Generalized tensor contraction with application to khatri-rao coded MIMO OFDM systems

Naskovska, Kristina; Haardt, Martin; Almeida, André L. F. de

doi:10.1109/camsap.2017.8313190

Cited by 11 publications

(5 citation statements)

References 18 publications

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“…Moreover, for a tensor with a CP structure, its unfoldings and generalized unfoldings can be expressed in terms of the factor matrices. For instance, the generalized unfolding [3,4]) of the tensor A satisfies [18,25] In a similar way, the rest of the tensor unfoldings and generalized unfoldings can be defined.…”

Section: The Cp Decomposition and Generalized Tensor Unfoldingsmentioning

confidence: 99%

“…The tensor Ỹ0 ∈ C N ×M R ×K represents the noiseless received signal in the frequency domain after the removal of the cyclic prefix. The frequency-selective propagation channel is represented by a channel tensor H ∈ C N ×N ×M R ×M T as we propose in [18] the structure of which is detailed as follows.…”

Section: Mimo-ofdmmentioning

confidence: 99%

“…More specifically, we first present the double contraction between an uncoded signal tensor and a channel tensor for OFDM systems, yielding the same spectral efficiency as matrix-based approaches (since no additional spreading is used) [17]. We propose an application of the double contraction operator to Khatri-Rao-coded MIMO-OFDM systems [18]. Due to the Khatri-Rao coding, the signal tensor has a richer structure and can be recast as a constrained CP-like model.…”

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confidence: 99%

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Using tensor contractions to derive the structure of slice-wise multiplications of tensors with applications to space–time Khatri–Rao coding for MIMO-OFDM systems

Naskovska

Sokal²,

Almeida³

et al. 2022

EURASIP J. Adv. Signal Process.

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The slice-wise multiplication of two tensors is required in a variety of tensor decompositions (including PARAFAC2 and PARATUCK2) and is encountered in many applications, including the analysis of multidimensional biomedical data (EEG, MEG, etc.) or multi-carrier multiple-input multiple-output (MIMO) systems. In this paper, we propose a new tensor representation that is not based on a slice-wise (matrix) description, but can be represented by a double contraction of two tensors. Such a double contraction of two tensors can be efficiently calculated via generalized unfoldings. It leads to new tensor models of the investigated system that do not depend on the chosen unfolding (in contrast to matrix models) and reveal the tensor structure of the data model, such that all possible unfoldings can be seen at the same time. As an example, we apply this new concept to the design of new receivers for multi-carrier MIMO systems in wireless communications. In particular, we consider MIMO-orthogonal frequency division multiplexing (OFDM) systems with and without Khatri–Rao coding. The proposed receivers exploit the channel correlation between adjacent subcarriers, require the same amount of training symbols as traditional OFDM techniques, but have an improved performance in terms of the symbol error rate. Furthermore, we show that the spectral efficiency of the Khatri–Rao-coded MIMO-OFDM can be increased by introducing cross-coding such that the “coding matrix” also contains useful information symbols. Considering this transmission technique, we derive a tensor model and two types of receivers for cross-coded MIMO-OFDM systems using the double contraction of two tensors.

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Section: The Cp Decomposition and Generalized Tensor Unfoldingsmentioning

confidence: 99%

Section: Mimo-ofdmmentioning

confidence: 99%

mentioning

confidence: 99%

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Using tensor contractions to derive the structure of slice-wise multiplications of tensors with applications to space–time Khatri–Rao coding for MIMO-OFDM systems

Naskovska

Sokal²,

Almeida³

et al. 2022

EURASIP J. Adv. Signal Process.

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“…The received data matrix Y (D) ∈ C M R L P ×KF D can be interpreted as a generalized unfolding [12] of the fourth-order received data tensor Y (D) ∈ C M R ×L P ×K×F D given by…”

Section: Stage 2: Data Estimationmentioning

confidence: 99%

“…Recently, tensor-based receivers were proposed for MIMO-OFDM systems [12][13][14][15][16]. However, these works do not take into account practical system impairments such as the phase-noise that leads to ICI.…”

Section: Introductionmentioning

confidence: 99%

Joint Channel, Data, and Phase-Noise Estimation in MIMO-OFDM Systems Using a Tensor Modeling Approach

Sokal

Gomes

Almeida

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this work, we propose a two-stage tensor-based receiver for joint channel, phase-noise (PN), and data estimation in MIMO-OFDM systems. First, we cast the received signal at the pilot subcarriers as a third-order PARAFAC model. Based on this model, we propose a closed-form algorithm based on the LS-KRF (Least Squares -Khatri-Rao Factorization) that estimates the channel gains and the phase-noise terms through multiple rank-one factorizations. From the estimated channel, the second stage of the receiver consists of data estimation based on a ZF (Zero-Forcing) receiver that capitalizes on the tensor structure of the received signal at the data subcarriers via a Selective Kronecker Product (SKP) approach. Our numerical simulations show that the proposed receiver achieves an improved performance compared to the state-of-art receivers.

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Efficient Computation of the PARAFAC2 Decomposition via Generalized Tensor Contractions

Naskovska

Cheng

Almeida

et al. 2018

2018 52nd Asilomar Conference on Signals, Systems, and Computers

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Generalized tensor contraction with application to khatri-rao coded MIMO OFDM systems

Cited by 11 publications

References 18 publications

Using tensor contractions to derive the structure of slice-wise multiplications of tensors with applications to space–time Khatri–Rao coding for MIMO-OFDM systems

Using tensor contractions to derive the structure of slice-wise multiplications of tensors with applications to space–time Khatri–Rao coding for MIMO-OFDM systems

Joint Channel, Data, and Phase-Noise Estimation in MIMO-OFDM Systems Using a Tensor Modeling Approach

Efficient Computation of the PARAFAC2 Decomposition via Generalized Tensor Contractions

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