Ionospheric Propagation Fundamentals

This document presents a systematic treatment of ionospheric propagation physics relevant to the design and operation of HF communication systems for maritime applications. The ionosphere’s role as a natural reflector enables beyond-line-of-sight (BLOS) communications but imposes constraints that must be understood for reliable system design.

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1. Introduction

High-frequency (HF) radio waves in the 3–30 MHz range exhibit unique propagation characteristics due to their interaction with the ionosphere—a region of ionized plasma extending from approximately 60 km to 1000 km altitude. Unlike VHF and higher frequencies that pass through the ionosphere into space, HF signals can be refracted back to Earth, enabling communication over distances exceeding 3000 km with a single ionospheric reflection (hop).

This capability has been exploited since the 1920s but remains challenging due to the ionosphere’s dynamic nature. Successful system design requires quantitative understanding of the underlying physics.

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2. Ionospheric Layer Structure

Solar extreme ultraviolet (EUV) radiation and X-rays ionize atmospheric gases at different altitudes, creating distinct layers with characteristic electron density profiles.

2.1 Layer Characteristics

Layer	Altitude (km)	Peak Ne (el/m³)	Primary Ion	Persistence
D	60–90	10⁸–10⁹	NO⁺, O₂⁺	Daytime only
E	90–150	10¹¹	O₂⁺, NO⁺	Day; weak at night
F1	150–220	2×10¹¹	O⁺, NO⁺	Daytime only
F2	220–500	10¹²–10¹³	O⁺	Day and night

Table 1 Ionospheric layer parameters under quiet solar conditions. N_e = electron density.

2.2 Layer Functions

D Layer (60–90 km): The D layer does not reflect HF signals but absorbs them. Absorption coefficient α is inversely proportional to frequency squared:

α ∝ N_e · ν / (ν² + ω²) — Eq. (1)

Where ν = collision frequency, ω = wave angular frequency. Lower frequencies suffer greater D-layer absorption, particularly during daylight hours.

E Layer (90–150 km): Provides reflection for frequencies up to approximately 4 MHz. Critical for short-range (under 500 km) propagation during daylight. Sporadic E (E_s) events can reflect frequencies to 50 MHz.

F Layer (150–500 km): The principal reflecting layer for long-distance HF propagation. During daytime, splits into F1 and F2 sublayers. The F2 layer supports the highest frequencies and provides the most reliable long-range paths.

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3. Critical Frequency and Maximum Usable Frequency

3.1 Critical Frequency

The critical frequency f_c is the highest frequency that will be reflected at vertical incidence:

f_c = 9 · √N_e,max — Eq. (2)

Where f_c is in Hz and N_e,max is the maximum electron density in electrons/m³.

Typical critical frequency values:

Layer	fc Range	Conditions
foE	2–4 MHz	Daytime
foF1	4–5 MHz	Daytime, solar max
foF2	3–15 MHz	Varies with solar cycle

Table 2 Critical frequency ranges by layer.

3.2 Maximum Usable Frequency

For oblique-incidence paths, the Maximum Usable Frequency (MUF) exceeds the critical frequency:

MUF = f_c · sec(θ_i) — Eq. (3)

Where θ_i = angle of incidence at the ionospheric layer. The factor sec(θ_i) is termed the M-factor or obliquity factor.

For a single-hop path of ground distance D and virtual reflection height h’:

sec(θ_i) ≈ √[1 + (D/2h’)²] — Eq. (4)

3.3 MUF Calculation Example

For a 1000 km path with h’ = 300 km and foF2 = 8 MHz:

sec(θ_i) = √[1 + (500/300)²] = √3.78 = 1.94

MUF = 8 × 1.94 = 15.5 MHz

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4. Operating Frequency Selection

4.1 Frequency Window

The operating frequency must satisfy:

LUF < f_op < MUF — Eq. (5)

Where LUF = Lowest Usable Frequency, determined by D-layer absorption and noise.

Frequency Relative to MUF	Signal Characteristics
f > MUF	No ionospheric return; signal lost to space
0.85 × MUF < f < MUF	Optimal; low absorption, stable propagation
0.5 × MUF < f < 0.85 × MUF	Usable; increased absorption
f < LUF	Excessive absorption; signal below noise

Table 3 Operating frequency selection guidelines.

4.2 Frequency of Optimum Traffic (FOT)

The FOT is defined as 85% of MUF to provide margin against ionospheric variability:

FOT = 0.85 × MUF — Eq. (6)

For the example above: FOT = 0.85 × 15.5 = 13.2 MHz

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5. Propagation Modes

5.1 Skywave Propagation

Single-hop F2 propagation supports paths from approximately 250 km to 4000 km. Multi-hop propagation extends range but with increased path loss.

Mode	Distance Range	Typical Path Loss
1F2	250–4000 km	100–130 dB
2F2	4000–8000 km	110–145 dB
3F2	>8000 km	120–155 dB

Table 4 Skywave propagation modes and typical path losses at 10 MHz.

5.2 Near Vertical Incidence Skywave (NVIS)

NVIS uses high-angle radiation (70°–90° elevation) to provide coverage within 0–500 km—the skip zone of conventional skywave. Operating frequencies must remain below foF2, typically 2–10 MHz.

NVIS is particularly valuable for maritime operations requiring local-area coverage without skip zone gaps.

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6. Prediction Methodologies

6.1 Empirical Models

Standard prediction methods include:

Model	Developer	Application
VOACAP	NTIA/ITS	Point-to-point HF planning
ICEPAC	NTIA/ITS	High-latitude propagation
REC533	ITU-R	Regulatory coordination
ASAPS	IPS Australia	Real-time prediction

Table 5 HF propagation prediction models.

6.2 Input Parameters

Predictions require:

1. Solar indices: Smoothed sunspot number (R12) or 10.7 cm solar flux (F10.7)
2. Geomagnetic indices: Kp, Ap for disturbed conditions
3. Path geometry: Transmitter/receiver locations, path length
4. Time: Month, hour, and year

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7. Engineering Implications

7.1 System Design Requirements

For maritime HF systems operating over 500 nm:

Requirement	Specification	Rationale
Frequency agility	2–30 MHz coverage	Adapt to varying MUF
Automatic Link Establishment	MIL-STD-188-141	Optimize frequency selection
NVIS capability	2–10 MHz, high-angle antenna	Eliminate skip zone
Prediction integration	Real-time propagation data	Proactive frequency management

Table 6 System requirements for reliable HF maritime communications.

7.2 Margin Allocation

Link budgets should include margin for ionospheric variability:

Condition	Additional Margin
Quiet	+3 dB
Unsettled	+6 dB
Disturbed	+10 dB

Table 7 Recommended fade margins by geomagnetic condition.

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8. References

1. Davies, K., Ionospheric Radio, Peter Peregrinus Ltd., 1990.
2. McNamara, L.F., The Ionosphere: Communications, Surveillance, and Direction Finding, Krieger Publishing, 1991.
3. ITU-R P.533-14, Method for the Prediction of the Performance of HF Circuits, ITU, 2019.
4. ITU-R P.373-12, Definitions of Maximum and Minimum Transmission Frequencies, ITU, 2019.
5. Lane, G., Signal-to-Noise Predictions Using VOACAP, NTIA Report 93-296, 1993.