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Ground-to-UAV and RIS-assisted UAV-to-Ground Communication Under Channel Aging: Statistical Characterization and Outage Performance

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

TL;DR

This work develops a comprehensive statistical framework for G2A and RIS-assisted UAV communications under channel aging, incorporating 3D mobility and Doppler effects. It derives exact SNR distributions: a G2A SNR that follows a mixture of noncentral χ^2 RVs and an A2G SNR that, under large RIS sizes, can be modeled as the product of two correlated noncentral χ^2 RVs, with exact PDF/CDF expressions for the product case. The RIS-assisted channel characterization uses conditional complex Gaussian modeling and the law of total cumulance to handle nonideal CSI, enabling insights into PSC design and performance, including a three-step adaptive spectral-efficiency approach to stabilize outage. The results demonstrate RISs’ effectiveness against channel aging within coherence time, and the adaptive SE method ensures reliable end-to-end performance for moving UAVs and ground users in dynamic environments. Practical implications include precise outage- and SE-aware design guidance for RIS-enabled UAV networks in 6G/TNTN contexts.

Abstract

This paper studies the statistical characterization of ground-to-air (G2A) and reconfigurable intelligent surface (RIS)-assisted air-to-ground (A2G) communications in RIS-assisted UAV networks under the impact of channel aging. A comprehensive channel model is presented, which incorporates the time-varying fading, three-dimensional (3D) mobility, Doppler shifts, and the effects of channel aging on array antenna structures. We provide analytical expressions for the G2A signal-to-noise ratio (SNR) probability density function (PDF) and cumulative distribution function (CDF), demonstrating that the G2A SNR follows a mixture of noncentral $χ^2$ distributions. The A2G communication is characterized under RIS arbitrary phase-shift configurations, showing that the A2G SNR can be represented as the product of two correlated noncentral $χ^2$ random variables (RVs). Additionally, we present the PDF and the CDF of the product of two independently distributed noncentral $χ^2$ RVs, which accurately characterize the A2G SNR's distribution. Our paper confirms the effectiveness of RISs in mitigating channel aging effects within the coherence time. Finally, we propose an adaptive spectral efficiency method that ensures consistent system performance and satisfactory outage levels when the UAV and the ground user equipments are in motion.

Ground-to-UAV and RIS-assisted UAV-to-Ground Communication Under Channel Aging: Statistical Characterization and Outage Performance

TL;DR

This work develops a comprehensive statistical framework for G2A and RIS-assisted UAV communications under channel aging, incorporating 3D mobility and Doppler effects. It derives exact SNR distributions: a G2A SNR that follows a mixture of noncentral χ^2 RVs and an A2G SNR that, under large RIS sizes, can be modeled as the product of two correlated noncentral χ^2 RVs, with exact PDF/CDF expressions for the product case. The RIS-assisted channel characterization uses conditional complex Gaussian modeling and the law of total cumulance to handle nonideal CSI, enabling insights into PSC design and performance, including a three-step adaptive spectral-efficiency approach to stabilize outage. The results demonstrate RISs’ effectiveness against channel aging within coherence time, and the adaptive SE method ensures reliable end-to-end performance for moving UAVs and ground users in dynamic environments. Practical implications include precise outage- and SE-aware design guidance for RIS-enabled UAV networks in 6G/TNTN contexts.

Abstract

This paper studies the statistical characterization of ground-to-air (G2A) and reconfigurable intelligent surface (RIS)-assisted air-to-ground (A2G) communications in RIS-assisted UAV networks under the impact of channel aging. A comprehensive channel model is presented, which incorporates the time-varying fading, three-dimensional (3D) mobility, Doppler shifts, and the effects of channel aging on array antenna structures. We provide analytical expressions for the G2A signal-to-noise ratio (SNR) probability density function (PDF) and cumulative distribution function (CDF), demonstrating that the G2A SNR follows a mixture of noncentral distributions. The A2G communication is characterized under RIS arbitrary phase-shift configurations, showing that the A2G SNR can be represented as the product of two correlated noncentral random variables (RVs). Additionally, we present the PDF and the CDF of the product of two independently distributed noncentral RVs, which accurately characterize the A2G SNR's distribution. Our paper confirms the effectiveness of RISs in mitigating channel aging effects within the coherence time. Finally, we propose an adaptive spectral efficiency method that ensures consistent system performance and satisfactory outage levels when the UAV and the ground user equipments are in motion.
Paper Structure (24 sections, 11 theorems, 59 equations, 8 figures, 1 table)

This paper contains 24 sections, 11 theorems, 59 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Time-Varying Fading Channel
  4. Continuous-Time Mobility Model
  5. Time-Varying Doppler Frequency
  6. Channel Aging Model
  7. Ground-to-Air Signal-to-Noise Ratio
  8. Air-to-Ground Signal-to-Noise Ratio
  9. Statistical Characterization of G2A and RIS-assisted A2G Communication
  10. Statistical Characterization of G2A Communication
  11. Statistical Characterization of RIS-assisted A2G Communication
  12. Effective Air-to-Ground Channel
  13. Effective Air-to-Ground Signal-to-Noise Ratio
  14. Phase-Shift Configurations
  15. Performance Analysis
  16. ...and 9 more sections

Key Result

Theorem 1

Under the delayed CSI-based MRT, the PDF of the G2A SNR is formulated as where $\Xi_{{\textnormal{U}}} \triangleq M K_{{\textnormal{S}}{\textnormal{U}}} \rho_{{\textnormal{S}}{\textnormal{U}}}^2 (K_{{\textnormal{S}}{\textnormal{U}}} +1) \bar{\gamma}_{{\mathsf{g2a}}}^{-1}$ and $\bar{\gamma}_{{\textnormal{S}}{\textnormal{U}}} = \frac{P_{\textnormal{S}}\ell_{{\textnormal{S}

Figures (8)

  • Figure 1: Illustrations of a G2A and RIS-assisted A2G wireless system, where the RIS is installed on houses and/or buildings.
  • Figure 2: Illustration of the nodes' initial positions are presented in the upper figures, where $\mathbf{p}_{{\textnormal{S}}_1} = \left[ 0, 0, 10 \right]^{\sf T}$ m, $\mathbf{p}_{{\textnormal{U}}} = \left[ 56, -10, 120 \right]^{\sf T}$ m, $\mathbf{p}_{{\textnormal{R}}_1} = \left[ 75, 0, 25 \right]^{\sf T}$ m, and $\mathbf{p}_{{\textnormal{D}}} = \left[ 80.68, 14.15, 1.5 \right]^{\sf T}$ m. The trajectories of the GUE and the UAV are presented in the lower figure.
  • Figure 3: Simulated and analytical results of (a) the G2A SNR's PDF in \ref{['eq:pdf_snrG2a']} and c) the G2A SNR's CDF in \ref{['eq:cdf_snrG2a']} with different number of antennas and $P_{\textnormal{S}} = 0$ dBm.
  • Figure 4: Simulated and analytical results of the normalized RIS-assisted A2G SNR PDF, defined as $\widetilde{{\gamma}}_{{\mathsf{a2g}}} \triangleq \frac{{\gamma}_{{\mathsf{a2g}}}}{\textnormal{E}\left[ {\gamma}_{{\mathsf{a2g}}} \right]}$, with different number of reflecting elements. Here, the right figure shows the relative entropy (Kullback–Leibler divergence) between the exact A2G SNR ${\gamma}_{{\mathsf{a2g}}}$ in \ref{['eq:snr_a2g']} and the proposed A2G SNR in \ref{['eq:Z2_cond']}.
  • Figure 5: CDF of the A2G SNR with different PSCs, where $N = 12^2$ elements and $P_{{\textnormal{U}}} = 0$ dBm.
  • ...and 3 more figures

Theorems & Definitions (12)

  • Remark 1
  • Theorem 1
  • Corollary 1
  • Lemma 1
  • Proposition 1
  • Lemma 2
  • Corollary 2
  • Lemma 3
  • Proposition 2
  • Proposition 3
  • ...and 2 more