Analytical insights into outage probability and ergodic capacity of fluid antenna systems

This letter analyzes the delivery performance of a point-to-point (P2P) fluid antenna system (FAS), where the receiver is equipped with a one-dimensional N-port fluid antenna. For the first time, we rigorously reveal the diversity order of the P2P FAS through mathematical proof. Motivated by this analysis, we propose a novel and tractable approximation for the signal-to-noise ratio (SNR) distribution after receiver combining. Using this approximation, we derive a simple closed-form expression for the outage probability (OP) composed solely of elementary functions, along with its high-SNR approximation. Furthermore, we analyze the ergodic capacity (EC) of the system and derive a closed-form expression for the EC. The high-SNR approximation of the EC is also presented, revealing the power offset in the high-SNR regime. Monte Carlo simulations validate the high accuracy of the proposed analytical models, demonstrating their effectiveness in capturing the performance of the P2P FAS.