82069 - Electromagnetic Propagation for Wireless Systems M

Academic Year 2023/2024

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Telecommunications Engineering (cod. 9205)

Learning outcomes

Mastery in engineering electromagnetic topics related to wave propagation. Knowledge of the main properties of radio propagation in real environment, expertise on path-loss models, multipath propagation modeling and radio channel wideband characterization. General comprehension of MIMO systems, diversity and spatial multiplexing techniques. Awareness of the main coverage and planning strategies for cellular radio, broadcasting and wireless systems. Assessment of wireless systems efficiency.

Course contents

Part I – Fundamentals of Electromagnetic Theory (30 hours approx.)

Maxwell’s Equations

Complex representation of sinusoidal fields. Polarization of sinusoidal, vectorial fields. Maxwell’s equations in the time and frequency domain, boundary conditions.

Electromagnetic Waves

The wave concept and the electromagnetic radiation.

Electromagnetic field of a source in homogeneous medium: potential vectors, electromagnetic field generated by a point-source and by a volume-source. Far-field conditions and radiation field. Spherical, uniform waves. The reasons for attenuation of electromagnetic waves, propagation speed.

Plane waves: wave vector, uniform and evanescent plane waves.

Reflection of waves, standing waves.

Short hint to near-field communication.

Electromagnetic resonance.


Poyinting and equivalence theorems, electromagnetic image principle.

Elettromagnetic Interactions

Reflection and refraction: reflection law and Fresnel coefficients for dielectric interfaces. Reflection and refraction in metals. Diffraction: Huygens principle and Kirhhoff’s theorem, Fresnel’s coefficient for single knife-edge diffraction.

Geometrical Theory of Propagation

Historical survey, definition of optical ray. Wave equation for an inhomogeneous medium. Eikonal and Transport equations. Rays equations and rays trajectory. Examples: planar and spherical stratified medium. Ray tube and spreading factor. General expression of the electromagnetic field along a ray. Geometrical Optics: reflected and refracted rays. Geometrical Theory of Diffraction: Keller’s cone and diffraction coefficients.

Part II – Propagation in Wireless Systems (60 hours approx.)

Tropospheric/ionospheric propagation for long-range wireleless communications

Rays trajectory in the troposphere: refractivity, vertical gradient of refractivity and tropospheric ray curvature. Tropospheric index and sub-standard, standard and super-standard atmosphere. Radio horizon and equivalent earth radius.

Wireless propagation in real environment

From ideal (Friis formula) to real propagation. Fading effects: radio link obstruction and multipath propagation. Dependence of a wireless digital system performance on the propagation conditions. Signal attenuation and distortion, flat and selective fading.

Introduction to the environmental effects: Impact of the terrain on the radio link (2-rays model).

Dispersive properties of the wireless channel: delay spread/coherence bandwidth, Doppler spread/coherence time, angle spread.

Radio channel modelling: narrowband and wideband characterization

Narrowband analyses of field distribution: path loss, shadowing and fast fading. Path Loss exponent and statistical distribution of fast/slow fluctuations. Narrowband propagation models (Okumura-Hata formula, Epstein-Peterson model,…). Fading margin and radio coverage.

Multipath effects and input-output functions of the (mobile) radio channel

WSSUS channel and characterization of the wideband propagation parameters (Delay Spread, Angle Spread, etc.) and wideband propagation models (rays models).

Multi-antenna systems

MIMO solutions and techniques for fading mitigation / channel capacity increase: spatial diversity, beamforming and spatial multiplexing


Course slides and notes.

D.A. McNamara. C.W.I Pistorius, J.A.G. Malherbe, Introduction to the uniform geometrical theory of diffraction, Artech House, 1990.

H. L. Bertoni, Radio Propagation for Modern Wireless Systems, Prentice Hall, 2000

S.J. Orfanidis, Electromagnetic Waves and Antennas, free download at: http://eceweb1.rutgers.edu/~orfanidi/ewa/

N. Costa, S. Haykin, Multiple-Input Multiple Output Channel Models – Theory and Practice, Wiley& Sons, 2010.

E. Björnson, J. Hoydis L. Sanguinetti, Massive MIMO Networks: Spectral, Energy, and Hardware Efficiency, free download at: https://massivemimobook.com/wp/free-pdf/

Teaching methods

The course includes lectures given by the professor, and exercises carried out by the professor/teaching assistant as well as assigned to the students.

Assessment methods

The exam is organized into a written part and a following oral discussion.

The written test may consist of an exercise with open questions on the topics addressed throughout the course. The use of books, notes and pocket calculator is allowed. Web browsing and access to social networks during the exam is on the contrary strictly forbidden.

The outcome of the written exercise must be positive (i.e. at least 18 out of 30) in order to proceed with the oral discussion.

The oral discussion (15/20 min approx.) aims at assessing the comprehension of the main concepts explained during the course.

The final mark is a synthetic, weighted evaluation of the outcomes of the written and oral parts.

Written and oral tests should be taken within the same exam session.

Teaching tools

Blackboard, PC, projector.

Office hours

See the website of Franco Fuschini


Industry, innovation and infrastructure

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.