative beamforming for wireless sensor networks with Gaussian distributed sensor nodes,” IEEE Trans. on Wireless Commun., vol. 8, pp. 638-643, Feb. 2009.
K. Buchanan, O. Sternberg, S. Wheeland, and J. Rockway, “Examination of the near field response of circular antenna arrays,” in United States National Committee of URSI National Radio Science Meeting (USNCURSI NRSM), Boulder, CO, Jan. 2017, pp. 1-2.
K. Buchanan, C. Flores-Molina, O. Sternberg, D. Overturf, S. Wheeland, and N. Johnson, “Near-field receive beamforming analysis using circularly distributed random arrays,” in IEEE Antennas and Propag. Int. Symp., San Diego, CA, 2017, pp. 1591-1592.
D. Overturf, K. Buchanan, J. Jensen, C. Flores-Molina, S. Wheeland and G. H. Huff, “Investigation of beamforming patterns from volumetrically distributed phased arrays,” in IEEE Military Communications Conference (MILCOM), Baltimore, MD, Oct. 2017, pp. 817-822.
K. Buchanan and G. Huff, “A comparison of geometrically bound random arrays in Euclidean space,” in IEEE Antennas and Propag. Soc. Int. Symp., Spokane, WA, July 2011, pp. 3-8.
K. R. Buchanan, “Theory and applications of aperiodic (random) phased arrays,” Ph.D. dissertation, Dept. Elect. & Com. Eng., Texas A&M University, TX, 2014.
K. Buchanan and G. Huff, “A stochastic mathematical framework for the analysis of spherically bound random arrays,” IEEE Trans. Antennas Propag., vol. 62, pp. 3002-3011, June 2014.
D. Yavuz, “Frequency response and bandwidth of a spherical random array,” in Electron. Lett., vol. 15, no. 11, pp. 314-315, May 1979.
L. Lewin, “Comment analytic expression for the frequency response and bandwidth of a spherical random array,” in Electron. Lett., vol 15. no. 19, pp. 585-586, Sept. 1979.
K. Buchanan, C. Flores, S. Wheeland, J. Jensen, D. Grayson, and G. Huff, “Transmit beamforming for radar applications using circularly tapered random arrays,” in IEEE Radar Conference (RadarConf), Seattle, WA, 2017, pp. 0112-0117.
B. D. Steinberg, Principles of Aperture & Array System Design. New York: Wiley, 1976.
Y. Lo, “A mathematical theory of antenna arrays with randomly spaced elements,” IEEE Trans. Antennas Propag., vol. 12, pp. 257-268, May 1964.