Finite-blocklength Fluid Antenna Systems

TL;DR

This work tackles finite-blocklength performance of fluid antenna systems (FBL-FAS) by modeling codeword correlation across ports and applying random matrix theory and extreme value theory. It derives distributions for codeword inner products, establishes average and maximum correlation metrics, and develops both CSI-known and CSI-unknown BLER bounds as well as SINR-based outage probabilities. A Taylor-expansion-assisted MVTI technique is introduced to simplify otherwise intractable integrals, enabling tractable evaluation of no-CSI performance. Comparisons with conventional L-antenna MRC demonstrate that a single-antenna FAS can achieve notable energy and spectral efficiency gains under finite blocklength, highlighting FAS as a promising enabler for next-generation networks.

Abstract

This work introduces and investigates finite blocklength fluid antenna systems (FBL-FASs). To meet the stringent key performance indicators (KPIs) of 6G and beyond networks, including ultra-massive machine-type communications (mMTC), ultra-reliable low-latency communications (URLLC), and enhanced mobile broadband (eMBB), it is necessary to evaluate the performance of FAS under limited channel uses across time, frequency, and other domains. By exploiting random matrix theory and extreme value theory (EVT), we characterize the effect of finite blocklength on key metrics such as the signal-to-noise ratio (SNR) and the signal-to-interference-plus-noise ratio (SINR), via accurate estimation of interference caused by codeword correlation. Closed-form expressions for block error rate (BLER) and outage probability are derived, covering both conditional BLER (with channel state information, CSI) and statistical BLER (without CSI). The proposed analysis leverages Chernoff bounds and introduces a Taylor-expansion-assisted mean value theorem for integrals (MVTI) to reduce computational complexity. Numerical results show that, compared with conventional multi-antenna systems, the proposed FBL-FAS framework achieves higher energy and spectral efficiency under finite blocklength, making it a promising enabler for next-generation wireless networks.

Figures (9)

• Figure 1: Illustration of analytical codeword correlation (dashed lines) under FBL with 2,000 Monte-Carlo (solid lines), codeword length $M\in\{10,20,50,100\}$ and number of codewords $U\in \{20,40,60,80\}$. 1) Left: maximum correlation $\rho_{\max}$ by \ref{['eq:10']} of Theorem 4. 2) Right: average correlation $\bar{\rho}$ by \ref{['eq:average_correlation']} of Theorem 3.
• Figure 2: Illustration of the simplified CDF and PDF of $|g_{\mathrm{FAS}}|$ in \ref{['simplifed_pdf_cdf']} of Theorem 7 with $10^{5}$ Monte-Carlo samples, $\sigma=1$, number of available ports $N=10$ and antenna length constant $W=0.5$.
• Figure 3: Illustration of BLER performance in different SNR region with antenna length constant $W=0.5$, number of codewords $U=10$, blocklength $M=5$. For FBL-FAS's conditional result and statistical result (No CSI), $\mathrm{DoFs}=M$; For $L$-antenna system, $\mathrm{DoFs}=L\times M$.
• Figure 4: Illustration of BLER performance under different number of available ports with antenna length constant $W=1$, number of codewords $U=10$, blocklength $M=5$ and $\mathrm{SNR}=12$ dB. For FBL-FAS, statistical results refer to No-CSI case by \ref{['eq:17']} and conditional results refer to the case of known channel response by \ref{['eq:15']}.
• Figure 5: Illustration of BLER performance under different number of available ports with antenna length constant $W=1$, blocklength $M=5$ and $\mathrm{SNR}=20$ dB. For FBL-FAS, statistical results refer to No-CSI case by \ref{['eq:17']} and conditional results refer to the case of known channel response by \ref{['eq:15']}.