Dimensional Scaling Laws for Continuous Fluid Antenna Systems

Authors:
  • PSPeter J. Smith
    Peter J. Smith
  • AIAmy S. Inwood
    Amy S. Inwood
  • MMMichail Matthaiou
    Michail Matthaiou
  • RSRajitha Senanayake
    Rajitha Senanayake
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Abstract
Consider the signal-to-noise ratio (SNR) of a continuous fluid antenna system (CFAS) operating over a Rayleigh fading channel. In this paper, we extend traditional system assumptions and consider spatially coherent isotropic correlation, continuous positioning of the antenna rather than discrete, and the use of multi-dimensional space (1D, 2D and 3D). By focusing on the upper tail of the received SNR distribution (the high SNR probability (HSP)), we are able to derive asymptotically exact closed-form formulas for the HSP. Finally, these results lead to scaling laws which describe the increase in the HSP as we employ more dimensions and the optimal CFAS dimensions.