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Recently, direction of arrival (DOA) estimation premised on the sparse arrays interpolation approaches, such as co-prime arrays (CPA) and nested array, have attained extensive attention because of the effectiveness and capability of providing higher degrees of freedom (DOFs). The co-prime array interpolation approach can detect O(MN) paths with O(M + N) sensors in the array. However, the presence of missing elements (holes) in the difference coarray has limited the number of DOFs. To implement co-prime coarray on subspace based DOA estimation algorithm namely multiple signal classification (MUSIC), a reshaping operation followed by the spatial smoothing technique have been presented in the literature. In this paper, an active coarray interpolation (ACI) is proposed to efficiently recovering the covariance matrix of the augmented coarray from the original covariance matrix of source signals with no vectorizing and spatial smoothing operation; thus, the computational complexity reduces significantly. Moreover, the numerical simulations of the proposed ACI approach offers better performance compared to its counterparts. [ABSTRACT FROM AUTHOR]