Table 1 Multipath parameter model summarization

Delay \(\tau\)

\(P_{\text{delay}} \left( \tau \right) = \frac{1}{{b_{\tau }^{{a_{\tau } }} \varGamma \left( {a_{\tau } } \right)}}\tau^{{a_{\tau } - 1}} e^{{ - \frac{\tau }{{b_{\tau } }}}}\)

Sat. elevation:

0–15°

15°–30°

30°–45°

45°–60°

60° –75°

75°–90°

\(a_{\tau }\)

2.62

2.77

2.81

2.56

2.47

2.40

\(b_{\tau }\)

129.83

105.52

80.93

65.12

53.22

43.24

Power Loss 20log \(\alpha\)

\(\overline{\text{PL}} \left( \tau \right) = {\text{PL}}_{{0|{\text{dB}}}} + d_{\text{dB}} \tau\)

\({\text{PL}}_{{0|{\text{dB}}}}\)

−12.35 dB

\(d_{\text{dB}}\)

−0.0016 dB/m

Doppler fading frequency \(v\)

Static scenario

\(P_{\text{fading}}^{s} \left( v \right) = \frac{\mu }{2}e^{ - \mu \left| v \right|}\)

Orbit type:

MEO

IGSO

GEO

\(\mu\)

12.3

23.8

1495.9

Dynamic scenario

\(P_{\text{fading}}^{d} \left( v \right) = \frac{1}{{\sqrt {2\pi } \sigma_{v} }}e^{{ - \frac{{v^{2} }}{{2\sigma_{v}^{2} }}}}\)

Vehicle speed:

<10 km/h

10 ~ 20 km/h

20 ~ 30 km/h

\(\sigma_{\nu }\)

7.56

11.34

10.62

Lifetime \(\varepsilon\)

\(P_{\text{lft}} \left( \varepsilon \right) = \left( {\frac{1}{{\sigma_{\varepsilon } }}} \right)\left( {1 + \xi_{\varepsilon } \frac{{\varepsilon - \eta_{\varepsilon } }}{{\sigma_{\varepsilon } }}} \right)^{{ - \frac{{1 + \xi_{\varepsilon } }}{{\xi_{\varepsilon } }}}}\)

Static scenario

Orbit type:

MEO

IGSO

GEO

\(\xi_{\varepsilon }\)

0.04

0.25

0.38

\(\sigma_{\varepsilon }\)

8.07

19.38

128

\(\eta_{\varepsilon }\)

0.3

0.3

0.3

Dynamic scenario

Vehicle speed:

0–3 km/h

3–10 km/h

10–20 km/h

20–30 km/h

\(\xi_{\varepsilon }\)

1.23

0.50

0.36

0.34

\(\sigma_{\varepsilon }\)

0.45

0.29

0.26

0.25

\(\eta_{\varepsilon }\)

0.3

0.3

0.3

0.3