Aperture Maximization with Half-Wavelength Spacing, via a 2-Circle Concentric Array Geometry that is Uniform but Sparse

Main Article Content

Musyoka Kinyili
Dominic Makaa Kitavi
Cyrus Gitonga Ngari


This paper proposes a new sensor-array geometry (the 2-circle concentric array geometry), that maximizes the array's spatial aperture mainly for bivariate azimuth-polar resolution of direction-of-arrival estimation problem. The proposed geometry provides almost invariant azimuth angle coverage and oers the advantage of full rotational symmetry (circular invariance) while maintaining an inter-sensor spacing of only an half wavelength (for non-ambiguity with
respect to the Cartesian direction cosines). A better-accurate performance in direction nding of the proposed array grid over a single ring array geometry termed as uniform circular array (UCA) is hereby analytically veried via Cramer-Rao bound analysis. Further, the authors demonstrate that the proposed sensor-array geometry has better estimation accuracy than a single ring array.

Antenna arrays, array signal processing, direction-of-arrival estimation, parameter estimation, planar circular arrays

Article Details

How to Cite
Kinyili, M., Kitavi, D., & Ngari, C. (2019). Aperture Maximization with Half-Wavelength Spacing, via a 2-Circle Concentric Array Geometry that is Uniform but Sparse. Journal of Advances in Mathematics and Computer Science, 32(3), 1-20. https://doi.org/10.9734/jamcs/2019/v32i330148
Original Research Article


Van Trees HL. Detection, estimation and modulation theory, Part IV: Optimum array
processing. New York, USA: John Wiley and Sons; 2002.

Kajaree D, Behera R. A survey on web crawler approaches. International Journal of Innovative
Research in Computer and Communication Engineering. 2017;5(2):1302-1309.

Devendra M, Manjunathachari K. Solar DC microgrid for rural electrication: A case study.
International Advanced Research Journal in Science, Engineering and Technology (IARJSET).

Rhode S. Introduction into theory of direction nding, radiomonitoring and radiolocation.
International Journal of Computer Applications . 2010;6(3):26-49.

Krishnaveni V, Kesavamurthy T, Aparna B. Beamforming for direction-of-arrival (DOA)
estimation-a survey. International Journal of Computer Applications. 2013;61(11).

Vorobyov SA, Gershman AB, Wong KM. Maximum likelihood direction-of-arrival estimation
in unknown noise elds using sparse sensor arrays. IEEE Transactions on Signal Processing.

Wong KT, Zoltowski MD. Self-initiating MUSIC-based direction nding and polarization
estimation in spatio-polarizational beamspace. IEEE Transactions on Antennas and
Propagation. 2000;48(8):1235-1245.

Abedin MJ, Mohan AS. Maximum likelihood near eld localisation using concentric circular
ring array. IEEE International Conference on In Electromagnetics in Advanced Applications.

Zoltowski MD, Wong KT. ESPRIT-based 2-D direction nding with a sparse uniform array of
electromagnetic vector sensors. IEEE Transactions on Signal Processing. 2000;48(8):2195-2204.

Friedlander B. Wireless direction-nding fundamentals in classical and modern direction-ofarrival
estimation. 2009;1-51. Elsevier

Kitavi DM, Hao T, Wong KT. A regular tetrahedral array whose constituent sensors fail
randomlyA lower bound for direction-of-arrival estimation. IEEE Conference on Antennas and
Propagation. 2016;1-5.

Tayem N, Kwon HM. L-shape 2-dimensional arrival angle estimation with propagator method.
IEEE Transactions on Antennas and Propagation. 2005;53(5):1622-1630.

Kitavi DM, Wong KT, Hung CC. An L-Shaped Array With Nonorthogonal AxesIts CramrRao
Bound for Direction Finding. IEEE Transactions on Aerospace and Electronic Systems.

Jiang Y, Zhang S. An innovative strategy for synthesis of uniformly weighted circular
aperture antenna array based on the weighting density method. IEEE Antennas and Wireless
Propagation Letters. 2013;12:725-728.

Singh U, Kamal TS. Synthesis of thinned planar concentric circular antenna arrays using
biogeography-based optimization. IET microwaves, antennas and propagation. 2012;6(7):822-

Wang L, Wang G, Chen Z. Joint DOA-polarization estimation based on uniform concentric
circular array. Journal of Electromagnetic Waves and Applications. 2013;27(13):1702-1714.

Zhao X, Zhang Y, Yang Q. Synthesis of sparse concentric ring arrays based on Bessel function.
IET Microwaves, Antennas and Propagation. 2017;11(11):1651-1660.

Ram G, Mandal D, Kar R, Ghoshal SP. Circular and concentric circular antenna array synthesis
using cat swarm optimization. IETE Technical Review. 2015;32(3):204-217.

Haupt RL. Optimized element spacing for low sidelobe concentric ring arrays. IEEE
Transactions on Antennas and Propagation. 2008;56(1):266-268.

Zhang L, Jiao YC, Chen B, Weng ZB. Design of wideband concentric-ring arrays with threedimensional
beam scanning based on the optimization of array geometry. Electromagnetics.

Wong KT, Chibuzo JN, Yue IW. A triad of cardioid sensors in orthogonal orientation and
spatial collocationIts spatial-matched-lter-type beam-pattern. IEEE Transactions on Signal
Processing. 2018;66(4):895-906.

Wong KT, Yang S, Caleb JF, Salman K, Wai-Yip T. Electrically Long dipoles in
a collocated/orthogonal triadfor direction nding and polarization estimation. IEEE
Transactions on Antennas and Propagation. 2017;65(11):6057-6067.

Khan S, Wong KT, Yang S, Wai-Yip T. Electrically large circular loops in the estimation of
an incident emitters direction-of-arrival or polarization. IEEE Transactions on Antennas and
Propagation. 2018;66(6):3046-3055.

Wong KT, Zoltowski MD. Extended-aperture underwater acoustic multisource
azimuth/elevation direction-nding using uniformly but sparsely spaced vector hydrophones.
IEEE Journal of Oceanic Engineering. 1997;22(4):659-672.

Chen K, Chen H, Wang L, Wu H. Modied real ga for the synthesis of sparse planar circular
arrays. IEEE Antennas Wirel. Propag. Lett. 2016;15:274-277.

Gregory MD, Namin FA, Werner DH. Exploiting rotational symmetry for the design of ultrawideband
planar phased array layouts. IEEE Transactions on Antennas and Propagation.

Spence TG, and Douglas HW. Design of broadband planar arrays based on the optimization
of aperiodic tilings. IEEE Transactions on Antennas and Propagation. 2008;56(1):76-86.

Alvarez-Folgueiras M, Juan ARG, Francisco AP. High-performance uniformly excited linear
and planar arrays based on linear semiarrays composed of subarrays with dierent uniform
spacings. IEEE Transactions on Antennas and Propagation. 2009;57(12):4002-4006.

Pralon MG, Del-Galdo G, Landmann M, Hein MA, Thoma RS. Suitability of compact antenna
arrays for direction-of-arrival estimation. IEEE Transaction on Antenna and Propagation.

Sun H, Chiu WY, Jiang J, Nallanathan A, Poor HV, Wideband spectrum sensing
with sub-Nyquist sampling in cognitive radios. IEEE Transaction on Signal Processing.

Olshausen BA, Aliasing. Sensory Processes. 2000;3-4.

Zoltowski MD, Mathews CP, Real-time frequency and 2-D angle estimation with sub-Nyquist
Ssatio-temporal sampling. IEEE Transaction on Signal Processing. 1994;42(10):2781-2794.

Kitavi DM, Wong KT, Zou M, Agrawal K. A lower bound of the estimation error of an
emitter's direction of arrival/polarization for collocated triad of orthogonal dipoles/loops that
fail randomly. IET Microwaves, Antennas, and Propagation. 2017;11(7):961-970.

Kitavi DM, Lin TC, Wong KT, Wu YI. Direction nding with the sensors gains suering
Bayesian uncertainty - hybrid CRB and MAP estimation. IEEE Transactions on Aerospace
and Electronic Systems. 2016;52(4):2038-2044.

Kitavi DM, Lin TC,Wong KT. A tetrahedral array of isotropic sensors, each suering a random
complex gainthe resulting hybrid Cramr-Rao bound for direction nding. IEEE National
Conference On Aerospace and Electronics Conference (NAECON) and Ohio Innovation
Summit (OIS). 2016;412-415.

Hui C, Zheng B. Performance analysis of self-calibration algorithm for concentric-UCA. IEEE
International Conference on Wireless Communications and Signal Processing. 2010;1-5.

Leong PH, Abhayapala TD, Lamahewa TA. Multiple target localization using wideband echo
chirp signals. IEEE Transactions on Signal Processing. 2013;61(16):4077-4089.

Liao B, Tsui KM, Chan SC. Frequency invariant uniform concentric circular arrays with
directional elements. IEEE Transactions on Aerospace and Electronic Systems. 2013;49(2):871-

Akkar S, Harabi F, Gharsallah A, Concentric circular-shaped electronically steerable parasitic
array radiator antennas for full-azimuth directions of arrival estimation with reduced
computational load. IET Microwaves, Antennas and Propagation. 2012;6(11):1236-1243.

Gazzah H, Delmas JP, Sergio MJL. Direction-nding arrays of directional sensors for randomly
located sources. IEEE Transactions on Aerospace and Electronic Systems. 2016;52(4):1995-

Vu DT, Alexandre R, Rmy B, Sylvie M. A Cramr Rao bounds based analysis of 3D antenna
array geometries made from ULA branches. Multidimensional Systems and Signal Processing.

Delmas JP. Performance bounds and statistical Analysis of DOA estimation. In Academic
Press Library in Signal Processing. 2014;3:719-764. Elsevier