Co-prime arrays can estimate the directions of arrival (DOAs) of O(MN) sources with\nO(M+ N) sensors, and are convenient to analyze due to their closed-form expression for the locations\nof virtual lags. However, the number of degrees of freedom is limited due to the existence of holes\nin difference coarrays if subspace-based algorithms such as the spatial smoothing multiple signal\nclassification (MUSIC) algorithm are utilized. To address this issue, techniques such as positive\ndefinite Toeplitz completion and array interpolation have been proposed in the literature. Another\nfactor that compromises the accuracy of DOA estimation is the limitation of the number of snapshots.\nCoarray-based processing is particularly sensitive to the discrepancy between the sample covariance\nmatrix and the ideal covariance matrix due to the finite number of snapshots. In this paper, coarray\ninterpolation based on matrix completion (MC) followed by a denoising operation is proposed to\ndetect more sources with a higher accuracy. The effectiveness of the proposed method is based on the\ncapability of MC to fill in holes in the virtual sensors and that of MC denoising operation to reduce\nthe perturbation in the sample covariance matrix. The results of numerical simulations verify the\nsuperiority of the proposed approach.
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