In 6G mobile communication systems, fluid antenna systems (FAS) have emerged as a promising technology for achieving additional diversity within limited spatial constraints. Although extensive research has been conducted on the performance analysis of FAS, existing analytical frameworks suffer from significant limitations, including inaccurate performance estimation and increased computational complexity as the number of antenna ports increases. This paper proposes a novel analytical framework utilizing matrix approximation to evaluate the outage probability of FAS, an emerging technology for 6G wireless communications. The framework effectively captures the intricate correlation structure of FAS channels while maintaining high analytical precision. Specifically, Jake's model-based covariance matrix, which characterizes the statistical properties of FAS channels, is approximated using the exponential correlation matrix. This approximation enables the derivation of closed-form expressions for the cumulative distribution function (CDF) of correlated FAS channels and the system's outage probability. The obtained results demonstrate excellent agreement with simulation results, even as the number of antenna ports increases. Notably, the proposed approach avoids computationally expensive multiple integrals, allowing efficient evaluation of outage probabilities through simple summation. This study offers rigorous analytical insights and provides significant contributions to the design and analysis of correlated communication systems.
