SCIENCE CHINA Information Sciences, Volume 64 , Issue 8 : 182309(2021) https://doi.org/10.1007/s11432-020-3103-3

Uplink transmission design for crowded correlated cell-free massive MIMO-OFDM systems

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  • ReceivedJul 7, 2020
  • AcceptedOct 30, 2020
  • PublishedJun 2, 2021



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  • Figure 1

    (Color online) Cell-free massive MIMO system. Active and inactive UEs are in red and gray, respectively.

  • Figure 2

    (Color online) Illustration of the transmission frame. In this example, the hopping pattern for a given UE is $\left\{a,a,b,\ldots,c\right\}$. Pilot signals among $N_c$ subcarriers are formulated based on this pattern, and transmitted during the pilot transmission phase. Data codewords are transmitted afterwards.

  • Table 1  

    Table 1System parameters for the simulation

    Parameter Value Unit
    Bandwidth B 20 MHz
    Carrier frequency $f_c$ 2 GHz
    Sampling duration $T_s$48.8 ns
    Subcarrier number $N_c$, guard interval $N_{\mathrm{cp}}$ 1024, 144
    The number of UEs $K$, the number of clusters $J$ $200,2$
    The number of OFDM symbols in a slot $Z_{a}$ $7$
    $h_{\mathrm{AP}}$, $h_{\mathrm{u}}$, $d_1$, $d_0$ 15, 1.65, 50, 10 m
    Maximum transmitting power $P_x$$0.5~$ W
    Pilot phase shift number per UE $\left|\mathcal{Y}~\right|$ 4
    $\gamma$ $10^{-8}~(Z=1),~10^{-13}(Z=2)$
    $\iota_k$ 0.4
    $P_{\mathrm{ip,}~k}$, $P_{\mathrm{ip,}~l}$, $P_{0,~l}$0.1, 0.1, 0.825W
    $P_{\mathrm{bt,}~l}$ 0.25 W/(Gbits/s)

    Algorithm 1 APSP set allocation algorithm


    Require:The angle-delay domain channel power spectrum $\{\mathbf{\Upsilon}_k:k\in\mathcal{K}\}$; the threshold $\lambda$ and $\gamma$; the phase shift set $\mathbf{\Psi}$; the large-scale fading $\boldsymbol{\beta}_k~\triangleq~~\left[\beta_{k,0}\!\;\;\beta_{k,1}\cdots~\beta_{k,L-1}~\right]$ for $\forall~k~\in~\mathcal{K}$.

    Output: The APSP set allocated to each UE $\left\{~\mathcal{Y}_k,~k\in~\mathcal{K}\right\}$.

    Centroids are randomly chosen as $\tilde{\boldsymbol{\beta}}_{j}\in~\mathbb{C}^{L\times~1}$ for $j=0,1,\ldots,J-1$;

    For $\forall~k~\in~\mathcal{K}$, UE $k$ is assigned to the cluster with $\max\nolimits_{j=0,1,\ldots,J-1}\xi(\boldsymbol{\beta}_k,~\tilde{\boldsymbol{\beta}}_{j})$;

    Centroids are updated by averaging over UEs belonging to respective clusters and UEs are reassigned until the assignments no longer change. Let $\mathcal{C}_j$ denote the set of UEs belonging to the $j$-th cluster;

    for $j=0,1,\ldots,J-1$

    $\left|\mathcal{Y}~\right|$ shifts are randomly chosen to form the set $\mathcal{Y}_{\mathcal{C}_j(0)}$ allocated for UE $\mathcal{C}_j(0)$. Initialize the allocated UE set $\mathcal{K}^{\rm{al}}_{j}=\{\mathcal{C}_j(0)\}$ and the unallocated UE set $\mathcal{K}^{\rm{un}}_{j}=\mathcal{C}_j\backslash\{\mathcal{C}_j(0)\}$.

    for $k\in~\mathcal{K}^{\mathrm{un}}_{j}$

    Search for $\left|\mathcal{Y}\right|$ pilot phase shifts $\phi\in\mathbf{\Psi}$ to form the APSP set $\mathcal{Y}_k$ allocated for the $k$-th UE, which should satisfy $~\sum\limits_{k^{\prime}\in\mathcal{K}^{\mathrm{al}}_{j}}~~{\frac{1}{|\mathcal{K}^{\mathrm{al}}_{j}~|}}~\mathop~{\max}\limits_{\phi_{k^{\prime}}\in~\mathcal{Y}_{k^{\prime}}}~\left\{\delta~\left(~\left\langle~{{\phi~}_{{{k}^{\prime}}}}\right\rangle_{Z}~-\left\langle~{{\phi~}}\right\rangle_{~Z}~\right)~\xi~\left(~\mathbf{\Upsilon}_k^0~\odot~\mathbf{\Upsilon}_k^0,~\mathbf{\Upsilon}_{k^{\prime}}^{\beta,\left\lfloor{{\phi~}_{{{k}^{\prime}}}}/Z\right\rfloor-\left\lfloor{{\phi~}}/Z\right\rfloor}~\right)~\right\}\leq~\gamma$;

    If $\left|\mathcal{Y}\right|$ pilot phase shifts are not found in step 7, then search for $\left|\mathcal{Y}\right|$ shifts from $\mathbf{\Psi}$ corresponding to the $\left|\mathcal{Y}\right|$ smallest $~\sum\limits_{k^{\prime}\in\mathcal{K}^{\mathrm{al}}_{j}}~~\mathop~{\max}\limits_{\phi_{k^{\prime}}\in~\mathcal{Y}_{k^{\prime}}}~\left\{\delta\left(~\left\langle~{{\phi~}_{{{k}^{\prime}}}}\right\rangle_{Z}~-~\left\langle~{{\phi~}}\right\rangle_{~Z}~\right)~\xi\left(~~\mathbf{\Upsilon}_k^0~\odot~~\mathbf{\Upsilon}_k^0,~\mathbf{\Upsilon}_{k^{\prime}}^{\beta,\left\lfloor{{\phi~}_{{{k}^{\prime}}}}/Z\right\rfloor-\left\lfloor{{\phi~}}/Z\right\rfloor}~\right)~\!\right\}$;

    Update $\mathcal{K}^{\rm{un}}_{j}:=\mathcal{K}^{\rm{un}}_{j}\backslash\{k\}, \mathcal{K}^{\rm{al}}_{j}:=\mathcal{K}^{\rm{al}}_{j}\cup\{k\}$


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