Single Snapshot R-D Unitary Tensor-ESPRIT Using an Augmentation of the Tensor Order

Abstract

Single snapshot R-D unitary tensor-ESPRIT using an augmentation of the tensor order (SS-U-TE-ATO) is a subspace-based parameter estimation technique for R-dimensional (R-D) undamped harmonics using a single snapshot of data. In SS-U-TE-ATO the measurement data is packed into a measurement tensor to which spatial smoothing is applied. We propose the construction of R higher-order tensors from the spatially smoothed tensor by exploiting the inherent structure of the spatially smoothed tensor. In the next step of SS-U-TE-ATO, R enhanced real-valued signal subspace estimates, one for each dimension, are obtained from the R complex-valued higher-order tensors. We show that SS-U-TE-ATO performs significantly better than unitary tensor-ESPRIT (U-TE) directly applied to the spatially smoothed tensor. Moreover, for each dimension, SS-U-TE-ATO is almost insensitive to changes in the number of sensors per subarray provided that the number of subarrays is greater than the number of sources. Thereby we avoid the problem of selecting the optimum subarray size for a given source configuration.