Uniform and nonuniform V‐shaped planar arrays for 2‐D direction‐of‐arrival estimation

Abstract

[1] In this paper, isotropic and directional uniform and nonuniform V-shaped arrays are considered for azimuth and elevation direction-of-arrival (DOA) angle estimation simultaneously. It is shown that the uniform isotropic V-shaped arrays (UI V arrays) have no angle coupling between the azimuth and elevation DOA. The design of the UI V arrays is investigated, and closed form expressions are presented for the parameters of the UI V arrays and nonuniform V arrays. These expressions allow one to find the isotropic V angle for different array types. The DOA performance of the UI V array is compared with the uniform circular array (UCA) for correlated signals and in case of mutual coupling between array elements. The modeling error for the sensor positions is also investigated. It is shown that V array and circular array have similar robustness for the position errors while the performance of UI V array is better than the UCA for correlated source signals and when there is mutual coupling. Nonuniform V-shaped isotropic arrays are investigated which allow good DOA performance with limited number of sensors. Furthermore, a new design method for the directional V-shaped arrays is proposed. This method is based on the Cramer-Rao Bound for joint estimation where the angle coupling effect between the azimuth and elevation DOA angles is taken into account. The design method finds an optimum angle between the linear subarrays of the V array. The proposed method can be used to obtain directional arrays with significantly better DOA performance.Citation: Filik, T., and T. E. Tuncer (2009), Uniform and nonuniform V-shaped planar arrays for 2-D direction-of-arrival estimation, Radio Sci., 44, RS5006,

A fast and automatically paired 2-D direction-of-arrival estimation with and without estimating the mutual coupling coefficients

“…Therefore c = [1 c 1 ] and MCM is an 11 × 11 banded Toeplitz matrix with five nonzero diagonals. The coupling coefficient is selected as, c 1 = 0.35 + 0.10 j as in the work of Filik and Tuncer [2009a, 2009b].…”

“…The normed expression in can be written as, where G c H QG c is The dimensions of the Q i , j submatrices are ( K + 1) × ( K + 1). It is possible to express tr { G c H QG c } as If we apply the Lagrangian approach for the solution of the modified constraint equation of , we obtain the coupling coefficients as, Once the coupling coefficients are found, banded Toeplitz MCM estimate, , can be constructed easily [ Friedlander and Weiss , 1991; Filik and Tuncer , 2009a, 2009b]. The array interpolation matrices 12 and 13 required for generating the two virtual arrays in Figure 2 can be found from, where A 1 (), A 2 () and A 2 () are constructed as explained in section 3.1 for the given angular sector.…”

“…In this case, the eigenvalues of the rotational transformation matrix for the ESPRIT algorithm [ Roy and Kailath , 1989; Stoica and Nehorai , 1991] contain the azimuth and elevation angle information both in the magnitude and phase terms. Closed form expressions for azimuth and elevation angles can be obtained from the resulting two equations [ Filik and Tuncer , 2009a, 2009b]. The proposed technique is integrated with array interpolation in order to use antennas efficiently.…”

V-Shaped Sparse Arrays for 2-D DOA Estimation

“…the estimation error of azimuth (or elevation) does not affect the accuracy of elevation (azimuth) estimation. In order to obtain uncoupled DOA estimation, the cross terms of the Fisher information matrix need to be zero [7,13]. This condition can be satisfied by placing the sensors in accordance with the V-angle selected as…”

Semi-circular antenna array for azimuth DOA estimation

“…Further development of array geometry expands for two-dimensional (2D) DOA estimation; circular [7][8][9][10], triangular and rectangular array [9,11]. Most recent array geometries for 2D DOA estimation are L-shape [12,13], V-shape [14], and sparse array [15]. Recent development of array design is motivated to solve 2D estimation problems such as pair matching, estimation failure and narrow aperture [13].…”