Tensor Approach for Eigenvector-Based Multi-Dimensional Harmonic Retrieval

In this paper, we propose an eigenvector-based frequency estimator for
R
-dimensional (
R
-D) sinusoids with
R
≥ 2 in additive white Gaussian noise. Our underlying idea is to utilize the tensorial structure of the received data and then apply higher-order singular value decomposition (HOSVD) and structure least squares (SLS) to perform estimation. After obtaining the tensor-based signal subspace from HOSVD, we decompose it into a set of single-tone tensors from which single-tone vectors can be constructed by another HOSVD. In doing so, the
R
-D multiple sinusoids are converted to a set of single-tone sequences whose frequencies are individually estimated according to SLS. The mean and variance of the frequency estimator are also derived. Computer simulations are also included to compare the proposed approach with conventional
R
-D harmonic retrieval schemes in terms of mean square error performance and computational complexity particularly in the presence of identical frequencies.