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SCIENCE CHINA Information Sciences, Volume 62, Issue 10: 209306(2019) https://doi.org/10.1007/s11432-019-9805-9

Angular domain precoding-based PAPR reduction for massive MIMO systems

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  • ReceivedJan 18, 2019
  • AcceptedMar 1, 2019
  • PublishedAug 16, 2019

Abstract

There is no abstract available for this article.


Acknowledgment

This work was supported in part by National Science Foundation for Distinguished Young Scholars of China (Grant No. 61625106) and National Natural Science Foundation of China (Grant No. 61531011).


References

[1] Cui Q M, Liu Y J, Liu Y S. Multi-pair massive MIMO amplify-and-forward relaying system with low-resolution ADCs: performance analysis and power control. Sci China Inf Sci, 2018, 61: 022311 CrossRef Google Scholar

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[3] Xie H X, Gao F F, Zhang S. A Unified Transmission Strategy for TDD/FDD Massive MIMO Systems With Spatial Basis Expansion Model. IEEE Trans Veh Technol, 2017, 66: 3170-3184 CrossRef Google Scholar

[4] Lin H, Gao F F, Jin S. A New View of Multi-User Hybrid Massive MIMO: Non-Orthogonal Angle Division Multiple Access. IEEE J Sel Areas Commun, 2017, 35: 2268-2280 CrossRef Google Scholar

[5] Ni L Y, Jin S, Gao F F, et al. Beam domain PAPR reduction for massive MIMO downlink. In: Proceedings of IEEE International Conference on Wireless Communications and Signal Processing (WCSP), Nanjing, 2017. 1--6. Google Scholar

[6] Studer C, Larsson E G. PAR-Aware Large-Scale Multi-User MIMO-OFDM Downlink. IEEE J Sel Areas Commun, 2013, 31: 303-313 CrossRef Google Scholar

[7] Wang C J, Wen C K, Jin S. Finite-Alphabet Precoding for Massive MU-MIMO With Low-Resolution DACs. IEEE Trans Wireless Commun, 2018, 17: 4706-4720 CrossRef Google Scholar

  • Figure 1

    (Color online) (a) SER of 4-QAM for different precoding PAPR reduction when $M=128$; (b) SER of 16-QAM with different number of BS antennas; (c) simulation parameters.

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    Algorithm 1 SRPR

    Require:$\boldsymbol{s},~\boldsymbol{H},~T_1,~T_2,$ $t~=~0,~{\boldsymbol~x}^0~=~\mathbf{0},~\gamma^0~=~1,~\mu^0~=~1,~\alpha~=~0.95~$;

    Output:$~{\boldsymbol{x}}~=~{{\boldsymbol{x}}}^{t+1}$;

    while $t~\le~T_1$ do

    $\bar{\boldsymbol{H}}~=~\mu^t~\boldsymbol{H}~$;

    ${\boldsymbol{\varOmega}}{\rm{~=~}}{\left(~{{{{\boldsymbol{\bar~H}}}^{\rm~H}}{\boldsymbol{\bar~H}}~+~{\gamma~^t}{\bf{I}}}~\right)^{-1}}{{\boldsymbol{\bar~H}}^{\rm~H}}$;

    $\boldsymbol{D}~=~[~\text{diag}~(~{\boldsymbol{\varOmega}}\bar{\boldsymbol{H}})]^{-1}~$;

    ${\boldsymbol{x}}^{t+1}~=~\prod_{\mathcal{X}^M}~(~{\boldsymbol{~x}}^t~+~\boldsymbol{D}{\boldsymbol{\varOmega}}~(~\boldsymbol{s}~-~\bar{\boldsymbol{H}}~{\boldsymbol{x}^t})~)~$;

    ${\gamma~^{t~+~1}}~=~{\rm{tr}}({{\boldsymbol{\bar~H}}^{\rm{H}}}{\boldsymbol{\bar~H}})/||\boldsymbol{s}~-~\boldsymbol{\bar~H}{\boldsymbol~{x}^{t~+~1}}||_2^2$;

    if $~\mod\left(~T_2,~t+1~\right)~==~0~$ then

    $\mu^{t+1}~=~\frac{\text{Re}~\left(~{\boldsymbol{~s}}^{\rm~H}~{\boldsymbol{H}}~{\boldsymbol{x}}^{t+1}~\right)}{\left\|~{\boldsymbol{H}}~{\boldsymbol{~x}}^{t+1}~\right\|_2^2~+~K_g~\sigma^2}$;

    else

    $\mu^{t+1}~=~\mu^{t}$;

    end if

    $~{\boldsymbol{x}}^{t+1}~\leftarrow~\alpha~{\boldsymbol{x}}^{t}~+~(~1~-~\alpha~)~{\boldsymbol{x}}^{t+1}~$;

    ${\gamma~^{t~+~1}}~\leftarrow~\alpha~{\gamma~^t}~+~(1~-~\alpha~){\gamma~^{t~+~1}}$;

    $~t~\leftarrow~t~+~1~$;

    end while

  •   

    Algorithm 2 CSRPR

    Require:${\boldsymbol{s}},~{\boldsymbol{H}},~T_1,~T_2,$ $t~=~0,~{\boldsymbol~x}^0~=~\mathbf{0},~\mu^0~=~1,~\alpha~=~0.95~$;

    Output:$~{\boldsymbol{x}}~=~{\boldsymbol{x}}^{t+1}$;

    while $t~\le~T_1$ do

    $\bar{\boldsymbol{H}}~=~\mu^t~\boldsymbol{H}~$;

    $~{\boldsymbol{\varTheta~}}~=~\left[~\text{diag}~\left(~{\boldsymbol{\bar{H}}}^{\rm~H}~{\boldsymbol{\bar{H}}}~\right)~\right]^{-1}~{\boldsymbol{\bar{H}}}^{\rm~H}~$;

    ${\boldsymbol{x}}^{t+1}~=~\prod_{\mathcal{X}^M}~(~{\boldsymbol{~x}}^t~+~{\boldsymbol{\Theta}}~(~\boldsymbol{s}~-~\bar{\boldsymbol{H}}~{\boldsymbol{x}}^t~)~)~$;

    if $~\mod\left(~T_2,~t+1~\right)~==~0~$ then

    $\mu^{t+1}~=~\frac{\text{Re}~\left(~{\boldsymbol{~s}}^{\rm~H}~{\boldsymbol{H}}~{\boldsymbol{x}}^{t+1}~\right)}{\left\|~{\boldsymbol{H}}~{\boldsymbol{~x}}^{t+1}~\right\|_2^2~+~K_g~\sigma^2}$;

    else

    $\mu^{t+1}~=~\mu^{t}$;

    end if

    $~{\boldsymbol{x}}^{t+1}~\leftarrow~\alpha~{\boldsymbol{x}}^{t}~+~(~1~-~\alpha~)~{\boldsymbol{x}}^{t+1}~$;

    $~t~\leftarrow~t~+~1~$;

    end while

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