2-D normalized frequency estimation using 4-way tensor processing

Abstract

We propose a novel subspace-based 2-D damped harmonic retrieval algorithm that uses a single snapshot of data. The data is packed into a measurement tensor and spatial smoothing is applied to it to get a spatially smoothed tensor. We observe a structure inherent in the spatially smoothed tensor. This structure can be fully exploited by constructing multiple higher-order tensors from the spatially smoothed tensor and by running parameter estimation algorithm multiple times, one for each dimension. In this paper we propose to construct a single higher-order tensor and perform a single higher-order singular value decomposition (HOSVD) for estimating the normalized frequencies along the two dimensions. The proposed algorithm performs significantly better than Tensor-ESPRIT applied to the spatially smoothed tensor, and matrix-based approaches. Moreover, it is insensitive to changes in the number of samples per subarray. Our work can be extended to R-D damped harmonic retrieval problems.