Abstract:
Source direction-of-arrival estimation problem has received much attention in recent years
following its significant role in array-signal processing and wide range of applications such
as radar, wireless communication, sonar, seismology among others. Direction finding has
been solved by several techniques such as Maximum likelihood estimator, MUltiple Signal
Classification, Estimation of Parameters via Rotational Invariance Technique and Cram´er-
Rao bound using array of sensors in both uniformly-spaced and non-uniformly-spaced.
The sensors have further been arranged in different geometric patterns ranging from onedimension
to three-dimensional. However, little effort has been made in direction finding
using concentric planar arrays with fixed centers at the Cartesian origin. In this study, a
new planar sensor-array geometry (the 2-circle concentric uniform array geometry) centered
at the Cartesian origin, that maximizes the array’s spatial aperture mainly for bivariate
azimuth-polar resolution of direction-of-arrival estimation problem was proposed. The
proposed geometry provides almost invariant azimuth angle coverage and offers the advantage
of full rotational symmetry (circular invariance) while maintaining an inter-sensor
spacing not exceeding half wavelength (for non-ambiguity with respect to the Cartesian
direction cosines) among other advantages. The study adopted Cram´er-Rao bound technique
of direction finding via a uniform circular array (single ring array) and the proposed
geometry to estimate the bivariate azimuth-polar angles-of-arrival. Both the array manifolds
and the Cram´er-Rao bounds for the uniform circular array and that of the proposed
array grid were derived. Further, a better-accurate performance in direction finding of the
proposed array grid over that of the single ring array grid was analytically verified under
different constraints of investigation. It was found that the proposed sensor-array geometry
has better estimation accuracy than a single ring array and the 2-circle concentric uniform
array geometry would have the best estimation accuracy for minimal number of sensors
hence reducing the hardware cost. The study therefore recommends that the 2-circle concentric
uniform array geometry should be used for direction finding with minimal number
of sensors and with an inter-sensor spacing not exceeding half a wavelength as opposed to
a uniform circular array geometry.
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