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SCIENCE CHINA Information Sciences, Volume 63 , Issue 9 : 192301(2020) https://doi.org/10.1007/s11432-019-2799-y

Hybrid beamforming design for mmWave OFDM distributed antenna systems

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  • ReceivedAug 12, 2019
  • AcceptedFeb 16, 2020
  • PublishedJul 28, 2020

Abstract

This paper presents a hybrid beamforming design for millimeter-wave (mmWave) orthogonal frequency division multiplexing (OFDM) distributed antenna systems (DASs). First, we derive a downlink signal transmission model that considers the delay spread differences (DSDs) caused by the distributed nature of the network. We then propose a cooperative wideband hybrid beamforming method under the transmitting power constraints of each remote access unit. In a simulation study, the proposed method performed comparably to fully-digital beamforming, even when operated with practical finite-resolution phase shifters. We further confirm that the DSDs are the dominant cause of performance degradation in mmWave OFDM DASs.


Acknowledgment

This work was supported in part by National Key Research and Development Program (Grant No. 2018YFE0205902), National Natural Science Foundation of China (NSFC) (Grant Nos. 61871122, 61971127), and Six Talent Peaks Project in Jiangsu Province.


Supplement

Appendixes A and B.


References

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  • Figure 1

    (Color online) An illustration of the effect of DSDs on downlink (DL) transmission in mmWave OFDM DASs, e.g., in the case of two RAUs and two UEs.

  • Figure 2

    (Color online) Average convergence performance of Algorithm 2versus per-RAU power with $K~=~6$ and $N_{\text{RF}}=~3$. (a) Number of iterations; (b) violation value.

  • Figure 3

    (Color online) Average rate versus per-RAU power with $K~=~6$ and $P_{\max}^{\text{rau}}=~30~\;\text{dBm}$ for different number of RF chains. (a) $N_\text{RF}=~3$; (b) $N_\text{RF}=~5$.

  • Figure 4

    (Color online) CDF of average rate over different subcarriers with $M~=~6$ and $P_{\max}^{\text{rau}}=~30~\;\text{dBm}$. (a) $K~=~6$;protectłinebreak (b) $K~=~12$.

  • Table 1  

    Table 1Simulation parameters

    Parameter Value
    Zone radius $R_0$ 120 m
    Number of RAUs $M$ 6
    Number of antennas (RAU) $N_{\text{A}}$ 8
    Carrier frequency $f_{\text{c}}$ 28 GHz
    Subcarrier spacing $\triangle~f~$ 60 kHz
    Subcarrier number $N_{\mathrm{c}}$ 72
    Guard interval $N_{\mathrm{g}}$ 16
    Number of channel paths $L$ 3
    Path loss $\beta_{m,k}^2$ $\alpha~+~10\beta~{{\log~}_{10}}\left(~d~\right)~+~\xi~$ dB $^{\rm~a)}$
    Path delay distribution $\mathcal{U}~\left(~{{\tau~_0},{\tau~_0}~+~{\Delta~_\tau~}}~\right)~$ $^{\rm~b)}$
    Path angle distribution $\mathcal{U}~\left(~0,~2\pi~\right)$

    a) The values adopted for the model parameters are $\alpha~=~72$, $\beta~=~2.92$, and $\xi~=~8.7~$, respectively in [27]. $d$ is the distance in meters.

  •   

    Algorithm 1 BCD-type algorithm for subproblem 23

    Require:$B$, ${\boldsymbol~R}_m~=~{{\boldsymbol~F}}_{\mathrm{R},m}~$, and ${\boldsymbol~Q}_m~=~{\boldsymbol~R}_m~{\boldsymbol~X}_m$.

    repeat

    for $(~{i,j}~)~\in~\{~{1,2,~\ldots~,{N_{\mathrm{A}}}}~\}~\times~\{~{1,2,~\ldots~,{N_{{\mathrm{RF}}}}}~\}$

    $b~=~{[~{{{{\boldsymbol~R}}_m}}~]_{i,j}}{[~{{{\boldsymbol~B}_m}}~]_{j,j}}~-~{[~{{{\boldsymbol~Q}_m}}~]_{i,j}}~+~{[~{{{\boldsymbol~X}_m}}~]_{i,j}}$;

    $x~=~\left\{~\begin{gathered} \exp~\{~{\jmath{\phi~_b}}~\},\;\;\;~\,{\text{if}}\;B~=~\infty~,~\\ \exp~\Big\{~{\jmath\frac{{2\pi~}}{{{2^B}}}~i^{\star}}~\Big\},\;{\text{otherwise},}~~\\ \end{gathered}~\right.$ where $\phi~_b~\in~[0,2\pi~)~$ is the phase of $b$ and $i^{\star} = \mathop {\arg \;\max }\nolimits_{i' \in \{ {0, \ldots ,{2^{B - 1}}} \}} \;| {{\phi _b} - \frac{{2\uppi i'}}{{{2^B}}}} |$;

    ${[~{{{\boldsymbol~Q}_m}}~]_{i,:}}~=~{[~{{{\boldsymbol~Q}_m}}~]_{i,:}}~+~(~{x~-~{{[~{{{{\boldsymbol~R}}_m}}~]}_{i,j}}}~){[~{{{\boldsymbol~B}_m}}~]_{j,:}}$;

    ${[~{{\boldsymbol~R}}_m~]_{i,j}}~=~x$;

    end for

    until some termination criterion is satisfied.

    Output:${{\boldsymbol~F}}_{\text{R},m}=~{\boldsymbol~R}_m$.

  •   

    Algorithm 2 Proposed hybrid beamforming algorithm

    Require:${{\boldsymbol~F}}_R^{(~0~)}$, ${{\boldsymbol~f}}_{{\text{B}},k}^{(~0~)}[~n~]$, ${{\boldsymbol~x}}_k^{(~0~)}[~n~]$, ${{\boldsymbol~y}}_{m,k}^{(~0~)}[~n~]$, $\boldsymbol{\Lambda}~_{k,n}^{(~0~)}$, and $\boldsymbol{\Gamma}~_{m,k,n}^{(~0~)}$.

    repeat

    repeat

    Update $a_{k,n}$ using Eq. 20;

    Update $w_{k,n}$ using Eq. 21;

    Update ${\boldsymbol~F}_{\text{R}}$ using Algorithm 1;

    Update ${\boldsymbol~f}_{\text{B},k}~[~n~]~$ using Eq. 26;

    Update ${\boldsymbol~x}_{k}~[~n~]~$ using Eq. 29;

    Update ${\boldsymbol~y}_{m,k}~[~n~]~$ using Eq. 30;

    until some termination criterion is satisfied;

    Update $\rho$, $\boldsymbol{\Lambda}~_{k,n}$, and ${\boldsymbol{\Gamma~}}_{m,k,n}$;

    until some termination criterion is satisfied;

    Output:${{{\boldsymbol~F}}_{\text{R}}}$ and ${{{\boldsymbol~f}}_{{\text{B}},k}}[~n~]$.

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