Attenuation and Loss of Spatial Coherence Modeling for Atmospheric Turbulence in Terahertz UAV MIMO Channels

TL;DR

This paper addresses turbulence-induced attenuation and loss of spatial coherence (LoSC) in Terahertz UAV UM-MIMO channels. It builds a turbulence model grounded in Kolmogorov statistics and frequency-/altitude-dependent refractive-index structure constants (RISC), then derives LoSC through Maxwell's equations and the Rytov approximation, yielding a closed-form normalized covariance ρ_{iji'j'} and LoSC loss L_{LoSC}. Turbulence fading is modeled by a Gamma-Gamma distribution with parameters α_c and β_c, and turbulence attenuation L_{tur} is derived from σ_Ψ^2 = 1/α_c + 1/β_c + 1/(α_c β_c); the Rytov variance is σ_R^2 = 0.5 C_n^2 k^{7/6} L^{11/6} with k = 2π f / c. Numerical results show that turbulence causes at most 10 dB attenuation for f < 1 THz and L < 10 km, while LoSC can contribute about 10 dB extra loss for a 1024×1024 UM-MIMO at L = 10 km and C_n^2 = 10^{-9}, highlighting the importance of turbulence-aware design for long-range THz UAV links.

Abstract

Terahertz (THz) wireless communications have the potential to realize ultra-high-speed and secure data transfer with miniaturized devices for unmanned aerial vehicle (UAV) communications. The atmospheric turbulence due to random airflow leads to spatial inhomogeneity of the communication medium, which is yet missing in most existing studies, leading to additional propagation loss and even loss of spatial coherence (LoSC) in MIMO systems. In this paper, the attenuation and loss of spatial coherence for atmospheric turbulence are modeled in THz UAV MIMO channels. Specifically, the frequency- and altitude-dependency of the refractive index structure constant (RISC), as a critical statistical parameter characterizing the intensity of turbulence, is first investigated. Then, the LoSC, fading, and attenuation caused by atmospheric turbulence are modeled, where the turbulence-induced fading is modeled by a Gamma-Gamma distribution, and the turbulence attenuation as a function of altitude and frequency is derived. Numerical results show that the turbulence leads to at most 10 dB attenuation with frequency less than 1 THz and distance less than 10 km. Furthermore, when the distance is 10 km and the RISC is 10^-9m^(-2/3), the loss of spatial coherence effect leads to 10 dB additional loss for a 1024*1024 ultra-massive MIMO system.

Figures (9)

• Figure 1: System Model: MIMO in turbulent media.
• Figure 2: Terahertz UAV channel model in turbulent media.
• Figure 3: Illustration of LoSC effect for THz UM-MIMO system.
• Figure 4: RISC at the different altitudes. $A$ represents the terrestrial RISC. $v$ stands for the average wind velocity.
• Figure 5: Rytov variance with the different frequency. (a) With varying propagation distance $L$; (b) With varying RISC $C_n^2$.