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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.20846 |
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| _version_ | 1866917356404473856 |
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| author | Wu, Tuo Zheng, Jianchao |
| author_facet | Wu, Tuo Zheng, Jianchao |
| contents | This paper develops a comprehensive analytical framework for the outage probability of fluid antenna system (FAS)-aided communications by modeling the antenna as a continuous aperture and approximating the Jakes (Bessel) spatial correlation with a Gaussian kernel $ρ_G(δ) = e^{-π^2δ^2}$. Three complementary analytical strategies are pursued. First, the Karhunen--Loève (KL) expansion under the Gaussian kernel is derived, yielding closed-form outage expressions for the rank-1 and rank-2 truncations and a Gauss--Hermite formula for arbitrary rank~$K$, with effective degrees of freedom $K_{\mathrm{eff}}^G \approx π\sqrt{2}\, W$. Second, rigorous two-sided outage bounds are established via Slepian's inequality and the Gaussian comparison theorem: by sandwiching the true correlation between equi-correlated models with $ρ_{\min}$ and $ρ_{\max}$, closed-form upper and lower bounds that avoid the optimistic bias of block-correlation models are obtained. Third, a continuous-aperture extreme value theory is developed using the Adler--Taylor expected Euler characteristic method and Piterbarg's theorem. The resulting outage expression $P_{\mathrm{out}} \approx 1 - e^{-x}(1 + π\sqrt{2}\, W\, x)$ depends only on the aperture~$W$ and threshold~$x$, is independent of the port count~$N$, and is identical for the Jakes and Gaussian models since both share the second spectral moment $λ_2 = 2π^2$. A Pickands-constant refinement for the deep-outage regime and a threshold-dependent effective diversity $N_{\mathrm{eff}} \approx 1 + π\sqrt{2}\, W\, x$ are further derived. Numerical results confirm that the Gaussian approximation incurs less than 10\% relative outage error for $W \leq 2$ and that the continuous-aperture formula converges with as few as $N \approx 10W$ ports. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20846 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Gaussian Process Framework for Outage Analysis in Continuous-Aperture Fluid Antenna Systems Wu, Tuo Zheng, Jianchao Signal Processing This paper develops a comprehensive analytical framework for the outage probability of fluid antenna system (FAS)-aided communications by modeling the antenna as a continuous aperture and approximating the Jakes (Bessel) spatial correlation with a Gaussian kernel $ρ_G(δ) = e^{-π^2δ^2}$. Three complementary analytical strategies are pursued. First, the Karhunen--Loève (KL) expansion under the Gaussian kernel is derived, yielding closed-form outage expressions for the rank-1 and rank-2 truncations and a Gauss--Hermite formula for arbitrary rank~$K$, with effective degrees of freedom $K_{\mathrm{eff}}^G \approx π\sqrt{2}\, W$. Second, rigorous two-sided outage bounds are established via Slepian's inequality and the Gaussian comparison theorem: by sandwiching the true correlation between equi-correlated models with $ρ_{\min}$ and $ρ_{\max}$, closed-form upper and lower bounds that avoid the optimistic bias of block-correlation models are obtained. Third, a continuous-aperture extreme value theory is developed using the Adler--Taylor expected Euler characteristic method and Piterbarg's theorem. The resulting outage expression $P_{\mathrm{out}} \approx 1 - e^{-x}(1 + π\sqrt{2}\, W\, x)$ depends only on the aperture~$W$ and threshold~$x$, is independent of the port count~$N$, and is identical for the Jakes and Gaussian models since both share the second spectral moment $λ_2 = 2π^2$. A Pickands-constant refinement for the deep-outage regime and a threshold-dependent effective diversity $N_{\mathrm{eff}} \approx 1 + π\sqrt{2}\, W\, x$ are further derived. Numerical results confirm that the Gaussian approximation incurs less than 10\% relative outage error for $W \leq 2$ and that the continuous-aperture formula converges with as few as $N \approx 10W$ ports. |
| title | A Gaussian Process Framework for Outage Analysis in Continuous-Aperture Fluid Antenna Systems |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2603.20846 |