Tensor-Based Spatial Smoothing (TB-SS) Using Multiple Snapshots

Arpita Thakre, Martin Haardt, Florian Roemer, K. Giridhar
2010 IEEE Transactions on Signal Processing  
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
more » ... bspace 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 Cramér-Rao bound (CRB) for the 1-D damped harmonic retrieval problem is also derived. Index Terms-Damped harmonics, direction of arrival (DOA) estimation, higher-order tensor, higher-order singular value decomposition (HOSVD), multidimensional signal processing, multilinear algebra, parameter estimation, tensor-based spatial smoothing (TB-SS), tensor-ESPRIT.
doi:10.1109/tsp.2010.2043141 fatcat:2tmvl2zqkvaudkjnb5dgqev7gy