An Eigenvector-Based Approach for Multidimensional Frequency Estimation With Improved Identifiability

This paper presents an algebraic method for two-dimensional (2-D) and multidimensional frequency estimation by exploiting eigenvector structure. The algorithm is based on multidimensional smoothing and data folding, and offers significantly improved identifiability (ID) over existing algebraic approaches, thus is termed the improved multidimensional folding (IMDF) algorithm. The ID, performance, and computational complexity of the proposed algorithm are analyzed in detail. In the 2-D case, it is shown that with the IMDF algorithm, up to approximately 0.34M₁(M₂+1) 2-D frequencies can be uniquely resolved with probability one from an M₁ by M₂ data mixture (assuming M₁gesM₂), while the most relaxed ID bound offered by existing algebraic approaches is approximately M₁M₂/4. Unlike most eigenvalue techniques that usually require an extra frequency association step, the IMDF algorithm achieves automatic frequency pairing once an eigenvalue decomposition problem is solved because frequencies are estimated from the eigenvectors instead of the eigenvalues. Theoretical analysis and simulation results demonstrate its competitive performance compared to the Crameacuter-Rao bound (CRB)