Introduction to Radio Wave Propagation

1. Learning Objectives

By the end of this unit, the student should be able to:

1. Explain the nature of electromagnetic (radio) waves and the relationship between frequency, wavelength and velocity of propagation.
2. Describe the three principal radio wave propagation mechanisms: free-space (line-of-sight), ground wave and sky wave (ionospheric) propagation.
3. Identify the layers of the ionosphere and their role in HF long-distance communication.
4. Apply the Friis free-space path loss equation and the plane-earth (two-ray) model to compute received signal power and path loss.
5. Define and distinguish between large-scale path loss, shadowing and small-scale (multipath) fading.
6. Relate the radio spectrum allocation (HF, VHF, UHF, SHF) to typical propagation behaviour and applications.
7. Use path-loss calculators to predict link budgets in practical wireless systems.

2. Introduction

Radio wave propagation is the study of how electromagnetic (EM) waves travel from a transmitting antenna to a receiving antenna through the environment. It is the physical foundation of all wireless systems — broadcast radio and television, cellular mobile networks (2G–5G), Wi-Fi, satellite links, radar and Bluetooth.

Unlike guided media (copper cables, optical fibre), radio waves travel through an unbounded medium (free space, atmosphere, or a combination of media). Their behaviour depends strongly on:

• Frequency of the wave;
• Distance between transmitter and receiver;
• Environment — urban, rural, indoor, over water, through foliage;
• Atmospheric and ionospheric conditions — reflection, refraction, absorption, scattering.

Understanding propagation allows engineers to predict the received signal strength, design link budgets, choose antenna heights and locations, and plan cellular coverage.

3. Electromagnetic Wave Fundamentals

3.1 Maxwell's Equations — the origin of radio waves

A time-varying electric field produces a time-varying magnetic field, and vice versa. Maxwell's equations show that accelerating charges radiate energy that propagates through space as a self-sustaining electromagnetic wave. An antenna converts guided currents in a conductor into radiating EM waves (transmit mode) or vice versa (receive mode).

3.2 Wave relationship: frequency, wavelength and velocity

where c = 3 × 10⁸ m/s (speed of light in free space), f = frequency (Hz), λ = wavelength (m).

3.3 Polarization

Polarization describes the orientation of the electric field vector as the wave travels:

• Linear — vertical or horizontal (e.g., FM broadcast, dipole antennas);
• Circular — rotating field (used in satellite links to avoid orientation loss);
• Elliptical — general case between linear and circular.

3.4 Power density and antenna gain

An antenna concentrates power in preferred directions. Antenna gain G (relative to an isotropic radiator, dBi) raises the power density in the direction of maximum radiation:

where EIRP = P_tG_t is the Effective Isotropic Radiated Power.

3.5 Free-space received power

The effective aperture of a receive antenna is A_e = G_r λ² / (4π). Combining with the power density gives the Friis equation:

Signal strength therefore falls with the square of distance in free space (20 dB per decade of distance).

4. Propagation Mechanisms

Radio energy reaches the receiver by three principal mechanisms. In practice a received signal is often a combination of several of them.

4.1 Ground Wave (Surface Wave) Propagation

• Wave follows the curvature of the earth, guided along the ground–air interface.
• The earth acts as a lossy dielectric; vertical polarization is strongly favoured, and losses increase rapidly with frequency.
• Reliable range: tens to a few hundreds of km; strongest at LF and MF (up to ~2 MHz).
• Applications: AM broadcast (MW), maritime and submarine communication (VLF).

4.2 Sky Wave (Ionospheric) Propagation

• The ionosphere (≈ 60 – 400 km altitude) contains free electrons created by solar UV radiation. It reflects (more correctly, refracts back) radio waves in the HF band (3 – 30 MHz).
• Skip distance / zone: area near the transmitter that receives no sky-wave signal.
• Maximum usable frequency (MUF): highest frequency returned by the ionosphere for a given path; using frequencies just below the MUF gives the longest hops.
• Critical frequency: highest frequency returned when the wave is launched vertically.
• Multi-hop propagation enables intercontinental links with modest power.

4.3 Free-Space / Line-of-Sight (LOS) Propagation

• Direct path between antennas, requiring an unobstructed path; dominant for VHF and above.
• Transmitter and receiver should be within radio line of sight, which extends beyond geometric LOS due to atmospheric refraction:

• At VHF/UHF, diffraction over hills and buildings and reflections from surfaces create multipath; hence mobile reception is rarely pure free-space.
• Applications: FM/TV broadcast, cellular, microwave links, satellite (space wave), Wi-Fi, radar.

4.4 Auxiliary mechanisms: reflection, diffraction, scattering

• Reflection — large smooth surfaces (buildings, ground, water) redirect waves; creates multipath.
• Diffraction — bending around obstacles / over rooftops; allows reception in shadow zones ("shadowing").
• Scattering — rough surfaces, foliage, rain, street furniture redistribute energy in many directions.

5. Path Loss Models

Path loss quantifies the reduction in signal power between transmitter and receiver, usually expressed in dB. Models range from ideal free space to empirical ones fitted to measurements.

5.1 Free-space path loss (FSPL)

5.2 Plane-earth (two-ray) model

For propagation over a reflecting ground (mobile radio), a direct ray and a ground-reflected ray combine. At large distances the received power becomes approximately independent of wavelength:

giving a path loss of 40 dB per decade of distance — much steeper than free space — and an antenna-height gain of 6 dB per doubling of height.

5.3 Empirical models (Okumura–Hata)

Real-world models (Okumura curves, Hata equations, COST-231, 3GPP models) add corrections for frequency, antenna height, and environment (urban, suburban, rural, open). They are the working tools of cellular network planning.

6. Fading, Shadowing and Multipath

6.1 Large-scale vs small-scale fading

6.2 Multipath parameters

• Delay spread (τ_rms): spread of arrival times of multipath components; produces intersymbol interference (ISI).
• Coherence bandwidth B_c ≈ 1 / (2π τ_rms): frequency range over which the channel response is roughly flat.
• Doppler spread f_d = v f_c / c (v = mobile speed): causes time-selective fading; coherence time T_c ≈ 1 / f_d.

where θ is the angle between the mobile's direction of motion and the incoming wave.

6.3 Flat vs frequency-selective fading; Rayleigh & Rician statistics

• Flat fading: signal bandwidth < coherence bandwidth — whole signal fades together.
• Frequency-selective fading: signal bandwidth > coherence bandwidth — different frequency components fade differently.
• Rayleigh envelope: many scattered paths, no dominant LOS component.
• Rician envelope: strong dominant LOS path plus scattered components (K-factor = LOS/scattered power ratio).

7. The Radio Spectrum and Propagation Behaviour

8. Interactive Calculators & Visualization

9. Summary of Key Points

1. Radio waves are EM waves obeying c = fλ; their propagation depends on frequency, distance, environment and atmosphere.
2. Three principal mechanisms: ground wave (LF/MF), sky wave via ionosphere (HF), and line-of-sight / space wave (VHF and above).
3. The ionosphere (D, E, F layers) enables long-range HF communication; MUF and critical frequency limit usable frequencies.
4. Free-space path loss increases with 20 dB/decade of distance and 20 dB/decade of frequency (Friis equation).
5. Over a reflecting ground the two-ray model gives 40 dB/decade decay — real mobile links decay much faster than free space predicts.
6. Radio horizon d(km) = 4.12(√h_t + √h_r) governs LOS systems.
7. Received signals experience path loss, log-normal shadowing and small-scale multipath fading (Rayleigh/Rician); delay spread and Doppler spread characterize the channel in frequency and time.
8. Frequency choice trades coverage and penetration (low bands) against bandwidth and data rate (high bands).

10. Review Questions

1. State the relationship between frequency, wavelength and velocity for a radio wave, and compute the wavelength of a 2.4 GHz Wi-Fi signal.
2. Explain why AM (MW) broadcast stations can be heard far beyond their radio horizon at night, while FM (VHF) stations cannot.
3. Describe the role of each ionospheric layer (D, E, F) in HF propagation.
4. A transmitter operates at 1.8 GHz with 20 W output and antenna gains of 15 dBi at each end. Calculate the free-space received power at 10 km.
5. Derive the 40 dB/decade distance dependence of the plane-earth (two-ray) model and explain its practical implication for cellular planning.
6. Distinguish between shadowing and multipath fading, indicating the typical spatial scale of each.
7. Define coherence bandwidth and coherence time, and state what each implies about a transmitted signal.
8. A mobile moving at 90 km/h receives a 1.9 GHz signal arriving at 0° to its direction of motion. Compute the maximum Doppler shift.
9. Compare the propagation characteristics of the UHF and SHF bands with respect to coverage, penetration and bandwidth, giving one application for each.
10. Explain why vertical polarization is preferred for ground-wave propagation at MF.