DOA Estimation for Generalized Three Dimensional Coprime Arrays: A Fast-Convergence Quadrilinear Decomposition Algorithm

• Published in: IEEE access Vol. 6; pp. 62419 - 62431
• Main Authors: Gong, Pan, Zhang, Xiaofei, Zhai, Hui
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; computational complexity; Computer simulation; Convergence; Cramer-Rao bounds; Decomposition; Direction of arrival; Direction of arrival (DOA) estimation; Direction-of-arrival estimation; Estimates; Estimation; fast convergence quadrilinear decomposition (FC-QD); generalized three dimensional coprime array (G-TDCA); Geometry; Mathematical models; Sensor arrays; Sensors; Signal processing algorithms; Steering; Two dimensional displays
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2018.2871028

In this paper, we construct the generalized 3-D coprime array (G-TDCA) configuration, which consists of two 2-D uniform subarrays, by selecting three pairs of coprime integers to obtain the extension of inter-element spacing. Meanwhile, we derive the analytical expression of Cramer-Rao bound for G-TDCA and verify that G-TDCA outperforms the conventional 3-D uniform array (TDUA) in the direction of arrival (DOA) (i.e., azimuth and elevation angles) estimation performance and resolution with numerical simulations. In addition, we propose a fast convergence quadrilinear decomposition (FC-QD) algorithm to extract the DOA estimates for G-TDCA. In the FC-QD algorithm, we first employ propagator method (PM) to achieve rough DOA estimates that are utilized to initialize the steering matrices. Subsequently, the received signal is constructed as two quadrilinear models and quadrilinear alternating least square algorithm is operated to attain fine DOA estimates. Moreover, phase ambiguity problem, caused by large adjacent distance between array sensors, is eliminated based on coprime property, where the uniqueness of DOA estimates can be achieved. Specifically, the proposed FC-QD algorithm has a fast convergence due to initialization via PM, and hence, FC-QD can significantly lower the computational cost without degrading the DOA estimation performance, which is demonstrated by extensive simulation results.