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Delay Performance of MISO Wireless Communications

Jesus Arnau, Marios Kountouris

TL;DR

This paper provides a statistical characterization of MISO diversity-oriented service process through closed-form expressions of its Mellin transform and derive probabilistic delay bounds using tools from stochastic network calculus and provides useful guidelines for the design of communication systems that can guarantee the stringent URLLC latency requirements.

Abstract

Ultra-reliable, low latency communications (URLLC) are currently attracting significant attention due to the emergence of mission-critical applications and device-centric communication. URLLC will entail a fundamental paradigm shift from throughput-oriented system design towards holistic designs for guaranteed and reliable end-to-end latency. A deep understanding of the delay performance of wireless networks is essential for efficient URLLC systems. In this paper, we investigate the network layer performance of multiple-input, single-output (MISO) systems under statistical delay constraints. We provide closed-form expressions for MISO diversity-oriented service process and derive probabilistic delay bounds using tools from stochastic network calculus. In particular, we analyze transmit beamforming with perfect and imperfect channel knowledge and compare it with orthogonal space-time codes and antenna selection. The effect of transmit power, number of antennas, and finite blocklength channel coding on the delay distribution is also investigated. Our higher layer performance results reveal key insights of MISO channels and provide useful guidelines for the design of ultra-reliable communication systems that can guarantee the stringent URLLC latency requirements.

Delay Performance of MISO Wireless Communications

TL;DR

This paper provides a statistical characterization of MISO diversity-oriented service process through closed-form expressions of its Mellin transform and derive probabilistic delay bounds using tools from stochastic network calculus and provides useful guidelines for the design of communication systems that can guarantee the stringent URLLC latency requirements.

Abstract

Ultra-reliable, low latency communications (URLLC) are currently attracting significant attention due to the emergence of mission-critical applications and device-centric communication. URLLC will entail a fundamental paradigm shift from throughput-oriented system design towards holistic designs for guaranteed and reliable end-to-end latency. A deep understanding of the delay performance of wireless networks is essential for efficient URLLC systems. In this paper, we investigate the network layer performance of multiple-input, single-output (MISO) systems under statistical delay constraints. We provide closed-form expressions for MISO diversity-oriented service process and derive probabilistic delay bounds using tools from stochastic network calculus. In particular, we analyze transmit beamforming with perfect and imperfect channel knowledge and compare it with orthogonal space-time codes and antenna selection. The effect of transmit power, number of antennas, and finite blocklength channel coding on the delay distribution is also investigated. Our higher layer performance results reveal key insights of MISO channels and provide useful guidelines for the design of ultra-reliable communication systems that can guarantee the stringent URLLC latency requirements.

Paper Structure

This paper contains 31 sections, 9 theorems, 43 equations, 9 figures.

Table of Contents

  1. Introduction
  2. System model
  3. Signal model
  4. Transmission mode
  5. Data transmission
  6. Asymptotically large blocklength
  7. Finite blocklength
  8. Queuing model
  9. Stochastic Network Calculus in the SNR Domain
  10. Mellin transform of arrival and service processes
  11. Delay Bound
  12. Delay with Large Blocklength: Exact Analysis
  13. MISO MRT
  14. Other MISO Diversity Techniques
  15. OSTBC
  16. ...and 16 more sections

Key Result

Theorem 1

The Mellin transform of $g(\gamma) = 1+\gamma$, where $\gamma \sim {\rm Gamma}(M,\zeta)$ with $M \in \mathbb{N}^+$ and $\zeta > 0$, is given by where $U(a,b,z)$ is Tricomi's confluent hypergeometric function Abramowitz1964 (also called confluent hypergeometric function of the second kind and denoted by $\Psi(a;b;z)$).

Figures (9)

  • Figure 1: Delay violation probability and associated bounds as a function of the target dealy, $\rho = 24$ kbps and $\mathsf{snr}=-2$ dB.
  • Figure 2: Delay violation probability bound as a function of the target delay, $\rho = 24$ kbps and $\mathsf{snr}=5$ dB. Curves labeled FB have been obtained using finite blocklength expressions.
  • Figure 3: Delay violation probability bound as a function of the target delay for different diversity techniques, $\rho = 24$ kbps and $\mathsf{snr}=5$ dB.
  • Figure 4: Bound on the probability of exceeding $3$ ms of delay as a function of the block error rate $\epsilon$, finite blocklength analysis, $\rho = 24$ kbps. Circles mark the minimum of each curve.
  • Figure 5: Bound on the probability of exceeding $1$ ms delay as a function of the number of antennas, asymptotically large blocklength, $\rho = 256$ kbps.
  • ...and 4 more figures

Theorems & Definitions (10)

  • Theorem 1
  • Theorem 2
  • Remark 1
  • Corollary 1
  • Theorem 3
  • Corollary 2
  • Corollary 3
  • Corollary 4
  • Theorem 4
  • Theorem 5