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On Fundamental Limits of Transmission Activity Detection in Fluid Antenna Systems

Zhentian Zhang, Kai-Kit Wong, Hao Jiang, Christos Masouros, Chan-Byoung Chae

TL;DR

The paper tackles the problem of detecting transmission activity under sporadic access in systems equipped with fluid antenna systems (FASs) and conventional FPAs. It proposes a unified CRB framework that relaxes the binary activity indicators to continuous amplitudes and derives both covariance-based CRBs (for multi-FPA setups and orthogonal vs non-orthogonal pilots) and coherent CRBs (for single-snapshot FAS and conventional systems), with universal results for FAS and random-matrix theory based approximations. Key contributions include closed-form covariance-based CRBs under orthogonal pilots, a universal coherent CRB for FAS that accounts for inter-user interference via a Beta-distributed factor, and a closed-form conventional-system CRB for comparison; the analysis reveals phase transitions when the number of active users approaches the pilot-space dimension. The findings show that FAS can deliver strong spatial-diversity gains with significantly reduced hardware complexity, approaching or surpassing the performance of larger multi-antenna FPAs in many regimes. Overall, the work provides a tractable, scalable benchmark framework for evaluating activity-detection performance across reconfigurable and fixed architectures in practical settings.

Abstract

In this letter, we develop a unified Cramér-Rao bound (CRB) framework to characterize the fundamental performance limits of transmission activity detection in fluid antenna systems (FASs) and conventional multiple fixed-position antenna (FPA) systems. To facilitate CRB analysis applicable to activity indicators, we relax the binary activity states to continuous parameters, thereby aligning the bound-based evaluation with practical threshold-based detection decisions. Closed-form CRB expressions are derived for two representative detection formulations, namely covariance-oriented and coherent models. Moreover, for single-antenna FASs, we obtain a closed-form coherent CRB by leveraging random matrix theory. The results demonstrate that CRB-based analysis provides a tractable and informative benchmark for evaluating activity detection across architectures and detection schemes, and further reveal that FASs can deliver strong spatial-diversity gains with significantly reduced complexity.

On Fundamental Limits of Transmission Activity Detection in Fluid Antenna Systems

TL;DR

The paper tackles the problem of detecting transmission activity under sporadic access in systems equipped with fluid antenna systems (FASs) and conventional FPAs. It proposes a unified CRB framework that relaxes the binary activity indicators to continuous amplitudes and derives both covariance-based CRBs (for multi-FPA setups and orthogonal vs non-orthogonal pilots) and coherent CRBs (for single-snapshot FAS and conventional systems), with universal results for FAS and random-matrix theory based approximations. Key contributions include closed-form covariance-based CRBs under orthogonal pilots, a universal coherent CRB for FAS that accounts for inter-user interference via a Beta-distributed factor, and a closed-form conventional-system CRB for comparison; the analysis reveals phase transitions when the number of active users approaches the pilot-space dimension. The findings show that FAS can deliver strong spatial-diversity gains with significantly reduced hardware complexity, approaching or surpassing the performance of larger multi-antenna FPAs in many regimes. Overall, the work provides a tractable, scalable benchmark framework for evaluating activity-detection performance across reconfigurable and fixed architectures in practical settings.

Abstract

In this letter, we develop a unified Cramér-Rao bound (CRB) framework to characterize the fundamental performance limits of transmission activity detection in fluid antenna systems (FASs) and conventional multiple fixed-position antenna (FPA) systems. To facilitate CRB analysis applicable to activity indicators, we relax the binary activity states to continuous parameters, thereby aligning the bound-based evaluation with practical threshold-based detection decisions. Closed-form CRB expressions are derived for two representative detection formulations, namely covariance-oriented and coherent models. Moreover, for single-antenna FASs, we obtain a closed-form coherent CRB by leveraging random matrix theory. The results demonstrate that CRB-based analysis provides a tractable and informative benchmark for evaluating activity detection across architectures and detection schemes, and further reveal that FASs can deliver strong spatial-diversity gains with significantly reduced complexity.
Paper Structure (16 sections, 35 equations, 3 figures)

This paper contains 16 sections, 35 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Covariance-Based CRB
  3. Signal Model for $M$-FPA Systems
  4. Benchmark 1---Covariance-Based CRB
  5. Coherent CRBs
  6. Coherent Detection Model for Single-Antenna FAS
  7. FAS Channel Response Model
  8. Universal Coherent CRB for FAS
  9. Benchmark 2---Coherent CRB for Conventional System
  10. Numerical Results
  11. Empirical vs. Analysis
  12. CRB vs. SNR
  13. CRB vs. Number of Available Ports $N$
  14. CRB vs. Number of Active Users $K$
  15. Conclusion
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Empirical (MSE) vs CRB: $K=20$. For FAS, $N=200$ and $W=2$. For covariance-based $M$-antenna system, $L=400$.
  • Figure 2: CRB versus SNR with $W=5$, $N\in\{10,2000\}$, and $M\in\{2,5,10\}$.
  • Figure 3: CRBs of FAS and multi-FPA under different models (a) CRB versus number of available ports $N$ with $W\in\{0.5,5,10\}$, $M\in\{6,8,12\}$, and $\mathrm{SNR}=-15$ dB; (b) CRB versus number of active users $K$ with $W=10$, $N=2000$, $M\in\{2,5,11\}$, and $\mathrm{SNR}=-10$ dB.