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Maximum Channel Coding Rate of Finite Block Length MIMO Faster-Than-Nyquist Signaling

Zichao Zhang, Melda Yuksel, Halim Yanikomeroglu, Benjamin K. Ng, Chan-Tong Lam

TL;DR

This work addresses the problem of determining the maximum channel coding rate $C(N,\epsilon)$ for finite-blocklength MIMO FTN channels under an output-power constraint, targeting ultra-low-latency requirements. It introduces a channel decomposition that yields $DN$ parallel complex Gaussian channels with gains $\sigma_h[d]\sigma_p[n]$, derives an optimal per-channel power allocation via KKT conditions, and provides a closed-form finite-blocklength MCCR formula $C(N,\epsilon)=\frac{N}{N+2L}\Bigl(C_{DN}-\sqrt{\frac{V_{DN}}{DN}}Q^{-1}(\epsilon)+\frac{\log_2(DN)}{2DN}+O(1/DN)\Bigr)$ with $C_{DN}$ and $V_{DN}$ defined. The paper also demonstrates that the MCCR under the output-power constraint generalizes SISO/FTN results and shows substantial gains from combining FTN with MIMO in simulations, including notable spectral efficiency improvements and favorable DoF scaling, making FTN-MIMO a promising candidate for URLLC in 6G-and-beyond systems.

Abstract

The pursuit of higher data rates and efficient spectrum utilization in modern communication technologies necessitates novel solutions. In order to provide insights into improving spectral efficiency and reducing latency, this study investigates the maximum channel coding rate (MCCR) of finite block length (FBL) multiple-input multiple-output (MIMO) faster-than-Nyquist (FTN) channels. By optimizing power allocation, we derive the system's MCCR expression. Simulation results are compared with the existing literature to reveal the benefits of FTN in FBL transmission.

Maximum Channel Coding Rate of Finite Block Length MIMO Faster-Than-Nyquist Signaling

TL;DR

This work addresses the problem of determining the maximum channel coding rate for finite-blocklength MIMO FTN channels under an output-power constraint, targeting ultra-low-latency requirements. It introduces a channel decomposition that yields parallel complex Gaussian channels with gains , derives an optimal per-channel power allocation via KKT conditions, and provides a closed-form finite-blocklength MCCR formula with and defined. The paper also demonstrates that the MCCR under the output-power constraint generalizes SISO/FTN results and shows substantial gains from combining FTN with MIMO in simulations, including notable spectral efficiency improvements and favorable DoF scaling, making FTN-MIMO a promising candidate for URLLC in 6G-and-beyond systems.

Abstract

The pursuit of higher data rates and efficient spectrum utilization in modern communication technologies necessitates novel solutions. In order to provide insights into improving spectral efficiency and reducing latency, this study investigates the maximum channel coding rate (MCCR) of finite block length (FBL) multiple-input multiple-output (MIMO) faster-than-Nyquist (FTN) channels. By optimizing power allocation, we derive the system's MCCR expression. Simulation results are compared with the existing literature to reveal the benefits of FTN in FBL transmission.
Paper Structure (5 sections, 2 theorems, 32 equations, 4 figures)

This paper contains 5 sections, 2 theorems, 32 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Capacity Derivation
  4. Simulation Results
  5. Conclusion

Key Result

Theorem 1

thesis The maximum channel coding rate of the finite block length parallel AWGN channel is a function of both the block length $N$ and the error probability $\epsilon$, and is given as where $C_K$ is the capacity of $K$ parallel AWGN channels and $V_K$ is the channel dispersion. The definition of $C_K$ and $V_K$ can be found in thesis.

Figures (4)

  • Figure 1: MCCR versus block length $N$ for MIMO and SISO FBL FTN, for $\beta=0.5$, and $\textsc{SNR}=20$ dB.
  • Figure 2: MCCR versus block length $N$ for different $\epsilon$ values, for both FTN ($\delta = 0.67$) and for Nyquist ($\delta = 1$) transmission, for $\beta= 0.5$, and $\textrm{SNR}= 10$ dB for $2 \times 2$ MIMO.
  • Figure 3: MCCR versus SNR for MIMO and SISO FBL FTN for different $(\delta,\beta)$ pairs, $\epsilon = 10^{-6}$, and $N=100$.
  • Figure 4: MCCR versus $\delta$ for different $N$ values, with $\text{SNR}=20$ dB, $\epsilon=10^{-6}$, and $\beta=0.5$.

Theorems & Definitions (5)

  • Theorem 1
  • Theorem 2
  • Remark 1
  • Remark 2
  • Remark 3