- Author final manuscript
**Rights statement:**©2022 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.Accepted author manuscript, 2.16 MB, PDF document

Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

- https://ieeexplore.ieee.org/document/9808393
Final published version

Research output: Contribution to Journal/Magazine › Journal article › peer-review

E-pub ahead of print

**Efficient Matrix Polynomial Expansion Detector for Large-Scale MIMO : An Inverse-Transform-Sampling Approach.** / Deng, Q.; Liang, X.; Ni, Q. et al.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Deng, Q, Liang, X, Ni, Q & Wu, J 2022, 'Efficient Matrix Polynomial Expansion Detector for Large-Scale MIMO: An Inverse-Transform-Sampling Approach', *IEEE Systems Journal*. https://doi.org/10.1109/JSYST.2022.3179299

Deng, Q., Liang, X., Ni, Q., & Wu, J. (2022). Efficient Matrix Polynomial Expansion Detector for Large-Scale MIMO: An Inverse-Transform-Sampling Approach. *IEEE Systems Journal*. https://doi.org/10.1109/JSYST.2022.3179299

Deng Q, Liang X, Ni Q, Wu J. Efficient Matrix Polynomial Expansion Detector for Large-Scale MIMO: An Inverse-Transform-Sampling Approach. IEEE Systems Journal. 2022 Jun 28. Epub 2022 Jun 28. doi: 10.1109/JSYST.2022.3179299

@article{880969a14e344631b8da488a85a48438,

title = "Efficient Matrix Polynomial Expansion Detector for Large-Scale MIMO: An Inverse-Transform-Sampling Approach",

abstract = "Matrix polynomial expansion (MPE) based detector incurs either complicated computation of polynomial coefficients or slow convergence in uplink large-scale multiple-input and multiple-output (LS-MIMO) systems. To solve these issues, an improved MPE (IMPE) detector is proposed, which can speed up the convergence significantly with uncomplicated polynomial coefficients. However, a challenging problem of performing IMPE is needed to compute all the eigenvalues of channel covariance matrix in real time. Unfortunately, directly calculating the eigenvalues of the channel covariance matrix requires complexity, which is as costly as the matrix inverse. To this end, an inverse-transform-sampling based IMPE (ITS-IMPE) detector is proposed to enhance the convergence rate and accuracy in a simple way. First, the closed-form expression of the eigenvalue spectral cumulative distribution function of the channel covariance matrix is deduced analytically, which is a critical factor that influence the eigenvalues estimation. Second, the improved polynomial coefficients of ITS-IMPE are then introduced by a fast online ITS-based eigenvalues estimation algorithm and a least-squares fitting procedure, which achieve a well trade-off between precision and computation. Simulation results exhibit that ITS-IMPE detector is able to achieve a significant enhancement performance with much lower complexity compared with many reported detectors under Rayleigh fading channel and low spatial correlated channel.",

keywords = "Complexity theory, Convergence, Covariance matrices, Detectors, Eigenvalues and eigenfunctions, Estimation, Fast convergence, MIMO communication, inverse-transform-sampling, large-scale multiple-input and multiple-output (MIMO), matrix polynomial expansion (MPE)",

author = "Q. Deng and X. Liang and Q. Ni and J. Wu",

note = "{\textcopyright}2022 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. ",

year = "2022",

month = jun,

day = "28",

doi = "10.1109/JSYST.2022.3179299",

language = "English",

journal = "IEEE Systems Journal",

issn = "1932-8184",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - JOUR

T1 - Efficient Matrix Polynomial Expansion Detector for Large-Scale MIMO

T2 - An Inverse-Transform-Sampling Approach

AU - Deng, Q.

AU - Liang, X.

AU - Ni, Q.

AU - Wu, J.

N1 - ©2022 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

PY - 2022/6/28

Y1 - 2022/6/28

N2 - Matrix polynomial expansion (MPE) based detector incurs either complicated computation of polynomial coefficients or slow convergence in uplink large-scale multiple-input and multiple-output (LS-MIMO) systems. To solve these issues, an improved MPE (IMPE) detector is proposed, which can speed up the convergence significantly with uncomplicated polynomial coefficients. However, a challenging problem of performing IMPE is needed to compute all the eigenvalues of channel covariance matrix in real time. Unfortunately, directly calculating the eigenvalues of the channel covariance matrix requires complexity, which is as costly as the matrix inverse. To this end, an inverse-transform-sampling based IMPE (ITS-IMPE) detector is proposed to enhance the convergence rate and accuracy in a simple way. First, the closed-form expression of the eigenvalue spectral cumulative distribution function of the channel covariance matrix is deduced analytically, which is a critical factor that influence the eigenvalues estimation. Second, the improved polynomial coefficients of ITS-IMPE are then introduced by a fast online ITS-based eigenvalues estimation algorithm and a least-squares fitting procedure, which achieve a well trade-off between precision and computation. Simulation results exhibit that ITS-IMPE detector is able to achieve a significant enhancement performance with much lower complexity compared with many reported detectors under Rayleigh fading channel and low spatial correlated channel.

AB - Matrix polynomial expansion (MPE) based detector incurs either complicated computation of polynomial coefficients or slow convergence in uplink large-scale multiple-input and multiple-output (LS-MIMO) systems. To solve these issues, an improved MPE (IMPE) detector is proposed, which can speed up the convergence significantly with uncomplicated polynomial coefficients. However, a challenging problem of performing IMPE is needed to compute all the eigenvalues of channel covariance matrix in real time. Unfortunately, directly calculating the eigenvalues of the channel covariance matrix requires complexity, which is as costly as the matrix inverse. To this end, an inverse-transform-sampling based IMPE (ITS-IMPE) detector is proposed to enhance the convergence rate and accuracy in a simple way. First, the closed-form expression of the eigenvalue spectral cumulative distribution function of the channel covariance matrix is deduced analytically, which is a critical factor that influence the eigenvalues estimation. Second, the improved polynomial coefficients of ITS-IMPE are then introduced by a fast online ITS-based eigenvalues estimation algorithm and a least-squares fitting procedure, which achieve a well trade-off between precision and computation. Simulation results exhibit that ITS-IMPE detector is able to achieve a significant enhancement performance with much lower complexity compared with many reported detectors under Rayleigh fading channel and low spatial correlated channel.

KW - Complexity theory

KW - Convergence

KW - Covariance matrices

KW - Detectors

KW - Eigenvalues and eigenfunctions

KW - Estimation

KW - Fast convergence

KW - MIMO communication

KW - inverse-transform-sampling

KW - large-scale multiple-input and multiple-output (MIMO)

KW - matrix polynomial expansion (MPE)

U2 - 10.1109/JSYST.2022.3179299

DO - 10.1109/JSYST.2022.3179299

M3 - Journal article

JO - IEEE Systems Journal

JF - IEEE Systems Journal

SN - 1932-8184

ER -