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This paper has made proposition of a nested array and an estimation algorithm for direction-of-arrival (DOA) of two-dimensional (2D) coherently distributed (CD) sources. According to the difference coarray concept, double parallel hole-free virtual uniform linear arrays are generated by virtue of vectorization operation on cross-correlation matrices of subarrays. Sensor coordinates of virtual arrays are derived. Rational invariance relationships of virtual arrays are derived. According to the rotational invariance relationships, matrices satisfying rotation invariance are constructed by extracting and regrouping the receive vectors of the virtual arrays, and then an estimation of signal parameters via rotational invariance techniques- (ESPRIT-) like framework on matrix reconstruction is deduced. Optimal configuration of the nested array as well as computational complexity are analyzed. Without pair matching, the proposed method can resolve more sources than the sensor number. Simulation outcomes indicate that the proposed method tends to have a better performance as compared to the traditional uniform arrays that have similar number of sensors. [ABSTRACT FROM AUTHOR]

A direction of arrival (DOA) estimator for two-dimensional (2D) incoherently distributed (ID) sources is presented under proposed double cross arrays, satisfying both the small interval of parallel linear arrays and the aperture equalization in the elevation and azimuth dimensions. First, by virtue of a first-order Taylor expansion for array manifold vectors of parallel linear arrays, the received signal of arrays can be reconstructed by the products of generalized manifold matrices and extended signal vectors. Then, the rotating invariant relations concerning the nominal elevation and azimuth are derived. According to the rotating invariant relationships, the rotating operators are obtained through the subspace of the covariance matrix of the received vectors. Last, the angle matching approach and angular spreads are explored based on the Capon principle. The proposed method for estimating the DOA of 2D ID sources does not require a spectral search and prior knowledge of the angular power density function. The proposed DOA estimation has a significant advantage in terms of computational cost. Investigating the influence of experimental conditions and angular spreads on estimation, numerical simulations are carried out to validate the effectiveness of the proposed method. The experimental results show that the algorithm proposed in this paper has advantages in terms of estimation accuracy, with a similar number of sensors and the same experimental conditions when compared with existing methods, and that it shows a robustness in cases of model mismatch. [ABSTRACT FROM AUTHOR]