Eigenvector-Based $N$-D Frequency Estimation From Sample Covariance Matrix

We propose an algebraic approach for N-D frequency estimation using the eigenvectors of a matrix pencil constructed from the signal subspace of the data sample covariance matrix. Unlike existing eigenvalue-based methods, the proposed algorithm achieves automatic frequency pairing without using joint diagonalization; thus, the computational complexity is reduced. The proposed algorithm remains operational in the presence of identical frequencies in one or more dimensions due to the introduction of weighting factors when constructing the matrix pencil. We also derive the theoretic variance of the estimation error and show that the proposed algorithm is a consistent one