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Asymptotic Performance Analysis of Fluid Antenna Systems: An Extreme Value Theory Perspective

Yi Zhang, Jintao Wang, Zheng Shi, Xu Wang, Guanghua Yang, Shaodan Ma, Kai-Kit Wong

TL;DR

The paper tackles how the outage probability (OP) and ergodic capacity (EC) of fluid antenna systems (FAS) scale as the number of ports grows large. It adopts extreme value theory (EVT) to model the maximum channel gain across closely spaced ports under spatial correlation, ultimately showing a double-exponential decay of OP with respect to $(\ln N)^{3/4}$ and a double-logarithmic growth of EC with $N$, both tempered by a correlation parameter $\mu$. The analysis hinges on the Gumbel limit for the conditional distribution of the maximal gain $g$ given the common channel state $g_0$, yielding tractable upper and lower bounds for EC and revealing that the mode of the mutual information grows only as $\ln\ln N$. Numerical results corroborate the asymptotic laws and demonstrate the detrimental effect of port correlation on both OP and EC, offering practical insight for the design of large-scale FAS deployments.

Abstract

Fluid antenna systems (FAS) allow dynamic reconfiguration to achieve superior diversity gains and reliability. To quantify the performance scaling of FAS with a large number of antenna ports, this paper leverages extreme value theory (EVT) to conduct an asymptotic analysis of the outage probability (OP) and ergodic capacity (EC). The analysis reveals that the OP decays approximately exponentially with the number of antenna ports. Moreover, we establish upper and lower bounds for the asymptotic EC, uncovering its double-logarithmic scaling law. Furthermore, we re-substantiate these scaling laws by exploiting the fact that the mode of the Gumbel distribution scales logarithmically. Besides, we theoretically prove that spatial correlation among antenna ports degrades both OP and EC. All analytical findings are conclusively validated by numerical results.

Asymptotic Performance Analysis of Fluid Antenna Systems: An Extreme Value Theory Perspective

TL;DR

The paper tackles how the outage probability (OP) and ergodic capacity (EC) of fluid antenna systems (FAS) scale as the number of ports grows large. It adopts extreme value theory (EVT) to model the maximum channel gain across closely spaced ports under spatial correlation, ultimately showing a double-exponential decay of OP with respect to and a double-logarithmic growth of EC with , both tempered by a correlation parameter . The analysis hinges on the Gumbel limit for the conditional distribution of the maximal gain given the common channel state , yielding tractable upper and lower bounds for EC and revealing that the mode of the mutual information grows only as . Numerical results corroborate the asymptotic laws and demonstrate the detrimental effect of port correlation on both OP and EC, offering practical insight for the design of large-scale FAS deployments.

Abstract

Fluid antenna systems (FAS) allow dynamic reconfiguration to achieve superior diversity gains and reliability. To quantify the performance scaling of FAS with a large number of antenna ports, this paper leverages extreme value theory (EVT) to conduct an asymptotic analysis of the outage probability (OP) and ergodic capacity (EC). The analysis reveals that the OP decays approximately exponentially with the number of antenna ports. Moreover, we establish upper and lower bounds for the asymptotic EC, uncovering its double-logarithmic scaling law. Furthermore, we re-substantiate these scaling laws by exploiting the fact that the mode of the Gumbel distribution scales logarithmically. Besides, we theoretically prove that spatial correlation among antenna ports degrades both OP and EC. All analytical findings are conclusively validated by numerical results.

Paper Structure

This paper contains 15 sections, 4 theorems, 31 equations, 1 figure.

Table of Contents

  1. Introduction
  2. System Model
  3. Correlation Channel Model
  4. Performance Metrics
  5. Outage Probability (OP)
  6. Ergodic Capacity (EC)
  7. EVT Based Performance Analysis
  8. OP
  9. EC
  10. Numerical Results
  11. Conclusion
  12. Proof of Theorem \ref{['th_h_dis']}
  13. Proof of Theorem \ref{['th_cap']}
  14. Upper Bound
  15. Lower Bound

Key Result

Lemma 1

The conditional PDF and CDF of $|h_n|^2$ given $g_0=|\vartheta_0|^2$ is written as where $g_0$ obeys the exponential distribution, i.e., $f_{g_0}(t)=e^{-t}$ for $t\ge 0$, $I_0(\cdot)$ denotes the modified Bessel function abramowitz1968handbook, and $Q_1(\cdot)$ is the first-order Marcum Q-function.

Figures (1)

  • Figure 1: (a) The OP versus $N$; (b) The OP versus $W$; (c) The EC versus $N$; (d) The EC versus $W$.

Theorems & Definitions (6)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • proof
  • Theorem 2
  • proof