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In this letter, we propose a coprime array interpolation approach to provide an off-grid direction-of-arrival (DOA) estimation. Through array interpolation, a uniform linear array (ULA) with the same aperture is generated from the deterministic non-uniform coprime array. Taking the observed correlations calculated from the signals received at the coprime array, a gridless convex optimization problem is formulated to recover all the rows and columns of the unknown correlation matrix entries corresponding to the interpolated sensors. The optimized Hermitian positive semidefinite Toeplitz matrix functions as the covariance matrix of the interpolated ULA, which enables to resolve off-grid sources. Simulation results demonstrate that the proposed array interpolation-based DOA estimation algorithm achieves improved performance as compared to existing coarray-based DOA estimation algorithms in terms of the number of …