Cramer-Rao Bounds for Activity Detection in Conventional and Fluid Antenna Systems

TL;DR

This paper develops a unified Cramér-Rao bound framework to evaluate the fundamental limits of activity detection in fluid and conventional antenna systems, highlighting the benefits of fluid antennas.

Contribution

It introduces a novel CRB analysis applicable to fluid antenna systems, deriving closed-form expressions and demonstrating performance advantages over traditional systems.

Findings

CRB analysis provides a benchmark for activity detection performance.

Fluid antennas offer significant spatial-diversity gains.

CRB expressions are derived for different detection models.

Abstract

In this letter, we develop a unified Cram\'{e}r-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.