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In this correspondence, a computationally efficient method that combines the subspace and projection separation approaches is developed for R -dimensional (R-D) frequency estimation of multiple sinusoids, where R ≥ 3, in the presence of white Gaussian noise. Through extracting a 2-D slice matrix set from the multidimensional data, we devise a covariance matrix associated with one dimension, from which the corresponding frequencies are estimated using the root-MUSIC method. With the use of the frequency estimates in this dimension, a set of projection separation matrices is then constructed to separate all frequencies in the remaining dimensions. Root-MUSIC method is again applied to estimate these single-tone frequencies while multidimensional frequency pairing is automatically attained. Moreover, the mean square error of the frequency estimator is derived and confirmed by computer simulations. It is shown that the proposed approach is superior to two state-of-the-art frequency estimators in terms of accuracy and computational complexity.