Robust Tensor Decomposition for Heterogeneous Beamforming Under Imperfect Channel State Information

Abstract

We propose a new robust variation of the tensor decomposition known as the multi-linear generalized singular value decomposition (ML-GSVD), and demonstrate its effectiveness in the design of joint TX and RX BF for both the DL and the UL of CF-mMIMO systems. The new technique, dubbed the robust orthogonality-enforcing ML-GSVD (ROEML-GSVD), mitigates the degradation in the DL and UL BF design due to the tensor decomposition error and the CSI imperfection by exploiting their independence. Numerical results demonstrate that the proposed method is highly effective, leading not only to a significant reduction on the tensor decomposition error compared to SotA methods, but also to the improvement in the data rate achieved by the subsequent beamformers in heterogeneous scenarios where users have distinct numbers of antennas.