Multilinear Generalized Singular Value Decomposition (ML-GSVD) and Its Application to Multiuser MIMO Systems

Khamidullina, Liana; Almeida, André L. F. de; Haardt, Martin

doi:10.1109/tsp.2022.3178902

Cited by 6 publications

(7 citation statements)

References 40 publications

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“…Thanks to the ML-GSVD [15], [16], each slice H k of the tensor H can be split into the private matrices B k and C k , and the common matrix A, as described by (see also Fig. 2)…”

Section: A the Roeml-gsvd Designmentioning

confidence: 99%

“…Before we move to the design of robust beamformers based on the aforementioned tensor decomposition, let us emphasize the distinction between the CSI-error-robust ROEML-GSVD here proposed and previous contributions, including our earlier OEML-GSVD algorithm offered in [5], and the ML-GSVD scheme of [15], [16].…”

Section: B Performance Of Roeml-gsvdmentioning

confidence: 99%

“…As a consequence of the latter, the optimized matrices B k obtained as in equation (12) are also functions of the channel estimation error factor γ, thus differing from those obtained under the SotA methods [5], [15]. And naturally, since the other terms C k and A are computed directly from B k as per equations ( 13) to (16), the decomposition matrices (B k , C k , A) obtained under the proposed ROEML-GSVD scheme are distinct from those obtained via the ML-GSVD and our earlier OEML-GSVD.…”

Section: B Performance Of Roeml-gsvdmentioning

confidence: 99%

“…H corresponding to the OEML-GSVD of [5], the ML-GSVD of [15], [16], and the here-proposed ROEML-GSVD of Subsection A, for two distinct scenarios with smaller and larger CSI errors. It can be seen that indeed the new algorithm has a convergence 3 slope similar to that of the OEML-GSVD.…”

Section: B Performance Of Roeml-gsvdmentioning

confidence: 99%

“…In turn, tensor decomposition algorithms such as OEML-GSVD and the earlier multilinear generalized singular value decomposition (ML-GSVD) [15], [16] have inherent decomposition errors even if perfect CSI is available, such that accuracy of the tensor-based BF approach is exposed to both sources of degradation. This article aims to mitigate this issue, by adding to the OEML-GSVD-based BF design method of [5] robustness to both CSI imperfection and to the tensor decomposition error, yielding a new robust OEML-GSVD (ROEML-GSVD) scheme and corresponding TX and RX BF for both downlink (DL) and uplink (UL) transmissions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Robust Tensor Decomposition for Heterogeneous Beamforming Under Imperfect Channel State Information

Ando

Ishibashi

Abreu

2023

IEEE Open J. Signal Process.

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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 transmit (TX) and receive (RX) beamforming (BF) for both the downlink (DL) and the uplink (UL) of cell-free massive multiple-input multiple-output (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 channel state information (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 state-of-the-art (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.INDEX TERMS Tensor decomposition, transmit and receive beamforming, heterogeneous cell-free massive MIMO systems.

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“…Thanks to the ML-GSVD [15], [16], each slice H k of the tensor H can be split into the private matrices B k and C k , and the common matrix A, as described by (see also Fig. 2)…”

Section: A the Roeml-gsvd Designmentioning

confidence: 99%