Sky Wave Propagation

1. Learning Objectives

By the end of this study guide, the learner should be able to:

1. Define sky wave (ionospheric) propagation and distinguish it from ground wave and space wave propagation.
2. Describe the structure, composition, and layered structure of the ionosphere (D, E, F1, F2 layers).
3. Explain the physical mechanism of ionospheric reflection and refraction of radio waves.
4. Apply the secant law, maximum usable frequency (MUF), lowest usable frequency (LUF), and critical frequency concepts to propagation problems.
5. Calculate skip distance, virtual height, and angle of elevation for given ionospheric conditions.
6. Analyse the effects of multipath propagation, fading, ionospheric storms, and diurnal/seasonal variations on HF communication.
7. Evaluate link budgets for ionospherically propagated signals and appreciate the practical limits of HF sky wave communication.

2. Introduction

Radio wave propagation between a transmitter and receiver can occur via three principal modes:

• Ground wave (surface wave) — propagation along the surface of the Earth; dominant at frequencies below ~2 MHz.
• Space wave (direct wave / line-of-sight) — direct path between antennas; dominant above ~30 MHz (VHF, UHF and above).
• Sky wave — propagation by reflection/refraction from the ionized layers of the upper atmosphere (the ionosphere); dominant for HF (3–30 MHz) over long distances.

Sky wave propagation is the basis of:

• Shortwave (HF) broadcasting and amateur radio;
• Long-distance maritime and aeronautical HF communication;
• Over-the-horizon radar and ionospheric research.

2.1 Frequency ranges of the principal propagation modes

3. The Ionosphere

The ionosphere is a region of the Earth's upper atmosphere, extending approximately from 60 km to 1000 km altitude, where free electrons and ions are produced mainly by solar ultraviolet (UV) and X-ray radiation, and by cosmic rays.

3.1 Formation of ionization

Solar radiation ionizes neutral atmospheric atoms and molecules:

where X is a neutral particle, hν is a photon of sufficient energy, X⁺ is a positive ion, and e⁻ is a free electron. The number of free electrons per unit volume — the electron density N (electrons/m³) — is the key parameter controlling radio wave refraction.

3.2 Layers of the ionosphere

3.3 Variations of the ionosphere

• Diurnal (day/night): D and F1 layers vanish at night; F2 electron density decreases at night; MUF drops significantly after sunset.
• Seasonal: F2 is denser in winter; E layer follows the Sun's elevation.
• Solar cycle (11-year): Higher sunspot number → higher electron density → higher MUF; sunspot maximum favours higher HF bands.
• Sudden ionospheric disturbances (SID): Solar flares abruptly increase D-layer absorption, causing shortwave fadeouts (SWF).
• Ionospheric storms: Geomagnetic disturbances degrade HF paths for hours or days.

4. Reflection Mechanism: Refraction in a Stratified Medium

The ionosphere is not a perfect mirror. Radio waves are progressively refracted (bent) as they pass through ionized layers of increasing electron density, because the refractive index of an ionized medium is less than unity.

4.1 Refractive index of the ionosphere

Here f is the wave frequency and f_N is the plasma frequency corresponding to electron density N. For a wave to propagate, f > f_N; if f = f_N at some height, the wave is bent back (reflected).

4.2 The reflection condition

For a wave entering the ionosphere at an angle of incidence θᵢ (measured from the vertical), applying Snell's law through successive layers shows that the wave returns to Earth when:

This is the secant law, where f_c is the critical frequency of the layer.

4.3 Critical frequency

Typical values: foE ≈ 3 – 4 MHz; foF1 ≈ 4 – 5 MHz; foF2 ≈ 5 – 12 MHz (varies with time of day, season, and solar activity).

4.4 Maximum Usable Frequency (MUF)

The MUF is the highest frequency usable for a given path at a given angle of incidence. Practical operating frequency (FOT, fréquence optimum de travail) is typically about 85% of MUF to allow for ionospheric variability.

4.5 Lowest Usable Frequency (LUF)

The LUF is set by absorption — primarily in the D layer — and by atmospheric/ galactic noise. The usable frequency window is therefore:

The LUF rises during the day (stronger D layer) and falls at night, while the MUF does the opposite. Daytime HF links therefore use higher frequencies than nighttime links.

4.6 Virtual height

Because refraction is gradual, the ionosphere appears (geometrically) as a mirror at a height h′ called the virtual height, greater than the true height of maximum ionization. Virtual heights: E ≈ 110 km; F1 ≈ 180–200 km; F2 ≈ 250–400 km.

5. Skip Distance, Coverage and Geometry

5.1 Skip distance

The skip distance is the minimum ground distance between the transmitter and the point where the sky wave first returns to Earth. Rays launched at steeper angles (closer to vertical) penetrate the ionosphere and escape to space; rays at shallower angles return farther away.

5.2 Geometry of a single-hop path

Consider a transmitter and receiver on the Earth's surface, separated by ground distance d, with the reflection point at virtual height h′. The single-hop distance is approximately:

where θ is the elevation angle. For large distances, Earth's curvature must be included; multi-hop propagation then occurs via successive ionospheric reflections.

5.3 Multi-hop propagation

Distances beyond ~4000 km (limit of a single F2 hop) are covered by successive reflections between the ionosphere and the Earth's surface. Each ground reflection introduces loss (especially over land), so multi-hop signals are weaker and more variable. Antipodal regions can also be reached by convergence of many hops.

5.4 Fading in sky wave links

Signals arrive via several paths (multi-hop, magneto-ionic components — ordinary and extraordinary waves) that interfere, producing fading:

• Selective fading: frequency-dependent, caused by multipath delay spread — distorts wideband signals.
• Interference fading: rapid amplitude variations (seconds) as path lengths change.
• Polarization fading: rotation of the plane of polarization (Faraday rotation) in the ionosphere.
• Absorption fading: slow variations with D-layer conditions.

6. Interactive Calculators

7. Summary of Key Points

• Sky wave propagation uses the ionosphere (60–1000 km) to return HF (3–30 MHz) signals to Earth over long distances.
• The ionosphere comprises D, E, F1, F2 layers; F2 has the highest electron density and controls the highest usable frequencies.
• Waves are refracted gradually; reflection follows the secant law: MUF = fo sec θᵢ.
• The critical frequency fo = 8.98√N_max is the highest frequency returned at vertical incidence.
• Operating frequency must lie between LUF (absorption-limited) and MUF (penetration-limited); FOT ≈ 0.85 × MUF.
• Skip distance defines the zone of no sky wave coverage; multi-hop extends range beyond a single hop (~4000 km).
• Fading arises from multipath, magneto-ionic splitting, and absorption variations; ionospheric conditions vary diurnally, seasonally, and with the 11-year solar cycle.

8. Review Questions

Section A: Short-answer questions Easy

1. Define sky wave propagation and state the frequency band in which it is dominant.
2. Name the four principal ionospheric layers in order of increasing altitude.
3. State the physical cause of ionization in the ionosphere.
4. Define (a) critical frequency, (b) MUF, (c) LUF, (d) virtual height.
5. Explain why the D layer is important mainly during daylight hours.

Section B: Numerical problems Moderate

6. An ionospheric layer has a maximum electron density of 1.44 × 10¹² electrons/m³. Determine the critical frequency.
7. For a layer with fo = 5 MHz and an angle of incidence of 70°, calculate the MUF.
8. Using the flat-Earth approximation, find the single-hop distance for h′ = 300 km and elevation angle 20°.
9. A Nairobi–London path is approximately 6800 km. If each F2 hop covers 3000 km, how many hops are required? State one practical consequence of multi-hop operation.
10. The critical frequency at noon is 9 MHz while at midnight it is 4 MHz. If the operating frequency must be 85% of MUF at an incidence angle of 60°, recommend operating frequencies for day and night.

Section C: Discussion questions Advanced

11. Explain, using the refractive-index expression, why higher-frequency waves are less effectively refracted by the ionosphere.
12. Discuss how the 11-year solar cycle and ionospheric storms affect HF link planning in East Africa.
13. Describe the mechanisms of selective fading in HF sky wave links and discuss mitigation techniques (e.g., diversity).
14. Compare sky wave, ground wave and space wave propagation with respect to frequency range, range achieved, and typical applications.

9. Glossary