High SNR Probabilities of Continuous Fluid Antenna Systems in Ricean Environments

Abstract: We consider a single-user (SU) continuous fluid antenna system (CFAS) employing matched filtering (MF) operating over a Ricean fading channel. Focusing on the upper tail of the received signal-to-noise ratio (SNR) distribution (the high SNR probability (HSP)), we derive accurate approximations for the HSP in 1, 2, and 3 dimensions using the expected Euler characteristic (EEC), presenting the first analytical results for a CFAS in a Ricean environment. In the process, we provide the first closed-form expression for the Euler characteristic density of a non-central chi-squared random field. We then examine the impact of the Ricean K-factor on the CFAS performance, emphasizing the critical role of channel variations in achieving a strong HSP.