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



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.


Appendixes A and B.


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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) $K~=~12$.


    Algorithm 1 BCD-type algorithm for subproblem 23

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


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


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



    end for

    until some termination criterion is satisfied.


  • 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 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 $\boldsymbol{\Gamma}~_{m,k,n}^{(~0~)}$.



    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 ${{{\boldsymbol~f}}_{{\text{B}},k}}[~n~]$.