Statistical Identifiability of Multidimensional Frequency Estimation with Finite Snapshots

Recently much progress has been made to improve the identifiability of frequency estimation from one snapshot of multidimensional frequency data mixture. However, in the case of multiple snapshots (or multiple trials of experiments), there are few identifiability results available. With multiple data snapshots, most existing algebraic approaches estimate frequencies from the sample covariance matrix. In this work we provide an upper bound on the maximum number of multidimensional frequencies that can be estimated for a given data size with finite snapshots. We show how the identifiability bound increases as the number of snapshots increases. An eigenvector-based algorithm is also obtained for N-D frequency estimation. Simulation results show the proposed algorithm offers competitive performance when compared with existing algebraic algorithms but with reduced complexity