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On the Fundamental Scaling Laws of Fluid Antenna Systems

Xusheng Zhu, Farshad Rostami Ghadi, Tuo Wu, Kaitao Meng, Chao Wang, Gui Zhou

TL;DR

Problem: characterize the SER performance of fluid antenna systems (FAS) in spatially correlated channels. Approach: derive a tight high-SNR SER expression $P_E(\overline{\gamma}) \approx C (\overline{\gamma})^{-N_{\rm eff}}$ with $N_{\rm eff}=\mathrm{Rank}\{\mathbf{J}\}$ using Jake's model, eigen-decomposition, and port-selection, plus explicit conditional/unconditional forms. Contributions: (i) fundamental scaling law relating SER to channel correlation via $\det(\mathbf{J})$ and eigenvalues; (ii) explicit diversity gain $G_d=N_{\rm eff}$; (iii) explicit coding gain $G_c = \left( \frac{2 k^{N_{\rm eff}}}{p(2N_{\rm eff}-1)!!} \right)^{1/N_{\rm eff}} \left(\prod_{n=1}^{N_{\rm eff}} \lambda_n\right)^{1/N_{\rm eff}}$; (iv) design guidance that expanding the movement space improves SER more than simply increasing port density. Significance: provides analytical tools for predicting SER and guides FAS design for future networks.

Abstract

Fluid antenna systems (FAS) offer a promising paradigm for enhancing wireless communication by exploiting spatial diversity, yet a rigorous analytical framework for their error probability has been notably absent. To this end, this paper addresses this critical gap by unveiling the \textbf{fundamental scaling laws} that govern the symbol error rate (SER) of FAS in realistic, spatially correlated channels. To establish these laws, we derive a tight, closed-form asymptotic expression for the SER applicable to a general class of modulation schemes. This result is pivotal as it establishes the fundamental scaling law governing the relationship between SER and the channel's spatial correlation structure. Based on this framework, we provide a complete characterization of the diversity and coding gains. The analysis culminates in a definitive design directive: SER can be fundamentally improved by expanding the antenna's movement space to increase diversity, while merely increasing port density within a constrained space yields diminishing returns.

On the Fundamental Scaling Laws of Fluid Antenna Systems

TL;DR

Problem: characterize the SER performance of fluid antenna systems (FAS) in spatially correlated channels. Approach: derive a tight high-SNR SER expression with using Jake's model, eigen-decomposition, and port-selection, plus explicit conditional/unconditional forms. Contributions: (i) fundamental scaling law relating SER to channel correlation via and eigenvalues; (ii) explicit diversity gain ; (iii) explicit coding gain ; (iv) design guidance that expanding the movement space improves SER more than simply increasing port density. Significance: provides analytical tools for predicting SER and guides FAS design for future networks.

Abstract

Fluid antenna systems (FAS) offer a promising paradigm for enhancing wireless communication by exploiting spatial diversity, yet a rigorous analytical framework for their error probability has been notably absent. To this end, this paper addresses this critical gap by unveiling the \textbf{fundamental scaling laws} that govern the symbol error rate (SER) of FAS in realistic, spatially correlated channels. To establish these laws, we derive a tight, closed-form asymptotic expression for the SER applicable to a general class of modulation schemes. This result is pivotal as it establishes the fundamental scaling law governing the relationship between SER and the channel's spatial correlation structure. Based on this framework, we provide a complete characterization of the diversity and coding gains. The analysis culminates in a definitive design directive: SER can be fundamentally improved by expanding the antenna's movement space to increase diversity, while merely increasing port density within a constrained space yields diminishing returns.

Paper Structure

This paper contains 11 sections, 1 theorem, 37 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Performance Analysis
  4. Conditional Error Probability
  5. Unconditional Error Probability
  6. Diversity and Coding Gain Analysis
  7. Diversity Gain Derivation
  8. Coding Gain Derivation
  9. Results and Discussion
  10. Conclusions
  11. Proof of Lemma 1

Key Result

Lemma 1

In the high-SNR regime, the PDF of $x=\gamma_F$ can be approximated as

Figures (4)

  • Figure 1: System model.
  • Figure 2: Validation of the asymptotic BER analysis for FAS with a normalized aperture ($W=1$).
  • Figure 3: Impact of port spacing $\Delta d$ on the FAS performance for a fixed aperture ($W=1$).
  • Figure 4: SER performance comparison under various FAS modulation schemes ($N=3$, $W=1$).

Theorems & Definitions (1)

  • Lemma 1