Spatial filtering method based on the Tucker decomposition

In the paper, an algorithm based on the Tucker decomposition is proposed for computing spatial filter coefficients. The most computationally expensive part of the spatial filtering algorithm is the singular value decomposition of the channel matrix. The Tucker decomposition allows us to calculate the compressed core of the channel tensor. Thus, the further calculation of the singular value decomposition takes place using matrices of a smaller dimension (tensor core), which reduces the computational costs of the algorithm. The paper provides analytical estimates of the rank for the tensor decomposition to preserve the precision of the representation, and also provides a condition of efficient usage the proposed method. A simulation of wireless data transmission was performed to demonstrate the accuracy of the proposed method. The main difference between the method and its existing analogues is that all operations are performed on the tensor core, followed by projection of the result using factorization matrices.