Volumetric array geometry design for direction of arrival estimation under array imperfections

Direction of arrival (DOA) estimation has been studied comprehensively for several decades. The DOA estimation performance depends on several parameters. Some of these important parameters are the number of sources, the direction of sources, the number and location of the sensors in the array. In practical DOA estimation systems, closely spaced antennas (sensors) inevitably cause electromagnetic mutual coupling (MC), and largely spaced array elements cause angle estimation ambiguity. Also, reflection, refraction, diffraction, and scattering of propagating waves distort the well-known array model. All these practical effects, which can be called as array imperfections, are challenging issues for DOA systems. Nowadays, DOA estimation systems are not located on the ground, they are flying, and the targets are also mobile. In this dynamic scenario, both the azimuth and elevation angles (i.e., two-dimensional, 2-D) estimation performance should be isotropic. The isotropic arrays have equal Cram\'{e}r-Rao lower bound levels for all azimuth and elevation directions. This can only be possible with some special volumetric arrays. In this study, new volumetric (i.e., three-dimensional, 3-D) sensor array geometry designs are investigated and analyzed under array imperfections. The proposed methods are based on adding a minimum number of additional sensors under constraints of 2-D isotropy, mutual coupling, and angle ambiguity. The constraints on the sensors' locations and numbers to be added over the given arrays are analytically derived. Firstly, the potentials of volumetric V-shaped arrays are considered for 2-D isotropic DOA estimation. Then more generic extension layout for centrosymmetric planar arrays is presented. Finally, an optimum array extension approach, which can be applicable to arbitrary linear and planar arrays, is proposed for 2-D isotropic DOA estimation. Analytical results have been verified with various simulation results for all these arrays. We also considered multiple UAVs as volumetric sensor array for 2-D DOA estimation of hidden emitters as the future airborne DF system scenario.