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An optimum 2-D DOA estimation algorithm with uniform circular array and its performance analysis

ABSTRACT This paper presents an optimum algorithm for two-dimensional (2-D) direction of arrival (DOA) estimation of a single source with uniform circular arrays (UCAs). The algorithm is computationally efficient due to its algebraic formulations for 2-D DOA estimation. It exploits Fourier transforms to expand the phase distribution and reformulate the underlying DOA estimation problem as an equivalent expansion coefficient extraction problem. Avoiding Fourier spectrum aliasing ensures that the minimum number of elements for 2-D DOA estimation is 3. Accuracy analysis demonstrates that it approaches the Cramer–Rao bound. In addition, mathematical insights into the relation between the estimation accuracy and the element number of a UCA are observed by employing Parseval’s theorem in the Fourier domain. Performance comparisons are made between a UCA and a linear array (LA) interferometer of the same aperture, showing that the ratio of accuracy of the UCA to that of the LA is , with N being the number of elements.