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A new direction-of-arrival (DOA) estimation method is proposed based on a novel data model using the concept of a sparse representation of array covariance vectors (SRACV), in which DOA estimation is achieved by jointly finding the sparsest coefficients of the array covariance vectors in an overcomplete basis. The proposed method not only has high resolution and the capability of estimating coherent signals based on an arbitrary array, but also gives an explicit error-suppression criterion that makes it statistically robust even in low signal-to-noise-ratio (SNR) cases. Simulation experiments are conducted to validate the effectiveness of the proposed method. The performance is compared with several existing DOA estimation methods and the Cramér-Rao lower bound (CRLB).