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SCIENCE CHINA Information Sciences, Volume 61, Issue 2: 022311(2018) https://doi.org/10.1007/s11432-017-9187-5

Multi-pair massive MIMO amplify-and-forward relaying system with low-resolution ADCs: performance analysis and power control

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  • ReceivedMay 22, 2017
  • AcceptedJul 26, 2017
  • PublishedOct 26, 2017

Abstract

In this paper, we focus on a general multi-pair massive MIMO amplify-and-forward (AF) relaying system where the relay antennas employ low-resolution analog-to-digital converters (ADCs) to reduce the hardware cost. First, considering the effect of low quantization on channel estimation, a tight closed form approximation of the system ergodic achievable rate is derived. Second, some asymptotic analysis is presented to reveal the impacts of the system parameters on the achievable rate. Particularly, the generalized power scaling schemes are characterized. The results indicate that in some cases, when the number of relay antennas grows without bound, the impact of the finite resolution ADCs on data transmission can be eliminated. To enhance the achievable rate of the quantized systems, the optimal user and relay power control schemes are proposed. Furthermore, to reap all the benefits of low-resolution ADCs, another power control scheme is also designed to minimize the total power consumption while guaranteeing the quality-of-service (QoS) requirement of each user, which can help draw some useful insights into the optimal ADC resolution from power saving perspectives. The simulation results confirm the accuracy of our theoretical analysis and the effectiveness of the proposed power control schemes.

  • Figure 1

    Multi-pair half-duplex relay system with low-resolution ADCs.

  • Figure 2

    (Color online) Sum achievable rate versus the number of relay antennas with ${\rho~_p}=~{p_{s,k}}=~10~\text{dB}$ and ${P_R}=~K{p_{s,k}}$.

  • Figure 3

    (Color online) Sum achievable rate versus the number of quantization bits with ${\rho~_p}=~{p_{s,k}}=~10~\rm{dB}$, ${P_R}=~K{p_{s,k}}$ and $N=128$.

  • Figure 4

    (Color online) Sum achievable rate versus the transmit power of source users and relay with ${p_{s,k}}=~{P_R}$ and $b=1$. The markers are the approximated results.

  • Figure 5

    (Color online) Sum achievable rate versus the number of relay antennas with ${E_{s,k}}=~{E_R}=~30~{\rm{dB}}$, $p_{s,k}=~E_{s,k}/N,~P_R~=~E_R/N$. The markers are the approximated results.

  • Figure 6

    (Color online) Sum achievable rate versus the different numbers of relay antennas with $E_{s,k}=10~{\rm{dB}}$, $E_{R}=15~{\rm{dB}}$, $p_{s,k}=~E_{s,k},~P_R~=~{E_R}/{N}$.

  • Figure 7

    (Color online) Sum achievable rate versus different numbers of relay antennas and power control schemes.

  • Figure 8

    (Color online) Convergence of Algorithm 1 with different initial points when $b=2$, $N=256$ and $\rho_p=10$ dB.

  • Figure 9

    (Color online) Total transmit power consumption versus different numbers of quantization bits when the QoS requirement is $0.5$ Mbps.

  • Figure 10

    (Color online) Total power consumption versus different numbers of quantization bits.

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    Algorithm 1 Power control scheme to maximize the sum achievable rate

    Initialize $\hat~\gamma~_k^{\left(~0~\right)}$ for $k~=~1,2,~\dots,~K$, the convergence conditions $\varepsilon$ and the maximal iterative steps $\theta$.

    Repeat:

    Let $t=1$, and calculating and

    Solving the following optimization problem, and obtain the optimal power $p_{s,k}^{\left(~t~\right)}$ and $P_R^{\left(~t~\right)}$.

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