Tensor decompositions with several block-Hankel factors and application in blind system identification

Frederik Van Eeghem, Mikael Sørensen, Lieven De Lathauwer


Several applications in biomedical data processing, telecommunications, or chemometrics can be tackled by computing a structured tensor decomposition. In this paper, we focus on tensor decompositions with two or more block-Hankel factors, which arise in blind multiple-input-multiple-output (MIMO) convolutive system identification. By assuming statistically independent inputs, the blind system identification problem can be reformulated as a Hankel structured tensor decomposition. By capitalizing on the available block-Hankel and tensorial structure, a relaxed uniqueness condition for this structured decomposition is obtained. This condition is easy to check, yet very powerful. The uniqueness condition also forms the basis for two subspace-based algorithms, able to blindly identify linear underdetermined MIMO systems with finite impulse response.

Code description

This package provides an implementation of the subspace methods discussed in the tensor decomposition for BSI paper for performing blind system identification of MIMO convolutive systems using tensor decompositions with block-Hankel structured factor matrices. It also provides files to generate the experiments from the paper. (The comparison with algorithms from external packages has not been implemented here.)


F. Van Eeghem, M. Sørensen and L. De Lathauwer, "Tensor decompositions with several block-Hankel factors and application in blind system identification," IEEE Transactions on Signal Processing, vol. 65, no. 15, pp. 4090-4101, Aug. 2017.

Download code

This repository can be cited as:
S. Hendrikx, M. Boussé, N. Vervliet, M. Vandecappelle, R. Kenis, and L. De Lathauwer, Tensorlab⁺, Available online, Version of Dec 2022 downloaded from https://www.tensorlabplus.net.