MASINDE MULIRO UNIVERSITY OF SCIENCE AND TECHNOLOGY
Department of Electrical & Communication Engineering

SKYWAVE COMMUNICATION

Ionospheric Propagation of Radio Waves
Course: ECE 523E — Antennas & Radiowave Communication
Level: 5th Year, Electrical & Communication Engineering
Topic 6: Skywave (Ionospheric) Propagation — Mechanisms, Parameters & Link Design

Learning Objectives

By the end of this lecture the student should be able to:

  1. Explain the structure and formation of the ionosphere (D, E, F1, F2 layers).
  2. Describe the mechanism of skywave propagation — refraction of HF waves by the ionised layers.
  3. Define and calculate the critical frequency fc, maximum usable frequency (MUF), lowest usable frequency (LUF) and optimum working frequency (OWF).
  4. Explain skip distance, skip zone and the geometry of an ionospheric hop.
  5. Distinguish between virtual height and real height of reflection.
  6. Analyse the effects of diurnal, seasonal and solar-cycle variations on skywave links.
  7. Apply skywave parameters to a practical HF link design.
EARTH F₂ (250–400 km) F₁ (150–200 km) E (90–130 km) D (60–90 km) TX RX one hop
Fig. 1 — Geometry of a single-hop skywave path via the F-region.

Radio-Wave Propagation Modes

Ionosphere Earth's Surface Ground (surface) wave Skywave (ionospheric) Space (LOS) wave TX RX
Fig. 2 — The three basic propagation modes: ground, space (LOS) and sky waves.
ModeFrequency rangeRangeNotes
Ground waveLF / MF (< 2 MHz)Tens–hundreds of kmHugs the surface; attenuates rapidly above a few MHz
Space (LOS) waveVHF / UHF and above (> 30 MHz)Line of sightPasses through ionosphere — used by satellites
Sky waveHF (3–30 MHz)100–4000 km per hopRefracted by ionosphere; worldwide coverage possible
Skywave propagation is the dominant mechanism for long-distance HF communication — broadcasting, maritime/aircraft HF, amateur radio, and over-the-horizon radar.

The Ionosphere: Formation & Structure

Formation

  • Solar EUV and X-ray radiation, plus cosmic rays, ionise the neutral constituents of the upper atmosphere (O, O₂, N₂).
  • Free electrons and positive ions form a weakly ionised plasma: electron density Ne ≈ 10⁹–10¹² electrons/m³.
  • Ionisation is balanced by recombination; equilibrium Ne depends on solar zenith angle, altitude chemistry and season.

Key property

Refractive index   n = √(1 − 80.8·Ne / f²)    (Ne in m⁻³, f in Hz)

As a wave enters a region of increasing Ne, n decreases below 1, the wave slows and its ray path bends away from the vertical — refraction.

Because n < 1 in the ionosphere, phase velocity exceeds c while group (signal) velocity is less than c — a frequent examination point!
Atmospheric layers (not to scale) Thermosphere F₂ region 250–400 km F₁ region 150–200 km E region 90–130 km D region 60–90 km Stratosphere / Troposphere EARTH
Fig. 3 — Ionised layers of the upper atmosphere produced by solar radiation.

Characteristics of the Ionospheric Layers

LayerHeight (km)Daytime electron densityNight-timeBehaviour
D60 – 90≈ 10⁹ m⁻³Practically disappearsHeavy absorption of LF/MF; does not reflect HF
E90 – 130≈ 10¹¹ m⁻³WeakReflects MF/HF up to its critical frequency (~3–4 MHz); sporadic-E clouds
F₁150 – 200≈ 3×10¹¹ m⁻³Merges with F₂Present only in daytime; partially reflects HF
F₂250 – 400≈ 10¹² m⁻³ (maximum)Persists, slightly weakerMain reflecting layer for HF; highest critical frequency
Why the layers? At lower altitudes the air is dense → fast recombination → layers vanish at night. In the F-region the air is thin → recombination is slow → ionisation survives through the night. This is why MF skywave broadcasting works best at night (D-layer absorption disappears).
Typical daytime critical frequencies: fc(E) ≈ 3–4 MHz,   fc(F₂) ≈ 5–12 MHz (varies strongly with latitude, season and solar activity)

Mechanism of Skywave Propagation

Ionosphere (Nₑ increases with height) EARTH increasing refraction TX RX turning point
Fig. 4 — Gradual refraction of an HF ray in a horizontally-stratified ionosphere; the ray bends continuously and returns to Earth.

Step-by-step mechanism

  1. Wave launched at take-off angle θ enters the ionosphere where electron density Ne increases with height.
  2. Refractive index n = √(1 − 80.8Ne/f²) decreases along the path → the ray bends gradually away from the normal (Snell's law applied continuously).
  3. At the height where Ne is large enough, the ray becomes horizontal and turns back toward Earth.
  4. The returned wave may be received directly or reflected from the ground for a second hop.
Reflection from the ionosphere is not a mirror reflection — it is cumulative refraction through a plasma gradient. Understanding this distinction is essential for explaining polarisation rotation (Faraday) and height calculations.

Critical Frequency, fc

Definition

The critical frequency is the highest frequency that, when sent vertically upward (incidence angle 0°), is returned to Earth by a given layer.

fc = 9·√(Ne,max)    [Hz, with Ne in electrons/m³]
Equivalently:   fc(MHz) ≈ 9·√(Ne,max[m⁻³]) / 10⁶

Physical meaning

  • If f < fc: vertical wave is reflected back.
  • If f > fc: vertical wave penetrates the layer and escapes to space.
  • For oblique incidence, higher frequencies can still be returned → this gives the MUF.
Example: F₂-layer Ne,max = 10¹² m⁻³ → fc = 9√10¹² = 9 MHz. A 9 MHz wave sent straight up just returns; anything higher escapes vertically.
Ionosphere f < fc : returned f > fc : penetrates TX EARTH
Fig. 5 — Vertical-incidence test: waves below fc are returned; waves above fc penetrate the layer.

Maximum Usable Frequency (MUF)

Ionosphere real path (curved ray) θ (take-off / incidence angle) virtual height h′ ground distance d TX RX EARTH
Fig. 6 — Flat-Earth triangle model for an oblique ionospheric hop.

Secant law

MUF = fc · sec(θ) = fc / cos(θ)

θ = angle of incidence at the ionosphere measured from the vertical. Because sec θ ≥ 1, the MUF is always greater than fc.

Practical rules

  • Operating near the MUF gives the longest single hop and least absorption, but the link margin is thin — the MUF varies hour-to-hour.
  • System designers use the Optimum Working Frequency: OWF ≈ 0.85 × MUF.
  • Typical F₂ MUF for a 3000 km path: 15–35 MHz depending on solar activity.
Worked mini-example: fc(F₂) = 9 MHz, θ = 60° → MUF = 9 / cos60° = 9 / 0.5 = 18 MHz; OWF ≈ 0.85 × 18 = 15.3 MHz.

Lowest Usable Frequency (LUF) & Optimum Working Frequency (OWF)

LUF

  • The lowest frequency that can be used for a given path with a specified transmitter power and receiver sensitivity.
  • Set by D-region absorption and by atmospheric/galactic noise: as f decreases, absorption ∝ 1/f² rises steeply and noise rises.
  • LUF rises during the day (D-layer present) and falls at night.

OWF (FOF — frequency of optimum traffic)

  • OWF ≈ 0.85 × MUF — high enough to escape D-layer absorption, low enough to stay below the time-varying MUF for most of the day.
Usable band: LUF < f < MUF. Communication is only possible inside this window. At night the window shifts downward (MUF and LUF both fall); around sunrise/sunset the window can close abruptly — a classic cause of HF link dropouts.
Time of day (hours) 000612 1824 Frequency (MHz) 3020100 MUF OWF ≈ 0.85 MUF LUF USABLE BAND day → lower absorption, higher MUF night → band shifts down
Fig. 7 — Diurnal variation of MUF, OWF and LUF defining the usable frequency window.

Skip Distance & Skip Zone

Ionosphere low θ → short skip high θ → short ground range, may escape if f > fc MUF ray → longest skip TX skip zone EARTH
Fig. 8 — Rays at different take-off angles. The skip zone is the ring around the transmitter receiving neither ground wave nor sky wave.

Definitions

  • Skip distance — minimum ground distance between TX and the point where the skywave first returns (for a given frequency and layer).
  • Skip zone (silent zone) — annular region inside the skip distance where the ground wave has died out and the skywave has not yet returned.

Behaviour with frequency

  • Increasing f (toward MUF) → refraction weaker → ray returns farther → skip distance increases, skip zone widens.
  • f > MUF → wave penetrates; no skywave at all.
  • Reducing f → skip distance shrinks; below LUF absorption is too high.
Amateur operators exploit this: calling "CQ" on a higher band reaches only stations beyond the skip zone, while a lower band fills the zone.

Virtual Height vs Real Height

Ionosphere real (curved) path virtual height h′ TX RX EARTH
Fig. 9 — The virtual height h′ is the height of the equivalent sharp mirror that would return the ray along the same path.

Virtual height, h′

  • Height at which a sharply reflecting layer would have to be placed to produce the same time delay as the real, gradually refracting ionosphere.
  • Obtained directly from ionograms (sweep-frequency vertical-incidence sounders, e.g. AIS-INGV network).
  • Used in all hop-geometry (secant-law) calculations because it replaces a curved path with straight lines.

Real (true) height

  • The actual altitude of the ray turning point, found by inverting the ionogram with the n(f) relation.
  • h′ > htrue — the virtual mirror always lies above the real turning point (delay includes slowing of the wave in the plasma).
h′(F₂) ≈ 300–450 km (day), 250–350 km (night);   h′(E) ≈ 100–120 km

Skywave Hop Geometry — Calculations

Single-hop ground range

d = 2·h′·tan θ = 2·h′·√(sec²θ − 1)

Skip distance (MUF condition)

dskip = 2·h′·√((MUF/fc)² − 1)

Multi-hop range

Total range D = N × d for N hops, with ground reflection between hops. Practical HF circuits commonly use 1–3 hops; each ground reflection introduces additional loss and polarisation changes.

Curved-Earth refinement

cos θ = (R / (R + h′)) · cos φ,   with central angle ψ ≈ d / R

R = 6370 km; φ = take-off angle at Earth's surface. Curved-Earth geometry matters for h′ > ~100 km or ranges > ~1000 km.

Ionosphere TX RX hop 1 hop 2 reflection point EARTH
Fig. 10 — A two-hop skywave path: the wave reflects from the ground between ionospheric returns.

Worked Example — HF Link Design

Problem. A Nairobi–Cairo HF link is 3500 km. The F₂ layer has fc = 9 MHz and virtual height h′ = 320 km at the planned hour. Design a single-band choice.

Step 1 — hops

Practical max single-hop F₂ range ≈ 3500–4000 km (MUF-limited). Choose two hops of ≈ 1750 km for margin.

Step 2 — required MUF

θ = arctan(d / 2h′) = arctan(1750 / 640) ≈ 70°
MUF = fc/cos θ = 9 / cos70° ≈ 26.3 MHz

Step 3 — choose operating frequency

OWF ≈ 0.85 × MUF ≈ 22.4 MHz → use the 21 MHz amateur/HF band or an adjacent assigned channel, verify LUF < 21 MHz from absorption charts.

Design checklist

  • ✓ f < MUF along the whole path (check ionosonde data for both terminal regions).
  • ✓ f > LUF (D-layer absorption by day; use higher bands by day, lower by night).
  • ✓ Take-off angle within antenna elevation capability (dipole at λ/2 height gives ~30–60°).
  • ✓ E-layer sporadic-E checked (can support 28–50 MHz at mid-latitudes).
  • ✓ Link budget: TX power, antenna gain, ionospheric absorption (~2–8 dB/hop), ground reflection loss (~5–15 dB), fading margin ≥ 10 dB.
Class exercise: Repeat the calculation for a 1-hop 3000 km link with fc = 8 MHz, h′ = 300 km. What OWF results? (Answer ≈ 0.85 × 8/cos(78.7°) ≈ 35.5 MHz → select 30 MHz band.)

Variations of the Ionosphere

Local time (h) → MUF (MHz) MUF (solar maximum, summer) MUF (night / solar minimum) sunrise sunset
Fig. 11 — Diurnal variation of F₂-layer MUF: strong daytime peak after sunrise, collapse at night.
VariationTimescaleEffect on skywave link
DiurnalHoursD-layer appears at sunrise → absorption ↑; MUF peaks mid-day, falls at night → shift to lower frequencies after sunset
SeasonalMonthsF₂ MUF highest in local summer/winter anomaly (winter daytime MUF can exceed summer at mid-latitudes); absorption lowest in winter
Sunspot cycle≈ 11 yearsSolar max → Ne ↑ → fc & MUF ↑ (up to ~2×); usable bands shift up (e.g. 21 MHz day at max vs 14 MHz at min)
Sporadic-EMinutes–hoursThin dense E-layer patches reflect VHF (up to ~50+ MHz) over 500–2000 km unexpectedly
Geomagnetic stormsHours–daysAuroral absorption, D-region PCA events → HF blackout at high latitudes
Design rule: HF frequency plans are seasonal/annual documents — ITU-R and ionosonde services (e.g. CCIR maps, URSI) provide predicted MUF(F₂) contours.

Multipath & Fading in Skywave Links

Ionosphere E-layer hop (h′≈110 km) F-layer hop (h′≈320 km) 2 × E hops TX RX EARTH
Fig. 12 — Multiple ray paths (E-hop, F-hop, two-hop E) arrive at the receiver with different delays and phases.

Types of skywave fading

TypeCauseMitigation
Interference fadingMultipath (E/F hops, magneto-ionic split) — signals add constructively/destructivelyDiversity: space (two antennas ≥ λ/2 apart), frequency, time
Polarisation fadingRotation of polarisation (Faraday effect) in the ionised mediumOrthogonal dual-polarisation receiver
Absorption fadingSlow variation of D-region absorption (SID, solar flares)Frequency/time diversity; AGC

Magneto-ionic splitting

The Earth's magnetic field splits an incident wave into Ordinary (O) and Extraordinary (X) components with different refractive indices and slightly different paths — the receiver sees two delayed replicas.

HF modems combat multipath with serial-tone waveforms & interleavers (e.g. STANAG 5069): symbol rates < multipath spread (~2 ms), interleaving longer than fade duration (~seconds).

Ionospheric Absorption

Non-deviative absorption (D-region)

  • Occurs where the ray is nearly straight (n ≈ 1) — mostly in the D-region below the reflection height.
  • Collisions between electrons and neutral particles convert wave energy to heat.
  • Increases rapidly as frequency decreases (∝ 1/f²) and as solar zenith angle decreases (noon, summer).
  • Can reach 30–100 dB at MF by day — this is why MW broadcast stations are only heard far away at night.

Deviative absorption

  • Occurs near the turning point where the wave slows strongly (n → 0); significant when operating near fc or during disturbances.

Solar events

  • SID (Sudden Ionospheric Disturbance) / SWF: X-ray flare → D-region enhancement → HF blackout on sunlit hemisphere lasting minutes–hours.
  • Polar Cap Absorption (PCA): energetic protons → D-region over poles; can black out HF for days.
Frequency (MHz) → Absorption (dB) day (D-layer present) night sunrise / sunset absorption ∝ 1/f² → use higher bands by day
Fig. 13 — Typical ionospheric absorption vs frequency: daytime D-region absorption dominates the LUF.

Ionograms: Measuring the Ionosphere

Virtual height h′ (km) 0100200 300400500 600 Echo amplitude (%) 02550 75100 noise floor E (110 km) F₁ F₂ (300 km) 2E 2F₁ 2F₂
Fig. 14 — Fixed-frequency vertical-incidence echo display: returned echo amplitude vs virtual height. Solid peaks are first-order layer echoes; dashed peaks are multiple-hop (2nd-order) echoes at ≈ 2h′.

Vertical-incidence sounding

  • A vertical-incidence sounder transmits pulses straight up at a fixed frequency and plots the amplitude of each returned echo versus its virtual height (Fig. 14, an A-scope-style display).
  • Each peak marks a layer echo — E, F₁, F₂; the delay of the echo gives h′ of that layer.
  • The smaller dashed peaks at ≈ 2h′, 3h′ are multiple-hop echoes that have bounced once between the layer and the ground — direct evidence the wave was returned from above, not reflected at the surface.
  • Sweeping the frequency and recording h′(f) produces the ionogram, whose trace cusps give fc of each layer; oblique-incidence sounders measure the actual link MUF between two points.

What these measurements give the engineer

  • fcE, fcF₁, fcF₂ → MUF via secant law.
  • h′(E), h′(F) → hop geometry and skip distance.
  • Spread-F, sporadic-E, D-region absorption indicators → link quality and fading forecasts.
Data sources: Global ionosonde network data via NASA CEDAR / GIRO (Digisonde Global Ionospheric Radio Observatory); ITU-R Recommendation P.533 gives HF prediction methods used for skywave link planning.

Applications of Skywave Communication

  • HF broadcasting (DRM) — international short-wave broadcasting reaching continents with one transmitter (BBC World Service, Voice of America).
  • Maritime & aeronautical HF — long-range links over oceans where no VHF/UHF infrastructure exists (GMDSS uses HF for sea area A4).
  • Military & diplomatic HF — beyond-line-of-sight, survivable communications; automatic link establishment (ALE, MIL-STD-188-141).
  • Amateur radio (ham) — worldwide contacts on 3.5–28 MHz bands; contests and emergency communication.
  • Over-the-horizon radar (OTH) — HF surface-wave and skywave radars detecting aircraft/ships at 1000–3000 km (e.g. JORN).
  • Ionospheric research & remote sensing — GPS scintillation studies, ionosonde networks, space-weather monitoring.
  • Back-up to satellite — independent of space segment; used when satellites are jammed, damaged or unavailable.
Why HF still matters in 2026: no satellite cost/latency, inherent LPI (low probability of intercept) at low power, and resilience — skywave remains a core competency for the communication engineer.
Ionosphere intercontinental HF paths HF TX remote RX EARTH
Fig. 15 — One HF transmitter can serve receivers thousands of kilometres away via successive ionospheric hops.

Summary & Key Takeaways

  1. Skywave propagation uses refraction (not reflection) of HF waves (3–30 MHz) by the ionised D, E, F₁ and F₂ layers.
  2. Refractive index n = √(1 − 80.8Ne/f²): the ray bends where electron density rises with height.
  3. fc = 9√Ne,max sets the vertical limit; oblique operation raises the limit via the secant law: MUF = fc·sec θ.
  4. Work near OWF ≈ 0.85 MUF and always above LUF (absorption/noise limit) — the usable band moves with time of day, season and sunspot number.
  5. Skip zone = region receiving neither ground wave nor skywave; grows as frequency → MUF.
  6. Virtual height h′ (from ionograms) models the ionosphere as an equivalent mirror for hop-geometry calculations.
  7. Multipath, magneto-ionic splitting and D-region absorption cause fading — mitigated by diversity and robust waveforms.
  8. Skywave provides resilient intercontinental links: broadcasting, aero/maritime, military, amateur radio and OTH radar.

Exam-style questions to revise

  • Derive the secant law and state its assumptions.
  • An ionosonde gives fcF₂ = 10 MHz, h′ = 350 km. Find the MUF and single-hop range at θ = 65°.
  • Explain why MF broadcast stations are received over long distances only at night.
  • Compare O and X magneto-ionic modes and their effect on a received signal.
Next lecture: Skywave link budget & HF channel simulation in MATLAB — bring your laptops.

References & Further Reading

  • Balmain, K. G. & Antennas and Radiowave Propagation-related texts — see course reading list for ECE 523E.
  • Saunders, S. R. & Aragón-Zavala, A., Antennas and Propagation for Wireless Communication Systems, 2nd ed., Wiley, 2007 — Ch. on ionospheric propagation.
  • Balanis, C. A., Antenna Theory: Analysis and Design, 4th ed., Wiley, 2016 — wave propagation chapters.
  • Davies, K., Ionospheric Radio, IEE Electromagnetic Waves Series, Peter Peregrinus, 1990.
  • Budden, K. G., The Propagation of Radio Waves, Cambridge University Press, 1985.
  • ITU-R Recommendation P.533 — Method for the prediction of the performance of HF circuits.
  • Hunsucker, R. D. & Hargreaves, J. K., The High-Latitude Ionosphere and its Effects on Radio Propagation, CUP, 2003.
  • GIRO / Digisonde global ionosonde data — Lowell Digisonde International; NASA CEDAR database.
QUESTIONS &
DISCUSSION

Figures in this deck are original schematic redrawings in textbook style.
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