Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

URLLC in IRS-Aided MIMO Systems: Finite Blocklength Analysis and Design

Xin Zhang, Shenghui Song

TL;DR

The paper tackles URLLC performance for IRS-aided MIMO under finite blocklength by deriving explicit upper and lower OAEP bounds via a central limit theorem for the mutual information density in a large-system regime where $M,N,L,n$ scale with fixed ratios. It introduces a gradient-based algorithm to minimize the OAEP lower bound by optimizing IRS phase shifts and validates the theory with simulations, demonstrating tight bounds and correlated LDPC performance improvements. The approach unifies random-matrix techniques with finite-blocklength information theory to quantify reliability bottlenecks in IRS-aided channels and offers a practical design tool for URLLC. Overall, the work provides tractable, closed-form performance predictions and a scalable phase-design method for reliable IRS-assisted MIMO communications.

Abstract

This paper investigates the ultra reliable and low latency communication (URLLC) performance of the IRS-aided MIMO system. The upper and lower bounds of the optimal average error probability (OAEP) for the coding rate 1/sqrt(Mn) of the capacity are derived, where n and M represent the blocklength and the number of transmit antennas, respectively. To achieve this goal, a new central limit theorem (CLT) for the mutual information density over the IRS-aided MIMO system is derived in the asymptotic regime where the block-length, the IRS size, and number of the antennas go to infinity with the same pace. The CLT is then utilized to derive the closed form upper and lower bounds for the OAEP. Based on the analysis result, a gradient-based algorithm is proposed to minimize the lower bound of the OAEP by optimizing the phase shift of the IRS. Simulation results validate the fitness of the CLT and the effectiveness of the proposed algorithm in optimizing the theoretical bound, as well as the performance of practical LDPC code.

URLLC in IRS-Aided MIMO Systems: Finite Blocklength Analysis and Design

TL;DR

The paper tackles URLLC performance for IRS-aided MIMO under finite blocklength by deriving explicit upper and lower OAEP bounds via a central limit theorem for the mutual information density in a large-system regime where scale with fixed ratios. It introduces a gradient-based algorithm to minimize the OAEP lower bound by optimizing IRS phase shifts and validates the theory with simulations, demonstrating tight bounds and correlated LDPC performance improvements. The approach unifies random-matrix techniques with finite-blocklength information theory to quantify reliability bottlenecks in IRS-aided channels and offers a practical design tool for URLLC. Overall, the work provides tractable, closed-form performance predictions and a scalable phase-design method for reliable IRS-assisted MIMO communications.

Abstract

This paper investigates the ultra reliable and low latency communication (URLLC) performance of the IRS-aided MIMO system. The upper and lower bounds of the optimal average error probability (OAEP) for the coding rate 1/sqrt(Mn) of the capacity are derived, where n and M represent the blocklength and the number of transmit antennas, respectively. To achieve this goal, a new central limit theorem (CLT) for the mutual information density over the IRS-aided MIMO system is derived in the asymptotic regime where the block-length, the IRS size, and number of the antennas go to infinity with the same pace. The CLT is then utilized to derive the closed form upper and lower bounds for the OAEP. Based on the analysis result, a gradient-based algorithm is proposed to minimize the lower bound of the OAEP by optimizing the phase shift of the IRS. Simulation results validate the fitness of the CLT and the effectiveness of the proposed algorithm in optimizing the theoretical bound, as well as the performance of practical LDPC code.
Paper Structure (20 sections, 4 theorems, 52 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 20 sections, 4 theorems, 52 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Performance Evaluation of IRS-Aided MIMO Systems
  3. Finite Blocklength Analysis
  4. System Model and Problem Formulation
  5. System Model
  6. Channel Model
  7. Average Error probability
  8. Optimal Average Error Probability
  9. Problem Formulation
  10. Bounds for OAEP and Optimization
  11. CLT for the MID
  12. Upper and Lower Bounds for the OAEP
  13. Lower Bound Minimization
  14. Numerical Simulations
  15. Simulation Settings
  16. ...and 5 more sections

Key Result

Lemma 1

hoydis2015second (Bounds for the OAEP) The upper and lower bounds of the OAEP are given by where where $I^{(n)}_{N,L,M}$ is given in (mid_exp) and (upp_bound) is induced by the normalized Gaussian input ${\bold{C}}^{(n)}\in \mathbb{C}^{M\times n}=\widetilde{\bold{C}}^{(n)}\left(\frac{1}{Mn}\mathop{\mathrm{Tr}}\nolimits (\widetilde{\bold{C}}^{(n)}\widetilde{\bold{C}}^{(n),H})\right)^{-\frac{1}{2

Figures (3)

  • Figure 1: Fitness of the CLT.
  • Figure 2: Upper and lower bounds of error probability.
  • Figure 3: LDPC performance.

Theorems & Definitions (9)

  • Lemma 1
  • Remark 1
  • Lemma 2
  • Remark 2
  • Theorem 1
  • proof
  • Remark 3
  • Theorem 2
  • proof