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The antispoofing method using the direction-of-arrival (DOA) feature can effectively improve the application security of the global navigation satellite system (GNSS) receivers. In this paper, a sparse reconstruction approach based on a coprime array of antennas is proposed to provide reliable DOA estimation under a GNSS spoofing attack. Specifically, the self-coherence property of genuine satellite signals and spoofing was fully exploited to construct a denoised covariance matrix that enables DOA estimation before receiver despreading. Based on this, an equivalent uniform linear array (ULA) was generated from the constructed covariance matrix via virtual array interpolation. By applying the ideal of sparse reconstruction to an equivalent ULA signal, the preliminary DOA estimation results could be obtained without the need for a number of signals. Considering that the sparse estimation technique suffers from basis mismatch effects, we designed an optimization problem with respect to off-grid error to compensate the initial DOA such that the performance loss of DOA estimation could be reduced. Numerical examples demonstrated the advantages of the proposed method in terms of degrees-of-freedom (DOFs), resolution and accuracy. [ABSTRACT FROM AUTHOR]