Multidimensional Single-Tone Frequency Estimation Based on QR Decomposition

In this paper, the problem of multidimensional single-tone frequency estimation of sinusoids embedded in white Gaussian noise is investigated. By extracting the two-dimensional (2-D) slice matrices from the multidimensional data, we construct a covariance matrix associated with only one dimension, from which the corresponding frequency is estimated with the utilization of a QR decomposition based iterative method. The frequencies of the remaining dimensions are then obtained following similar procedures. Moreover, the mean square error of the estimated frequencies is devised. The computer simulations are also included to evaluate the performance of the proposed method by comparing with the several state-of-the-art algorithms and Cramér–Rao lower bound.