Radio-Wave Propagation and Satellite Channel Models

Introduction

A satellite link is not governed by free-space spreading alone. Its signal also interacts with atmospheric gases, hydrometeors, refractive turbulence, the ionosphere, terrain, buildings and moving terminals. These mechanisms determine received power, phase, polarization, delay spread, Doppler spectrum and ultimately service availability.

Propagation effects vary strongly with frequency. Ionospheric effects dominate many links below approximately 3 GHz, while gaseous absorption, clouds and rain become increasingly significant in Ku-, Ka- and higher-frequency systems. Mobile satellite links must additionally contend with shadowing, blockage and multipath. Reliable design therefore requires a combination of deterministic geometry, statistical propagation models and time-dependent channel models.

The International Telecommunication Union Radiocommunication Sector (ITU-R) provides widely adopted procedures. Important recommendations include P.618 for Earth–space propagation design, P.676 for atmospheric gases, P.837 for rainfall rate, P.838 for rain-specific attenuation, P.839 for rain height, P.840 for clouds, P.531 for ionospheric effects and P.681 for land-mobile satellite channels. Recommendation versions and input databases are periodically revised; professional studies must identify the edition used.

Learning Objectives

After completing this chapter, the reader should be able to:

1. Derive and calculate free-space path loss for satellite links.

2. Model attenuation due to atmospheric gases, rain and clouds using relevant ITU-R procedures.

3. explain tropospheric scintillation and ionospheric delay, rotation and scintillation.

4. Calculate satellite Doppler shift and identify its variation over a pass.

5. Construct statistical shadowing and multipath models for mobile satellite channels.

6. Apply state-based ITU-R P.681 concepts to land-mobile satellite links.

7. Convert propagation statistics into fade margins and availability estimates.

8. Critically assess model assumptions, uncertainty and joint impairment occurrence.

1. Structure of an Earth–Space Propagation Channel

A convenient narrowband representation of the received complex envelope is

\[

y(t)=h(t)x(t-\tau)+n(t),

\]

where \(x(t)\) is the transmitted waveform, \(h(t)\) is the complex channel coefficient, \(\tau\) is propagation delay and \(n(t)\) is receiver noise. A useful decomposition is

\[

h(t)=h_{\mathrm{FS}}h_{\mathrm{gas}}h_{\mathrm{hyd}}h_{\mathrm{ion}}h_{\mathrm{sh}}h_{\mathrm{mp}},

\]

where the factors describe free-space propagation, gases, hydrometeors, ionospheric effects, shadowing and multipath. This multiplication is conceptual: several components are correlated and cannot always be simulated independently.

For a wideband channel, delayed replicas must be represented explicitly:

\[

h(t,\tau)=\sum_{\ell=0}^{L-1}a_\ell(t)e^{j\phi_\ell(t)}\delta(\tau-\tau_\ell(t)).

\]

Here, \(a_\ell\), \(\phi_\ell\) and \(\tau_\ell\) are the amplitude, phase and delay of path \(\ell\). The channel is frequency-selective when the signal bandwidth is comparable to or exceeds its coherence bandwidth.

Propagation mechanisms have different time scales. Gaseous loss changes slowly; rain fades evolve over seconds to minutes; scintillation can vary more rapidly; and mobile blockage may change abruptly at street corners or beneath vegetation. A single percentage attenuation value therefore cannot reproduce channel dynamics.

2. Free-Space Propagation

2.1 Friis transmission relation

For ideal antennas in the far field, with unobstructed line of sight and matched polarization and impedance, the Friis equation is

\[

P_r=P_tG_tG_r\left(\frac{\lambda}{4\pi d}\right)^2,

\]

where \(P_t\) and \(P_r\) are transmitted and received powers, \(G_t\) and \(G_r\) are dimensionless antenna gains, \(\lambda\) is wavelength and \(d\) is propagation distance.

The free-space path loss is consequently

\[

L_{\mathrm{FS}}=\left(\frac{4\pi d}{\lambda}\right)^2.

\]

In decibels,

\[

L_{\mathrm{FS,dB}}=20\log_{10}\left(\frac{4\pi df}{c}\right),

\]

or, for \(d\) in kilometres and \(f\) in gigahertz,

\[

\boxed{L_{\mathrm{FS,dB}}=92.45+20\log_{10}d_{\mathrm{km}}+20\log_{10}f_{\mathrm{GHz}}.}

\]

Free-space loss is a geometric spreading ratio, not atmospheric absorption. The formula also excludes feeder loss, pointing error, polarization mismatch and antenna gains.

2.2 Numerical example

For a 20 GHz link over 36,000 km,

\[

L_{\mathrm{FS}}=92.45+20\log_{10}(36000)+20\log_{10}(20)

\approx209.60\ \mathrm{dB}.

\]

The large value is offset by high antenna gains and high effective isotropic radiated power. A 1 dB modelling error can nevertheless be important when the operational margin is only a few decibels.

3. Tropospheric Attenuation

The neutral atmosphere introduces gaseous absorption, cloud attenuation, rain attenuation and refractive effects. For link-budget work, total attenuation may be written schematically as

\[

A_T=A_g+A_c+A_r+A_s,

\]

where the terms denote gas, cloud, rain and scintillation attenuation. Directly adding percentile values is conservative only under explicitly stated assumptions because the impairments are not perfectly coincident.

3.1 Atmospheric gases: ITU-R P.676

Molecular oxygen and water vapour absorb electromagnetic energy at resonance lines and in their continua. Oxygen has a strong complex near 60 GHz and a line near 118.75 GHz; water vapour has important lines near 22.2 and 183.3 GHz.

The local specific attenuation is

\[

\gamma_g=\gamma_o+\gamma_w\quad \mathrm{dB/km},

\]

where the oxygen and water-vapour terms depend on frequency, pressure, temperature and water-vapour density. For a nonuniform atmosphere, slant-path attenuation is obtained from

\[

A_g=\int_0^{s_a}\gamma_g(f,p(s),T(s),\rho_w(s))\,ds.

\]

ITU-R P.676 provides line-by-line and approximate procedures. A simple cosecant mapping from zenith attenuation is useful only when a plane-parallel atmosphere is adequate and the elevation angle is not very low. Near the horizon, curvature and refractive ray bending require the full slant-path method.

Gaseous attenuation is normally a persistent baseline loss. Water-vapour variability may still be important at millimetre-wave frequencies and in humid climates.

3.2 Rain attenuation: P.837, P.838, P.839 and P.618

Rain attenuation is usually the dominant fade mechanism for Ku-, Ka- and Q/V-band Earth–space links. The design process combines four types of information:

1. Rainfall-rate statistics from ITU-R P.837 or reliable local measurements.

2. Frequency- and polarization-dependent specific attenuation from P.838.

3. Rain height from P.839.

4. Slant-path reduction and percentage extrapolation from P.618.

For rainfall rate \(R\) in mm/h, the rain-specific attenuation is

\[

\gamma_R=kR^\alpha\quad \mathrm{dB/km},

\]

where \(k\) and \(\alpha\) depend on frequency, polarization and path elevation. They must be obtained from the applicable P.838 procedure; coefficients from a different frequency or polarization are not interchangeable.

Let \(R_{0.01}\) be the rain rate exceeded for 0.01% of an average year. For station height \(h_s\), rain height \(h_R\) and elevation angle \(\theta\), the geometric slant length through rain is, for the normal P.618 geometry above its stated minimum elevation,

\[

L_s=\frac{h_R-h_s}{\sin\theta},

\qquad

L_G=L_s\cos\theta,

\]

where lengths and heights are in kilometres.

Rain cells do not normally fill a long path uniformly. The horizontal reduction factor is

\[

r_{0.01}=\frac{1}{1+0.78\sqrt{\frac{L_G\gamma_R}{f}}-0.38\left(1-e^{-2L_G}\right)},

\]

where \(f\) is in GHz. Define

\[

\zeta=\tan^{-1}\left(\frac{h_R-h_s}{L_Gr_{0.01}}\right).

\]

The reduced rain-path length is

\[

L_R=\begin{cases}

\dfrac{L_Gr_{0.01}}{\cos\theta}, & \zeta>\theta,\\[6pt]

\dfrac{h_R-h_s}{\sin\theta}, & \zeta\leq\theta.

\end{cases}

\]

P.618 then applies a vertical adjustment factor \(v_{0.01}\), giving

\[

L_E=L_Rv_{0.01},

\qquad

A_{0.01}=\gamma_RL_E.

\]

The complete current P.618 expression for \(v_{0.01}\) should be implemented rather than replacing it by unity without checking. Attenuation exceeded for another percentage \(p\), over the range specified by P.618, is estimated from

\[

A_p=A_{0.01}\left(\frac{p}{0.01}\right)^{-\left[0.655+0.033\ln p-0.045\ln A_{0.01}-\beta(1-p)\sin\theta\right]},

\]

where \(p\) is expressed as a percentage and \(\beta\) is selected from the latitude-, elevation- and percentage-dependent P.618 rules. This is an empirical extrapolation, not a universal probability law.

Rain also causes depolarization through differential attenuation and phase shift between orthogonal field components. The resulting cross-polarization degradation can limit frequency reuse even when co-polar power remains adequate.

3.3 Clouds and fog: ITU-R P.840

Cloud attenuation arises mainly from liquid water droplets. Ice clouds usually have much lower microwave attenuation because their dielectric loss is smaller.

For a cloud liquid-water column \(L_{\mathrm{red}}\) in kg/m² and a sufficiently high elevation angle for plane-parallel mapping,

\[

A_c=\frac{L_{\mathrm{red}}K_l}{\sin\theta}\quad \mathrm{dB},

\]

where \(K_l\) is the specific attenuation coefficient in dB/(kg/m²), determined by frequency and cloud temperature. P.840 supplies statistical liquid-water content and the required coefficient model.

Cloud attenuation is modest at lower microwave frequencies but becomes relevant at Ka-band and above, especially for high-availability systems where persistent small losses consume fade margin.

3.4 Tropospheric scintillation

Small-scale refractive-index irregularities cause rapid amplitude and phase fluctuations. Scintillation becomes stronger with increasing frequency, decreasing elevation angle and increasing turbulence, and depends on antenna averaging. A larger antenna averages the wavefront over its aperture and therefore reduces amplitude scintillation.

The P.618 procedure uses local wet refractivity, elevation angle, frequency, effective path length and antenna diameter to estimate a reference standard deviation and then a fade depth for a specified percentage of time. The output is a statistical fade level rather than an additional constant loss.

Scintillation can interact with rain. Simply adding a 0.1% rain fade and a 0.1% scintillation fade assumes simultaneous extreme occurrence and may be overly conservative. P.618 includes a combined rain-and-scintillation treatment for appropriate design conditions.

4. Ionospheric Propagation: ITU-R P.531

The ionosphere contains free electrons extending roughly from 60 km to more than 1,000 km altitude. Its effects are dispersive and are most significant at VHF, UHF and L-band. P.531 provides prediction methods and data for Earth–space ionospheric effects.

4.1 Total electron content and group delay

Total electron content is

\[

\mathrm{TEC}=\int N_e(s)\,ds,

\]

where \(N_e\) is electron density in electrons/m³. One TEC unit is

\[

1\ \mathrm{TECU}=10^{16}\ \mathrm{electrons/m^2}.

\]

To first order, the excess group-path length is

\[

\Delta L_g=\frac{40.3\,\mathrm{TEC}}{f^2}\quad \mathrm{m},

\]

with TEC in electrons/m² and \(f\) in hertz. The corresponding delay is \(\Delta t=\Delta L_g/c\). Carrier phase experiences an advance of equal first-order path magnitude but opposite sign. Because the error varies as \(f^{-2}\), dual-frequency measurements can estimate and largely remove it.

For 10 TECU at 1.5 GHz,

\[

\Delta L_g=\frac{40.3(10^{17})}{(1.5\times10^9)^2}\approx1.79\ \mathrm{m},

\]

corresponding to approximately 5.97 ns.

4.2 Faraday rotation

A magnetized plasma rotates the plane of linear polarization. In SI units, a first-order expression is

\[

\Omega=\frac{2.36\times10^4}{f^2}\int N_e(s)B_{\parallel}(s)\,ds,

\]

where \(\Omega\) is in radians, \(f\) is in hertz, \(B_{\parallel}\) is the geomagnetic-field component along the path in tesla, and distance is in metres. The sign depends on propagation direction and magnetic-field orientation.

Faraday rotation can produce severe polarization mismatch at lower frequencies. Circular polarization or polarization tracking can reduce sensitivity, although circular polarization is itself affected by differential plasma propagation at sufficiently high precision.

4.3 Ionospheric scintillation

Irregular electron-density structures cause amplitude and phase scintillation, particularly near the geomagnetic equator after sunset and at high latitudes during disturbed conditions. Severity is commonly represented by the amplitude scintillation index

\[

S_4=\frac{\sqrt{E[I^2]-E[I]^2}}{E[I]},

\]

where \(I\) is received intensity. Phase scintillation is characterized using detrended phase statistics.

P.531 modelling should distinguish climatological occurrence, fade depth and temporal dynamics. For simulation, a practical procedure is to select the geographic region, local time, season, solar activity and frequency; obtain occurrence and intensity statistics; generate correlated amplitude and phase processes with suitable spectra; and validate level-crossing rates and fade durations. A static lognormal fade alone does not reproduce acquisition loss or carrier-tracking stress.

4.4 Other P.531 effects

Additional ionospheric concerns include absorption at lower frequencies, polarization effects, refraction, apparent direction changes and increased sky noise. Model inputs are uncertain during geomagnetic storms, so safety-critical navigation and timing systems should combine propagation modelling with real-time ionospheric monitoring.

5. Doppler Shift and Delay Dynamics

Relative motion changes path length and carrier frequency. If \(R(t)\) is transmitter–receiver range, then

\[

\tau(t)=\frac{R(t)}{c},

\qquad

f_D(t)=-\frac{f_c}{c}\frac{dR(t)}{dt},

\]

where \(f_c\) is carrier frequency. A decreasing range produces positive Doppler under this sign convention.

For a 2 GHz carrier and radial speed of 7 km/s, the Doppler magnitude is

\[

|f_D|=\frac{2\times10^9}{3\times10^8}(7000)\approx46.7\ \mathrm{kHz}.

\]

LEO Doppler varies rapidly during a pass and crosses near zero around closest approach. Oscillator offset, orbit-prediction error and terminal motion add residual frequency error. Compensation may use ephemeris-based pre-correction followed by acquisition and tracking loops.

Each multipath component can have a different Doppler shift. The resulting Doppler spectrum determines coherence time. The approximation \(T_c\sim1/f_{D,\max}\) indicates scale only; the numerical coefficient depends on the selected correlation criterion and spectrum.

6. Shadowing, Blockage and Multipath

6.1 Lognormal shadowing

Large objects produce slowly varying attenuation. A common local model is

\[

P_r^{\mathrm{dB}}=\overline{P_r^{\mathrm{dB}}}-X_\sigma,

\qquad X_\sigma\sim\mathcal N(\mu_s,\sigma_s^2),

\]

where positive \(X_\sigma\) represents excess loss. Spatial correlation is often modelled as

\[

\rho(\Delta x)=e^{-\Delta x/d_c},

\]

where \(d_c\) is decorrelation distance. Independent shadow samples at every simulation instant are physically unrealistic.

Complete blockage can be modelled as a separate state rather than as the far tail of a lognormal distribution. This is particularly important for urban canyons, tunnels and dense tree cover.

6.2 Small-scale fading

With no dominant component, the complex received field may be Gaussian and its envelope Rayleigh distributed:

\[

p_R(r)=\frac{r}{\sigma^2}e^{-r^2/(2\sigma^2)},\quad r\geq0.

\]

With a deterministic dominant component of amplitude \(s\), the envelope is Rician:

\[

p_R(r\mid s)=\frac{r}{\sigma^2}

\exp\left[-\frac{r^2+s^2}{2\sigma^2}\right]

I_0\left(\frac{rs}{\sigma^2}\right).

\]

The Rician \(K\)-factor is the ratio of dominant-path power to diffuse power. Neither Rayleigh nor Rician fading alone captures long-duration satellite shadowing.

6.3 Loo model

The Loo model combines a lognormally varying direct component with diffuse Rayleigh multipath. In complex baseband form,

\[

h=s e^{j\phi}+z,

\]

where \(20\log_{10}s\) is Gaussian and \(z\) is circular complex Gaussian. Conditional on \(s\), the envelope is Rician; the unconditional density is obtained by integrating the Rician density over the lognormal distribution of \(s\).

This model captures gradual direct-path shadowing plus local diffuse scattering. Its parameters must be conditioned on environment, elevation, frequency and terminal configuration.

7. ITU-R P.681 Land-Mobile Satellite Channel Modelling

P.681 provides propagation data and modelling guidance for land-mobile satellite services. At postgraduate level, it is important to move beyond naming distributions and construct a channel with state occupancy, state transitions, within-state fading and temporal correlation.

7.1 State-based representation

A common model uses three propagation states:

• Good or clear: a strong line-of-sight component is present.
• Shadowed: the direct component is attenuated by vegetation or structures.
• Blocked: direct visibility is absent or deeply suppressed.

Let \(S_n\in\{G,S,B\}\) be the state at sample \(n\). A first-order Markov model has transition matrix

\[

\mathbf P=

\begin{bmatrix}

p_{GG}&p_{GS}&p_{GB}\\p_{SG}&p_{SS}&p_{SB}\\p_{BG}&p_{BS}&p_{BB}

\end{bmatrix},

\qquad \sum_jp_{ij}=1.

\]

The stationary state probabilities satisfy

\[

\boldsymbol\pi=\boldsymbol\pi\mathbf P,

\qquad \sum_i\pi_i=1.

\]

If samples correspond to distance increment \(\Delta x\), the mean dwell distance in state \(i\) for this discrete Markov model is

\[

\bar d_i=\frac{\Delta x}{1-p_{ii}}.

\]

Thus transition probabilities must be rescaled when simulation speed or sampling interval changes. Copying a transition matrix to a different spatial step changes the physical blockage lengths.

7.2 State-conditioned fading

Each state requires its own distribution. The clear state may use Rician fading with a high \(K\)-factor; the shadowed state may use a Loo distribution; and the blocked state may use a low-power diffuse distribution plus diffraction loss. Parameters are selected from measurements appropriate to urban, suburban, rural or wooded environments and to the satellite elevation angle.

A practical narrowband simulator proceeds as follows:

1. Generate the state sequence using the transition matrix or measured segment-length distributions.

2. Generate correlated direct-path shadowing within each state.

3. Generate diffuse fading with the required Doppler spectrum.

4. Apply state-specific mean power, variance and \(K\)-factor.

5. Preserve phase continuity when appropriate at state transitions.

6. Validate the amplitude distribution, autocorrelation, level-crossing rate and fade-duration distribution.

For wideband modelling, each state is assigned a tapped delay-line profile. Tap powers, delays and Doppler spectra may change at transitions. A narrowband P.681 model should not be used to infer delay spread unless corresponding wideband parameters are available.

7.3 Limitations of P.681-type models

A stationary first-order Markov chain can reproduce state probabilities and average dwell lengths, but not necessarily the heavy-tailed blockage intervals found in urban routes. Semi-Markov models, in which state duration has an explicit distribution, are often more realistic. Site-specific ray tracing and map-based visibility models can add geometry, while stochastic residuals retain local variability.

Model transfer is hazardous: parameters measured for a vehicle-mounted L-band antenna cannot automatically be applied to a handheld Ka-band terminal. Frequency-dependent diffraction, foliage loss, antenna pattern, body blockage and beam tracking must be reconsidered.

8. Availability and Fade-Margin Engineering

If \(A_p\) is the attenuation exceeded for \(p\)% of an average year, a propagation margin \(M=A_p\) nominally supports availability

\[

\mathcal A=100-p\ \%.

\]

For \(p=0.1\%\), annual outage is approximately

\[

0.001\times8760=8.76\ \mathrm{h/year}.

\]

This interpretation assumes propagation is the limiting cause. Hardware failures, interference, gateway diversity switching, congestion and maintenance must be included separately in an end-to-end service-level model.

Mitigation methods include uplink power control, adaptive coding and modulation, site diversity, gateway diversity, larger antennas, lower-order modulation, packet interleaving and traffic rerouting. Adaptive systems should use hysteresis and prediction to avoid unstable mode switching during fast fades.

9. Detailed Applied Case: Ka-Band Gateway Availability

This is an illustrative engineering case. Its numerical inputs are selected to demonstrate the P.618 procedure and do not represent a specific licensed site.

Background and problem

An 18 GHz downlink gateway operates at elevation \(\theta=20^\circ\). The station height is 0.50 km and the P.839 rain height is 4.03 km. The P.837 rainfall rate exceeded for 0.01% of an average year is 44.7 mm/h. For the selected polarization, the applicable P.838 coefficients are taken as \(k=0.0560\) and \(\alpha=1.116\). The clear-sky link has 12 dB available propagation margin. Determine whether 99.9% propagation availability is supported.

Step 1: Specific rain attenuation

\[

\gamma_R=kR_{0.01}^{\alpha}

=0.0560(44.7)^{1.116}

\approx3.89\ \mathrm{dB/km}.

\]

Step 2: Rain geometry

\[

L_s=\frac{4.03-0.50}{\sin20^\circ}

\approx10.32\ \mathrm{km},

\]

\[

L_G=L_s\cos20^\circ\approx9.70\ \mathrm{km}.

\]

Step 3: Horizontal reduction

\[

r_{0.01}=\frac{1}{1+0.78\sqrt{9.70(3.89)/18}-0.38(1-e^{-19.4})}

\approx0.572.

\]

The reduced horizontal projection is

\[

L_Gr_{0.01}\approx9.70(0.572)=5.55\ \mathrm{km}.

\]

Also,

\[

\zeta=\tan^{-1}\left(\frac{3.53}{5.55}\right)\approx32.5^\circ>20^\circ.

\]

Therefore the applicable reduced rain length is

\[

L_R=\frac{L_Gr_{0.01}}{\cos20^\circ}

\approx5.90\ \mathrm{km}.

\]

This distinction is essential: 9.54 km would not follow from the stated geometry and reduction factor.

Using the full P.618 vertical adjustment for the assumed site inputs gives approximately \(v_{0.01}=0.995\), hence

\[

L_E=L_Rv_{0.01}\approx5.87\ \mathrm{km}.

\]

Step 4: Rain attenuation at 0.01%

\[

A_{0.01}=3.89(5.87)\approx22.8\ \mathrm{dB}.

\]

Step 5: Extrapolation to 0.1%

Assume a latitude for which the relevant P.618 rule gives \(\beta=0\). Then

\[

A_{0.1}=22.8(10)^{-[0.655+0.033\ln(0.1)-0.045\ln(22.8)]}

\approx8.3\ \mathrm{dB}.

\]

Step 6: Combined propagation allowance

Suppose the design study assigns, at the target condition, 0.7 dB for gases, 0.5 dB for clouds and 0.4 dB for scintillation. A conservative arithmetic combination gives

\[

A_T\approx8.3+0.7+0.5+0.4=9.9\ \mathrm{dB}.

\]

The remaining margin is

\[

M_{\mathrm{res}}=12.0-9.9=2.1\ \mathrm{dB}.

\]

Outcome

Under the stated conservative combination and ITU-R assumptions, the link supports the 99.9% propagation target with approximately 2.1 dB residual margin. It does not support a 99.99% target with the same margin because the 0.01% rain attenuation alone is about 22.8 dB.

The conclusion is conditional rather than absolute. Exact end-to-end availability requires joint impairment statistics, equipment reliability, interference allowance and uncertainty in rainfall climatology.

Learning points

• The reduction factor must be applied within the specified P.618 geometry.
• The effective rain length is approximately 5.9 km, not the unreduced slant length.
• Percentage extrapolation is performed after calculating \(A_{0.01}\).
• Marginal links require uncertainty and implementation reserves, not only median model outputs.

10. Model Limitations and Contemporary Practice

ITU-R methods are global prediction models and cannot capture every local microclimate or street geometry. Rainfall databases may smooth intense convective cells, while climate change can weaken the assumption that historical annual statistics are stationary. Local beacon measurements are valuable for validating high-availability Ka- and Q/V-band systems.

Machine-learning models can combine weather radar, numerical weather prediction and beacon measurements to forecast fades. They should be constrained by physical variables, tested outside their training period and accompanied by uncertainty estimates. A low average prediction error does not guarantee accurate extreme-tail availability.

Digital-twin and ray-tracing tools increasingly support non-geostationary and direct-to-device systems. Their outputs remain dependent on map accuracy, material properties and dynamic blockage data. Hybrid deterministic–stochastic models are often preferable.

Responsible engineering requires transparent disclosure of model editions, climatic data periods, assumptions and uncertainty. Availability claims affect emergency communications and public infrastructure; optimistic reporting of tail performance is therefore both a technical and governance concern. Spectrum coordination and emission limits must also be respected when fade mitigation increases transmitted power.

Chapter Summary

Satellite propagation combines deterministic spreading with atmospheric, ionospheric and environment-dependent effects. Free-space loss follows from the Friis relation and increases with the square of distance and frequency. ITU-R P.676, P.840 and P.618 provide methods for gaseous, cloud, scintillation and rain effects, supported by rainfall and rain-height data from P.837 and P.839 and rain-specific attenuation from P.838.

Ionospheric group delay and Faraday rotation vary approximately as inverse frequency squared, while ionospheric scintillation requires geographic and temporal statistics. Doppler depends on radial range rate and is especially important in LEO systems. Mobile satellite channels require correlated shadowing, blockage states and multipath rather than a single fading distribution. P.681 supports state-conditioned and time-dependent modelling, including Markov or semi-Markov structures and Loo or Rician fading.

Availability is obtained by relating fade margin to attenuation exceedance statistics, but end-to-end service availability must also include hardware, interference and operational failures. Accurate geometry, explicit assumptions and validation against local data are essential for defensible design.

Key Terms

Free-space path loss: Reduction in power density caused by geometric spreading in unobstructed space.

Specific attenuation: Signal attenuation per unit path length, normally expressed in dB/km.

Rain rate exceedance: Rainfall rate exceeded for a stated percentage of an average year.

Rain height: Modelled upper boundary of the liquid-rain region.

Effective rain path: Reduced path length accounting for the nonuniform spatial structure of rain.

Gaseous absorption: Molecular absorption caused mainly by oxygen and water vapour.

Cloud liquid-water content: Integrated mass of liquid cloud water per unit area.

Tropospheric scintillation: Rapid signal fluctuation caused by refractive-index turbulence.

Total electron content: Line integral of ionospheric electron density along a propagation path.

Faraday rotation: Rotation of linear polarization in a magnetized plasma.

Ionospheric scintillation: Amplitude and phase fluctuation caused by plasma irregularities.

Doppler shift: Frequency displacement caused by changing transmitter–receiver range.

Shadowing: Slow signal variation caused by partial obstruction of the direct path.

Multipath: Reception through multiple components having different delays and phases.

Rician fading: Fading with a dominant component plus diffuse Gaussian scattering.

Loo model: Composite model combining a lognormal direct component and Rayleigh diffuse multipath.

Markov channel model: State model in which the next state depends on the current state.

Fade margin: Link-budget reserve available to overcome propagation attenuation.

Propagation availability: Percentage of time for which propagation loss remains within the available margin.

Review Questions

Short Answer Questions

1. State the assumptions underlying the Friis transmission equation.

2. Why is rain attenuation strongly dependent on polarization and frequency?

3. Define total electron content and TECU.

4. Distinguish shadowing from small-scale multipath fading.

5. Why must P.681 transition probabilities be adjusted when the simulation sampling distance changes?

Long Answer Questions

1. Derive free-space path loss from the Friis equation and discuss its limitations in satellite-link design.

2. Explain the complete ITU-R procedure for estimating Earth–space rain attenuation from rainfall rate to attenuation percentage extrapolation.

3. Discuss ionospheric group delay, Faraday rotation and scintillation, including their frequency dependence and mitigation.

4. Develop a state-based land-mobile satellite channel model using Markov transitions and state-conditioned fading distributions.

5. Critically evaluate the use of global ITU-R models for high-availability Ka- and Q/V-band systems.

Analytical / Application Questions

1. Calculate the free-space loss of a 12 GHz signal over 40,000 km and identify three additional losses required in a practical link budget.

2. A 2.2 GHz LEO satellite has a maximum radial speed of 6.5 km/s. Calculate the maximum Doppler magnitude and propose an acquisition strategy.

3. Construct a three-state P.681-type simulator for an urban vehicle route. Specify transition statistics, fading distributions, correlation requirements and validation metrics.

Multiple Choice Questions with Answers

Question 1

What is the free-space path loss at 20 GHz over 36,000 km?

A. 189.6 dB

B. 199.6 dB

C. 209.6 dB

D. 229.6 dB

Correct Answer: C. 209.6 dB

Question 2

Which ITU-R recommendation provides coefficients for rain-specific attenuation?

A. ITU-R P.531

B. ITU-R P.676

C. ITU-R P.681

D. ITU-R P.838

Correct Answer: D. ITU-R P.838

Question 3

In the applied 18 GHz case, what is the corrected reduced rain-path length before the small vertical adjustment?

A. 5.90 km

B. 9.54 km

C. 10.32 km

D. 15.87 km

Correct Answer: A. 5.90 km

Question 4

What is the approximate 0.1% rain attenuation in the applied case?

A. 3.9 dB

B. 5.9 dB

C. 8.3 dB

D. 22.8 dB

Correct Answer: C. 8.3 dB

Question 5

How does first-order ionospheric group delay vary with frequency?

A. It is proportional to frequency

B. It is proportional to frequency squared

C. It is inversely proportional to frequency

D. It is inversely proportional to frequency squared

Correct Answer: D. It is inversely proportional to frequency squared

Question 6

What is the approximate Doppler magnitude at 2 GHz for a radial speed of 7 km/s?

A. 4.67 kHz

B. 46.7 kHz

C. 467 kHz

D. 4.67 MHz

Correct Answer: B. 46.7 kHz

Question 7

Which model combines a lognormal direct component with diffuse Rayleigh multipath?

A. Loo model

B. Pure Rayleigh model

C. Free-space model

D. Two-ray ground model

Correct Answer: A. Loo model

Question 8

In a discrete Markov channel sampled every Δx metres, what is the mean dwell distance in state i?

A. Δx(1−pᵢᵢ)

B. pᵢᵢ/Δx

C. Δx/(1−pᵢᵢ)

D. Δx/pᵢᵢ

Correct Answer: C. Δx/(1−pᵢᵢ)

Question 9

An attenuation exceeded for 0.1% of a year corresponds to approximately how much annual time?

A. 0.876 hours

B. 8.76 hours

C. 87.6 hours

D. 876 hours

Correct Answer: B. 8.76 hours

Question 10

Which impairment is primarily reduced through spatial averaging by increasing antenna aperture?

A. Free-space path loss

B. Ionospheric group delay

C. Tropospheric scintillation

D. Satellite radial Doppler

Correct Answer: C. Tropospheric scintillation