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Statistical Characterization of RIS-assisted UAV Communications in Terrestrial and Non-Terrestrial Networks Under Channel Aging

Thanh Luan Nguyen, Georges Kaddoum, Tri Nhu Do, Zygmunt J. Haas

TL;DR

The study addresses the statistical characterization of G2A and RIS-assisted A2G UAV communications under channel aging in terrestrial and non-terrestrial networks. It adopts a rigorous approach by modeling ${\gamma}_{\mathsf{G2A}}$ as a non-central complex Gaussian quadratic form and ${\gamma}_{\mathsf{A2G}}$ as the product of two SNCCS RVs, deriving exact PDFs via Laplace transforms and SNCCS theory; it also shows that for large $N$ the A2G cascade behaves like a single Rician channel. The work further derives an end-to-end outage bound and a maximum target spectral efficiency for given outage constraints, and reveals channel hardening phenomena at low UAV speeds, with RIS size and BS antennas improving performance only up to a finite limit. The results provide design insights and performance benchmarks for RIS-enabled UAV networks operating under mobility and CSI aging, highlighting the limits imposed by high UAV speeds and imperfect phase shifts.

Abstract

This paper studies the statistical characterization of ground-to-air (G2A) and reconfigurable intelligent surface (RIS)-assisted air-to-ground (A2G) communications with unmanned aerial vehicles (UAVs) in terrestrial and non-terrestrial networks under the impact of channel aging. We first model the G2A and A2G signal-to-noise ratios (SNRs) as non-central complex Gaussian quadratic random variables (RVs) and derive their exact probability density functions, offering a unique characterization for the A2G SNR as the product of two scaled non-central chi-square RVs. Moreover, we also find that, for a large number of RIS elements, the RIS-assisted A2G channel can be characterized as a single Rician fading channel. Our results reveal the presence of channel hardening in A2G communication under low UAV speeds, where we derive the maximum target spectral efficiency (SE) for a system to maintain a consistent required outage level. Meanwhile, high UAV speeds, exceeding 50 m/s, lead to a significant performance degradation, which cannot be mitigated by increasing the number of RIS elements.

Statistical Characterization of RIS-assisted UAV Communications in Terrestrial and Non-Terrestrial Networks Under Channel Aging

TL;DR

The study addresses the statistical characterization of G2A and RIS-assisted A2G UAV communications under channel aging in terrestrial and non-terrestrial networks. It adopts a rigorous approach by modeling as a non-central complex Gaussian quadratic form and as the product of two SNCCS RVs, deriving exact PDFs via Laplace transforms and SNCCS theory; it also shows that for large the A2G cascade behaves like a single Rician channel. The work further derives an end-to-end outage bound and a maximum target spectral efficiency for given outage constraints, and reveals channel hardening phenomena at low UAV speeds, with RIS size and BS antennas improving performance only up to a finite limit. The results provide design insights and performance benchmarks for RIS-enabled UAV networks operating under mobility and CSI aging, highlighting the limits imposed by high UAV speeds and imperfect phase shifts.

Abstract

This paper studies the statistical characterization of ground-to-air (G2A) and reconfigurable intelligent surface (RIS)-assisted air-to-ground (A2G) communications with unmanned aerial vehicles (UAVs) in terrestrial and non-terrestrial networks under the impact of channel aging. We first model the G2A and A2G signal-to-noise ratios (SNRs) as non-central complex Gaussian quadratic random variables (RVs) and derive their exact probability density functions, offering a unique characterization for the A2G SNR as the product of two scaled non-central chi-square RVs. Moreover, we also find that, for a large number of RIS elements, the RIS-assisted A2G channel can be characterized as a single Rician fading channel. Our results reveal the presence of channel hardening in A2G communication under low UAV speeds, where we derive the maximum target spectral efficiency (SE) for a system to maintain a consistent required outage level. Meanwhile, high UAV speeds, exceeding 50 m/s, lead to a significant performance degradation, which cannot be mitigated by increasing the number of RIS elements.
Paper Structure (11 sections, 3 theorems, 23 equations, 3 figures, 1 table)

This paper contains 11 sections, 3 theorems, 23 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Ground-to-Air Signal-to-Noise Ratio
  4. Air-to-Ground Signal-to-Noise Ratio
  5. Statistical Characterization and Performance Analysis
  6. Statistical Characterization of G2A communication
  7. Statistical Characterization of A2G communication
  8. End-to-End Outage Probability
  9. Channel Hardening
  10. Results and Discussions
  11. Conclusion

Key Result

Theorem 1

Under the LOS scenario, the exact PDF of the G2A SNR is formulated as where $\Xi_{{\textnormal{U}}} \triangleq M \kappa_{{\textnormal{S}}{\textnormal{U}}} \rho_{{\textnormal{S}}{\textnormal{U}}}^2 (\kappa_{{\textnormal{S}}{\textnormal{U}}} +1) \bar{{\gamma}}_{{\textnormal{S}}{\textnormal{U}}}^{-1}$.

Figures (3)

  • Figure 1: Simulated and analytical PDFs of a) the G2A SNR, b) and c) the A2G SNR, where c) is based on \ref{['eq:scale_snrR']} for practical RIS settings.
  • Figure 2: Simulated and derived analytical OP (a) at the target SE $R = \frac{1}{2}\log_2(1+\widehat{{\gamma}}_{\sf th})$ (b) in terms of the required outage level $L$, where $P_{\textnormal{S}} = P_{\textnormal{U}} = P$ [dBm], $M = 4$, and $N = 20^2$.
  • Figure 3: Maximum target SE with respect to a) the UAV’s speed ($v$) and sample index ($n$), and b) the UAV’s speed, where $P_{\textnormal{S}} = P_{\textnormal{U}} = 33$ dBm.

Theorems & Definitions (3)

  • Theorem 1
  • Lemma 1
  • Theorem 2