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This paper presents a direction of arrival (DOA) estimation method. Spectral-domain interferometer equation is first established based on integral transforms of spatial interferometer equations. The direction finding problem in the spatial domain is thereby mapped to that in the spectral domain, relating angular parameters to spatial spectrums. This method is then applied to DOA estimation with circular arrays and spherical arrays. As a result, the elevation angle and azimuth angle are decoupled, giving closed-form and analytical formulae for DOA estimations by discrete phase samples on a sampling aperture. Algebraic relations between angular parameters and phase samples are established, and this method is hence computationally efficient. The Cramer-Rao lower bound (CRLB) of the proposed method is derived, and accuracy analysis demonstrates that the proposed method approaches the CRLB. In addition, mathematical insights into accuracy enhancement by large number of samples are observed via Parseval’s theorem. Finally, numerical simulations and experimental measurements are provided to verify the effectiveness and appealing performance of the proposed method.

FAST DOA ESTIMATION IN THE SPECTRAL DOMAIN AND ITS APPLICATIONS