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Is Synchronization a Bottleneck for Pilot-Assisted URLLC Links?

A. Oguz Kislal, Madhavi Rajiv, Giuseppe Durisi, Erik G. Ström, Urbashi Mitra

TL;DR

N numerical results indicate that the number of pilot symbols needed to estimate the fading channel gains to the level of accuracy required in ultra-reliable low-latency communication is also sufficient to acquire sufficiently good synchronization when synchronization becomes the bottleneck for the system performance.

Abstract

We propose a framework to evaluate the so-called random-coding union bound with parameter $s$ (RCUs) on the achievable error probability in the finite-blocklength regime for a pilot-assisted transmission scheme operating over an imperfectly synchronized and memoryless block-fading waveform channel. Unlike previous results, which disregard the effects of imperfect synchronization, our framework utilizes pilots for both synchronization and channel estimation. Specifically, we provide an algorithm to perform joint synchronization and channel estimation, and verify its accuracy by observing its tightness in comparison with the Cramer-Rao bound. Then, we develop an RCUs bound on the error probability, which applies for a receiver that treats the estimates provided by the algorithm as accurate. Additionally, we utilize the saddlepoint approximation to provide a numerically efficient method for evaluating the RCUs bound in this scenario. Our numerical experiments verify the accuracy of the proposed approximation. Moreover, when the delays are modeled as fully dependent across fading blocks, numerical results indicate that the number of pilot symbols needed to estimate the fading channel gains to the level of accuracy required in ultra-reliable low-latency communication is also sufficient to acquire sufficiently good synchronization. However, when the delays are modeled as independent across blocks, synchronization becomes the bottleneck for the system performance.

Is Synchronization a Bottleneck for Pilot-Assisted URLLC Links?

TL;DR

N numerical results indicate that the number of pilot symbols needed to estimate the fading channel gains to the level of accuracy required in ultra-reliable low-latency communication is also sufficient to acquire sufficiently good synchronization when synchronization becomes the bottleneck for the system performance.

Abstract

We propose a framework to evaluate the so-called random-coding union bound with parameter (RCUs) on the achievable error probability in the finite-blocklength regime for a pilot-assisted transmission scheme operating over an imperfectly synchronized and memoryless block-fading waveform channel. Unlike previous results, which disregard the effects of imperfect synchronization, our framework utilizes pilots for both synchronization and channel estimation. Specifically, we provide an algorithm to perform joint synchronization and channel estimation, and verify its accuracy by observing its tightness in comparison with the Cramer-Rao bound. Then, we develop an RCUs bound on the error probability, which applies for a receiver that treats the estimates provided by the algorithm as accurate. Additionally, we utilize the saddlepoint approximation to provide a numerically efficient method for evaluating the RCUs bound in this scenario. Our numerical experiments verify the accuracy of the proposed approximation. Moreover, when the delays are modeled as fully dependent across fading blocks, numerical results indicate that the number of pilot symbols needed to estimate the fading channel gains to the level of accuracy required in ultra-reliable low-latency communication is also sufficient to acquire sufficiently good synchronization. However, when the delays are modeled as independent across blocks, synchronization becomes the bottleneck for the system performance.
Paper Structure (18 sections, 1 theorem, 67 equations, 8 figures, 2 tables, 2 algorithms)

This paper contains 18 sections, 1 theorem, 67 equations, 8 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Overview
  4. Signal Model
  5. Synchronization and Channel Estimation Phase
  6. Per-Block Synchronization for Independent Delays
  7. Joint Synchronization for Fully Dependent Delays
  8. Codeword Decoding Phase
  9. A Non-Asymptotic Upper Bound on The Error Probability
  10. The RCUs Finite-Blocklength Bound
  11. A Saddlepoint Approximation on the Conditional Error Probability in \ref{['eq:RCUsSym-cond']}
  12. Saddlepoint Expansion for Sum of Independent but not Identically Distributed Random Variables
  13. Closed-Form Evaluation of the Moment Generating Function
  14. A Case Study: BPSK Constellation
  15. Numerical Results and Discussion
  16. ...and 3 more sections

Key Result

Theorem 1

Suppose that there exists a $\zeta_{0}>0$ such that and also positive constants $m_{\text{{}l}}\leq m_{\text{{}u}}$ such that holds for all $n \in \mathbb{N}$ and for all $\left\lvert\zeta\right\rvert\leq\zeta_{0}$. Assume that there exists a $\zeta \in [-\zeta_{0},\zeta_{0}]$ satisfying $-\mu(\zeta)=\mathrm{R}$. If $\zeta \in [0,1]$ then where $\beta_a = a \sqrt{n\sigma^2(\zeta) }$. If $\zeta>

Figures (8)

  • Figure 1: Block diagram of the system model. In the case of fully dependent delays
  • Figure 2: Block diagrams of the receiver.
  • Figure 3: Comparison between NMSE of the estimators and CRB for $\mathrm{N}=10$, $n_{\text{p}} =7$, $n_{\text{b}}=4$.
  • Figure 4: Achievable packet error probability evaluated using the RCUs bound as a function of the average synchronization error. Here $n=288$, $n_{\text{b}} =8$, $\mathrm{R} = 0.104$ bit per channel use; $s$ is optimized.
  • Figure 5: NMSE for the delay estimation for both joint and per-block synchronization for $\mathrm{N} = 10$, $n_{\text{b}}=4$, $n_{\text{p}} =7$.
  • ...and 3 more figures

Theorems & Definitions (1)

  • Theorem 1