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Dimensional Scaling Laws for Continuous Fluid Antenna Systems

Peter J. Smith, Amy S. Inwood, Michail Matthaiou, Rajitha Senanayake

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.

Dimensional Scaling Laws for Continuous Fluid Antenna Systems

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.
Paper Structure (11 sections, 3 theorems, 24 equations, 3 figures, 1 table)

This paper contains 11 sections, 3 theorems, 24 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Analysis
  4. Fixed Antenna
  5. One Dimension
  6. Arbitrary Numbers of Dimensions
  7. Optimal Shapes
  8. Numerical Results
  9. High SNR Probability and Dimensional Scaling
  10. Impact of Antenna Shape
  11. Conclusion

Key Result

Lemma 1

In 0 dimensions, In 1 dimension, In 2 dimensions, In 3 dimensions,

Figures (3)

  • Figure 1: Fluid antenna geometries for multiple dimensions.
  • Figure 2: A comparison of the analytical, simulated and scaling law HSPs for 0-3 dimension CFAs, where each dimension is set to $0.25\lambda$.
  • Figure 3: The analytical HSP for 2 and 3 dimensional CFASs, where each dimension is set in multiples of $\lambda$ according to the legend.

Theorems & Definitions (6)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof