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Table 2 Ground-reflected ray parameters

From: Quasi-deterministic millimeter-wave channel models in MiWEBA

Parameter Value
Delay Ground-reflected ray delay is calculated from the model geometry:
τ G  = d G /c
\( {d}_G=\sqrt{L^2+{\left({H}_{tx}+{H}_{rx}\right)}^2} \)
Power Ground-reflected power calculated as free-space path loss with oxygen absorption, with additional reflection loss calculated on the base of the Fresnel equations. Reflection loss R is different for vertical and horizontal polarizations
\( {P}_{\perp }=20{ \log}_{10}\left(\frac{\lambda }{4\pi {d}_G}\right)-{A}_0{d}_G+{R}_{\perp }+F; \)
\( {P}_{\parallel }=20{ \log}_{10}\left(\frac{\lambda }{4\pi {d}_G}\right)-{A}_0{d}_G+{R}_{\parallel }+F \)
\( F=\raisebox{1ex}{$80$}\!\left/ \!\raisebox{-1ex}{$ \ln 10$}\right.{\left(\pi {\sigma}_h \sin \phi /\lambda \right)}^2 \)
\( {R}_{\perp }=20{ \log}_{10}\left(\frac{ \sin \phi -\sqrt{B_{\perp }}}{ \sin \phi +\sqrt{B_{\perp }}}\right);\ {R}_{\parallel }=20{ \log}_{10}\left(\frac{ \sin \phi -\sqrt{B_{\parallel }}}{ \sin \phi +\sqrt{B_{\parallel }}}\right) \)
B  = ε r  − cos2 ϕ for horizontal polarization.
\( {B}_{\perp }=\left({\varepsilon}_r-{ \cos}^2\phi \right)/{\varepsilon}_r^2 \) for vertical polarization,
where \( \tan \phi =\frac{H_{tx}+{H}_{rx}}{L} \) and σ h is a surface roughness.
Channel matrix \( \mathbf{H}=\left[\begin{array}{cc}\hfill {10}^{P_{\perp }/20}\hfill & \hfill \xi \hfill \\ {}\hfill \xi \hfill & \hfill {10}^{P_{\parallel }/20}\hfill \end{array}\right]{e}^{\frac{j2\pi {d}_G}{\lambda }} \)
AoD Azimuth: 0°, elevation: \( {\theta}_{AoD}={ \tan}^{-1}\left(\frac{L}{H_{tx}-{H}_{rx}}\right)-{ \tan}^{-1}\left(\frac{L}{H_{tx}+{H}_{rx}}\right) \)
AoA Azimuth: 0°, elevation: \( {\theta}_{AoA}={ \tan}^{-1}\left(\frac{H_{tx}+{H}_{rx}}{L}\right)-{ \tan}^{-1}\left(\frac{H_{tx}-{H}_{rx}}{L}\right) \)
  1. AoD angle of departure, AoA angle of arrival