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SCIENCE CHINA Information Sciences, Volume 60, Issue 10: 100303(2017) https://doi.org/10.1007/s11432-017-9194-y

Pilot reuse and power control of D2D underlaying massive MIMO systems for energy efficiency optimization

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  • ReceivedApr 21, 2017
  • AcceptedJul 27, 2017
  • PublishedSep 1, 2017

Abstract

It is predicted that there will be billions of machine type communication (MTC) devices to be deployed in near future. This will certainly cause severe access congestion and system overload which is one of the major challenges for the proper operation of 5G networks. Adopting device-to-device (D2D) communications into massive multiple-input multiple-output (MIMO) systems has been considered as a potential solution to alleviate the overload of MTC devices by offloading the MTC traffic onto D2D links. This work proposes a novel pilot reuse (PR) and power control (PC) for energy efficiency (EE) optimization of the uplink D2D underlaying massive MIMO cellular systems. Although the use of large scale antenna array at the base station (BS) can eliminate most of the D2D-to-Cellular interference, the Cellular-to-D2D interference and the channel estimation error caused by PR will remain significant. Motivated by this, and in order to reduce the channel estimation error, in this paper a novel heuristic PR optimum pilot reuse scheme is proposed for D2D transmitters (D2DTs) selection. By taking into account the interference among users as well as the overall power consumption, the overall system EE is maximized through power optimization while maintaining the quality-of-service (QoS) provisions for both cellular users (CUEs) and D2D pairs. The power optimization problem is modeled as a non-cooperative game and, as such, a distributed iterative power control algorithm which optimizes users' power sequentially is proposed. Various performance evaluation results obtained by means of computer simulations have shown that the proposed PR scheme and PC algorithm can significantly increase the overall system EE.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61371109, 61671278), National Science Foundation for Excellent Young Scholars of China (Grant No. 61622111), and Shandong Provincial Natural Science Foundation for Young Scholars of China (Grant No. ZR2017QF008).


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  • Figure 1

    (Color online) System model of D2D underlaying massive MIMO system under consideration.

  • Figure 2

    (Color online) The system sum energy efficiency vs. $\Gamma$ for different numbers of users and for $N=1000$.

  • Figure 3

    (Color online) Convergence of the individual users' power in proposed power control algorithm with $K=5$, $M=10$, $N=1000$.

  • Figure 4

    (Color online) Convergence of the average power of CUEs and D2DTs in proposed power control algorithm with $N=1000$.

  • Figure 5

    (Color online) The system sum energy efficiency for different pilot reuse schemes with proposed power control algorithm when $K=5$, $M=20$.

  • Figure 6

    (Color online) The system sum energy efficiency for different power control algorithms with proposed pilot reuse scheme when $K=5$, $M=20$.

  •   

    Algorithm 1 Pilot reuse scheme

    Initialize the set of D2D pairs which have not been allocated with pilot as $\lambda = \mathcal{M}$

    Calculate $\sigma_{kj}$ for all $k\in\mathcal{K}, j\in\mathcal{M}$, and get $\mathcal{C}_m$

    Allocate pilots for D2D pairs randomly, get $\mathcal{D}_k$ for all $k\in\mathcal{K}$, and $\Omega_m$ for all $m\in\mathcal{M}$

    while $\lambda\neq \emptyset$ do

    $m=\arg\max\limits_{m_{0}\in\lambda}\; \sum_{k\in\mathcal{K}}\sigma_{km_0}$

    $\mathcal{D}_{\Omega_m}=\mathcal{D}_{\Omega_m}\backslash m$

    for $k\in\mathcal{C}_m$

    $\mathcal{D}_{k}=\mathcal{D}_{k}\bigcup m$

    get $R_{k}^c$ and $R_{i}^d$ for all $i\in \mathcal{D}_k$

    $\Delta_{km}=R_{k}^c+\sum_{i\in\mathcal{D}_k}R_{i}^d$

    $\mathcal{D}_{k}=\mathcal{D}_{k}\backslash m$

    end for

    $k^*=\arg\max\limits_{k\in\mathcal{K}}\; \Delta_{km}$

    $\mathcal{D}_{k^*}=\mathcal{D}_{k^*}\bigcup m$, $\lambda = \lambda\backslash m$

    end while

  •   

    Algorithm 2 Distributed iterative power control algorithm

    $\kappa=10^{-3},I_{\max}=20,q(0)=0$

    Allocate power for CUEs and D2DTs randomly, get $\mathcal{P}_c$ and $\mathcal{P}_d$

    for $n=1$ to $I_{\max}$

    for $k\in\mathcal{K}$

    get $P_{k,\min}^c$ and $P_{k,\max}^c$ from $(\ref{eq27})$ and $(\ref{eq28})$

    if $\zeta_k^c(P_{k,\min}^c)\leq 0$ then

    $P_k^{c*}(n)=P_{k,\min}^c$ELSIF$\zeta_k^c(P_{k,\max}^c)\geq 0$

    $P_k^{c*}(n)=P_{k,\max}^c$

    else

    $P_{k}^{c*}(n)=\arg\min\limits_{P_{k,\min}^c\leq P_k^c\leq P_{k,\max}^c}\;{|\zeta_k^c(P_k^c)|}$

    end if

    end for

    for $j\in\mathcal{M}$

    get $P_{m,\min}^d$ and $P_{m,\max}^d$ from $(\ref{eq35})$ and $(\ref{eq36})$

    if $\zeta_m^d(P_{m,\min}^d)\leq 0$ then

    $P_m^{d*}(n)=P_{m,\min}^d$ELSIF$\zeta_m^d(P_{m,\max}^d)\geq 0$

    $P_m^{d*}(n)=P_{m,\max}^d$

    else

    $P_{m}^{d*}(n)=\arg\min\limits_{P_{m,\min}^d\leq P_m^d\leq P_{m,\max}^d}\;{|\zeta_m^d(P_m^d)|}$

    end if

    end for

    $q=\max{\{|\mathcal{P}_c(n)-\mathcal{P}_c(n-1)|, |\mathcal{P}_d(n)-\mathcal{P}_d(n-1)|\}}$

    if $q\leq\kappa$ then

    break

    else

    update $\mathcal{P}_c$ and $\mathcal{P}_d$

    end if

    end for

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