Publication Type:

Journal Article


IEEE Transactions on Signal Processing, Volume 58, Number 5, p.2715-2728 (2010)


1D damped harmonic retrieval problem, Damped harmonics, direction of arrival (DOA) estimation, Harmonic analysis, high structured measurement tensor, higher-order singular value decomposition (HOSVD), higher-order tensor, matrix-based subspace estimation, measurement tensor, multichannel data, multidimensional invariance property, multidimensional signal processing, multilinear algebra, one-dimensional damped harmonics, Parameter estimation, Singular value decomposition, Smoothing methods, spatial smoothed matrix, stochastic Crame??r-Rao bound, subspace-based parameter estimation, tensor-based signal subspace estimation scheme, tensor-based spatial smoothing, tensor-based spatial smoothing (TB-SS), tensor-ESPRIT, Tensors


Tensor-based spatial smoothing (TB-SS) is a preprocessing technique for subspace-based parameter estimation of damped and undamped harmonics. In TB-SS, multichannel data is packed into a measurement tensor. We propose a tensor-based signal subspace estimation scheme that exploits the multidimensional invariance property exhibited by the highly structured measurement tensor. In the presence of noise, a tensor-based subspace estimate obtained via TB-SS is a better estimate of the desired signal subspace than the subspace estimate obtained by, for example, the singular value decomposition of a spatially smoothed matrix or a multilinear algebra approach reported in the literature. Thus, TB-SS in conjunction with subspace-based parameter estimation schemes performs significantly better than subspace-based parameter estimation algorithms applied to the existing matrix-based subspace estimate. Another advantage of TB-SS over the conventional SS is that TB-SS is insensitive to changes in the number of samples per subarray provided that the number of subarrays is greater than the number of harmonics. In this paper, we present, as an example, TB-SS in conjunction with ESPRIT-type algorithms for the parameter estimation of one-dimensional (1-D) damped and undamped harmonics. A closed form expression of the stochastic Crame??r-Rao bound (CRB) for the 1-D damped harmonic retrieval problem is also derived.

Cite this Research Publication

Arpita Thakre, Haardt, M., Roemer, F., and Giridhar, K., “Tensor-Based Spatial Smoothing (TB-SS) Using Multiple Snapshots”, IEEE Transactions on Signal Processing, vol. 58, pp. 2715-2728, 2010.