Mode- ${cal R}$ Subspace Projection of a Tensor for Multidimensional Harmonic Parameter Estimations

In Multidimensional Harmonic Retrieval (MHR) problems, it is understood that the multidimensional structure of the measurement data, with a tensor representation, can be exploited to improve the parameter estimation accuracy. In this paper, the mode-ℜ subspace of the tensor representation, based on the general matricization of the tensor, is first defined. It is found that there is a subordinate relation among the different mode- ℜ signal subspaces. As a result, the measurement tensor can be projected to the mode- ℜ signal subspaces in a bottom-up way, and the long-vector signal subspace required by the many signal subspace based parameter estimation algorithms can be refined. As an example, a mode-ℜ projection based Tensor-ESPRIT algorithm is presented. The reason why mode-ℜ subspace projections bring about performance improvement becomes obvious by the first order perturbation analyses. These analyses also generate two criteria on how the mode-ℜ subspace based projection technique should be carried out. Simulations are conducted to verify the effectiveness of the algorithm and the analytical results.