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Balancing Queueing and Retransmission: Latency-Optimal Massive MIMO Design

Xu Du, Yin Sun, Ness B. Shroff, Ashutosh Sabharwal

TL;DR

This paper develops a low-complexity closed-form policy named Large-arraY Reliability and Rate Control (LYRRC), which is proven to be asymptotically latency-optimal as the number of antennas increases.

Abstract

One fundamental challenge in 5G URLLC is how to optimize massive MIMO systems for achieving low latency and high reliability. A natural design choice to maximize reliability and minimize retransmission is to select the lowest allowed target error rate. However, the overall latency is the sum of queueing latency and retransmission latency, hence choosing the lowest target error rate does not always minimize the overall latency. In this paper, we minimize the overall latency by jointly designing the target error rate and transmission rate adaptation, which leads to a fundamental tradeoff point between queueing and retransmission latency. This design problem can be formulated as a Markov decision process, which is theoretically optimal, but its complexity is prohibitively high for real-system deployments. We managed to develop a low-complexity closed-form policy named Large-arraY Reliability and Rate Control (LYRRC), which is proven to be asymptotically latency-optimal as the number of antennas increases. In LYRRC, the transmission rate is twice of the arrival rate, and the target error rate is a function of the antenna number, arrival rate, and channel estimation error. With simulated and measured channels, our evaluations find LYRRC satisfies the latency and reliability requirements of URLLC in all the tested scenarios.

Balancing Queueing and Retransmission: Latency-Optimal Massive MIMO Design

TL;DR

This paper develops a low-complexity closed-form policy named Large-arraY Reliability and Rate Control (LYRRC), which is proven to be asymptotically latency-optimal as the number of antennas increases.

Abstract

One fundamental challenge in 5G URLLC is how to optimize massive MIMO systems for achieving low latency and high reliability. A natural design choice to maximize reliability and minimize retransmission is to select the lowest allowed target error rate. However, the overall latency is the sum of queueing latency and retransmission latency, hence choosing the lowest target error rate does not always minimize the overall latency. In this paper, we minimize the overall latency by jointly designing the target error rate and transmission rate adaptation, which leads to a fundamental tradeoff point between queueing and retransmission latency. This design problem can be formulated as a Markov decision process, which is theoretically optimal, but its complexity is prohibitively high for real-system deployments. We managed to develop a low-complexity closed-form policy named Large-arraY Reliability and Rate Control (LYRRC), which is proven to be asymptotically latency-optimal as the number of antennas increases. In LYRRC, the transmission rate is twice of the arrival rate, and the target error rate is a function of the antenna number, arrival rate, and channel estimation error. With simulated and measured channels, our evaluations find LYRRC satisfies the latency and reliability requirements of URLLC in all the tested scenarios.

Paper Structure

This paper contains 22 sections, 5 theorems, 53 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Physical Layer Model
  5. Buffer Dynamics with Retransmission
  6. Transmission Power adaptation
  7. Single-user Latency Minimization Problem
  8. Latency-Optimal Single-User Transmission Control
  9. Lagrange Duality of the MDP
  10. A Value Iteration Based Algorithm
  11. Large-Array Latency-Optimal Control
  12. Array-Latency Scaling Lower Bound
  13. Large-Array Optimal Target Error Rate and Transmission Rate Control
  14. Latency Performance of Transmission Rate adaptation $\mu^{*}$
  15. Asymptotic Optimality of LYRRC
  16. ...and 7 more sections

Key Result

Theorem 1

The optimum array-latency curve $D^{*}\left(M\right)$ satisfies where $\epsilon_{o}$ is given by where $F_{\eta}\left(\cdot\right)$ is the CDF of the effective channel gain $\eta$ in equ:eta_def, $\rho \in \left[0, 1\right)$ is the utilization factor in equ:rho_def, and $\tau$ is the number of pilots.

Figures (9)

  • Figure 1: An example illustrating the overall latency for different target error rates, where the transmission rate has been optimized for each given target error rate. A massive MIMO uplink system with $4$ single-antenna users and $32$ base-station antennas is considered. The channel traces are measured in an over-the-air channel on the Rice Argos platform and the base-station estimates the channel based on $8$ pilot symbols per user. Please find the evaluation details in Section \ref{['sec:numerical']}.
  • Figure 2: Single-user uplink system consisting of a single antenna user and an $M$-antenna base-station.
  • Figure 3: Structure of the self-contained frames. Each self-contained frame consists of uplink data resource blocks (blue), downlink feedback signals (green) and the guard periods (gray). The transmitted data is encoded over $N$ subcarriers with a single code-block.
  • Figure 4: Block error rate of a coded system as a function of $\mathrm{SINR}$ mean with $N=1$. In simulation, the channel gain follows the normal distribution with labeled variance. The approximations are obtained by \ref{['equ:p_to_epsilon']}. And the simulation is done with LDPC code MATLAB and sparse parity-check matrix comes from the DVB-S.2 standard. The transmission is at a rate of $1.5$ bits per symbol ($8$-QAM, $0.5$ code rate).
  • Figure 5: Evolution of the queue-length $q_t$ under any target error rate $\epsilon \in \left(0, 1\right)$ and the transmission rate adaptation $\mu^{*}$ as a Markov chain. If $\epsilon>0.5$, the average queue-length hence queueing latency is infinite.
  • ...and 4 more figures

Theorems & Definitions (11)

  • Theorem 1: Latency Scaling Lower Bound
  • proof
  • Definition 1
  • Lemma 1
  • proof
  • Theorem 2: Optimal Large-Array Control
  • proof
  • Theorem 3: Large-Array Latency Scaling
  • proof
  • Theorem 4
  • ...and 1 more