Introduction to the Propagation of Radio Waves

1.1 Introduction

One of the prerequisites for the development of telecommunication services is the understanding of the propagation of the waves, either acoustic, electromagnetic, radio or light waves, which are used for the transmission of information.

In this work, we shall limit ourselves to the study of radio waves: this term apply to the electromagnetic waves used in radio communications. Their frequency spectrum is very broad, and is divided into the following frequency bands : ELF waves (f < 3 kHz), VLF (3-30 kHz), LF waves (30-300 kHz), MF waves (300-3000 kHz), HF (3-30 MHz), VHF waves (30-300 MHz), UHF waves (300-3000 MHz), SHF waves (3-30 GHz), EHF waves (30-300 GHz) and sub-EHF waves (300-3000 GHz).

1.1.1 Propagation Mechanisms

Radio waves propagate in space according to several different physical mechanisms: free-space propagation or line-of-sight propagation, reflection, transmission, diffraction, scattering and wave guiding.

In free space a wave propagates without encountering any obstacle. The surface of the wave is the set of all points reached at a certain time after the moment of emission of the wave within a homogeneous medium. The attenuation in free space results from the scattering of energy which occurs as the wave propagates away from the transmitter. Free-space attenuation is a function of the distance and the frequency. The excess attenuation compared to free-space attenuation is defined as the difference between the path loss and free-space attenuation (atmospheric absorption, hydrometeor attenuation, building penetration loss, vegetation attenuation, attenuation due to diffraction, etc).

Reflection is the phenomenon whereby vibrations or waves are reflected at a surface according to Snell-Descartes law. This phenomenon occurs when a propagating wave impinges upon a surface with large dimensions compared to the wavelength. A distinction is commonly drawn between specular reflection, occurring in the presence of a perfectly plane, homogeneous surface, and diffuse reflection, which takes place in the presence of a rough surface, i.e. a surface presenting irregularities. The reflection coefficient is defined as the ratio between the received energy flux and the incident energy flux.

The phenomenon of transmission is the process whereby vibrations or waves propagate through a medium, for instance vacuum, the air or an obstacle, without a change of frequency according to Snell-Descartes law. Different types of transmission are usually distinguished. In regular transmission, the wave propagates through an object without diffusion. In diffuse transmission a phenomenon of diffusion occurs at a macroscopic scale independently of the refraction laws: the incident wave, while being transmitted, is scattered over a range of different angles. At last, mixed transmission is a partly regular and partly diffuse transmission. The transmission coefficient is defined as the ratio between the transmitted energy flux and the incident energy flux.

The building penetration loss is defined as the power attenuation that an electromagnetic wave undergoes as it propagates from outside a building towards one or several places inside this building. This parameter is determined from the comparison between the external field and the field present in different parts of the building where the receiver is located.

The phenomenon of diffraction occurs when waves impinge upon an obstacle or an aperture with large dimensions compared to the wavelength. This phenomenon is one of the most important factors in the propagation of radio waves, and results in disturbances affecting the propagation of these waves, for instance the bending of the path around obstacles or beam divergences.

Scattering is the phenomenon whereby the energy of an electromagnetic wave is distributed in a propagation medium along several directions after meeting a rough surface or heterogeneities with small dimensions compared to the wavelength.

The emitted energy can be channelled along a given direction using a waveguide. The propagation is achieved in this case by successive reflections of the waves off the surfaces of the waveguide. Certain environments, for instance canyon streets, corridors, or tunnels behave like waveguides with respect to the propagation of radio waves.

Interferences result from the superposition of oscillations or waves of same nature and equal frequency. These interferences can be either constructive when the different paths arrive in phase, leading to a signal reinforcement, or destructive, causing in this case a fading of the signal. It might be further noted that the mobile itself moves inside this figure of interferences, so that it propagates successively through luminous and dark regions (interference fringes), which results in a fading of the signal.

After a wave has been emitted, a wave may follow different paths between the emitter and the receiver. Depending on the nature of the obstacles that the waves encounter during their propagation, they are submitted to different phenomena of reflection, for instance at walls or at atmospheric or ionospheric layers, as well as different refraction, transmission, scattering or guiding phenomena. This results in a multitude of elementary paths. Each such path is characterised at receiver level by an attenuation, a delay and a specific phase difference. This mode of propagation is referred to as a multipath propagation. The different waves propagated along such multiple paths interfere at the reception.

For a radio transmission system, the propagation channel is defined as the physical ratio between signal e(t) at the modulator output and signal s(t) at the demodulator input. This concept takes into account the microwave channel as well as the emission and reception antennas. The propagation channel is generally described through its time-dependent impulse response h(t, t), where t is the delay and t represents the time dependence (and accordingly, since the vehicle is moving, the space dependence). The impulse response is a function of two variables, and expresses the three characteristics of the channel: its attenuation, its variability (t) and its selectivity (t). The dual variables by t and t Fourier transforms respectively are the frequency and the Doppler speed

1.1.2 Propagation Environment

The propagation environment is the geographical environment considered for the description of the propagation of waves between a transmitter and a receiver. This environment is generally described from the physical parameters of the medium, like the pressure, the temperature, the humidity or the refractive index and from geographical databases containing data concerning the topography, the vegetation and land use, the street axes and buildings. Geographical databases are constructed and maintained through a complex process combining satellite and aerial photographs or the maps of buildings with complex digitalisation processes. Depending on the physical base station antenna and on its geographical coverage area, these databases allow the definition of four different types of cell with respect to the propagation of radio waves: macrocell, small cell, microcell and picocell. The characteristics of each of these cells are dependent on the location, on the power and on the height of the base station antenna height as well as on the geographical environment.

The largest cell is the macrocell, with an activity radius of the order of several ten thousand kilometres. The environment of cells of this type is generally rural or mountainous, and the base station antenna is located at an elevated point: the typical height of the base station is 15 metres on a mast and 20 metres on top of a building. The geographical coverage area is predominantly rural and induces for a number of paths important delays (up to 30 ^s). Further, due the limited number of diffusers and the distance between them, no significant fast fading occurs.

With the increase in users, in urban areas for the most part, the dimensions of the cells had to be decreased in order to reduce the reuse distance of the allocated frequencies. The most current urban cell is the small cell. Its coverage area has a radius lower than a few kilometres and the base station antenna is located above roof level, i.e. from 3 to 10 metres above ground level. The maximum duration of the impulse response is 10 ^s.

In very dense urban areas, small cells are replaced by microcells with an activity radius of a few hundreds metres. The antennas are located below roof level, and the waves are guided by the streets. The maximum duration of the impulse response is 2 ^s.

Picocells, with a radius equal to a few tens of metres, correspond to communications occurring in the building where the base station antenna is located. The maximum duration of the impulse response is 1 ^s.

1.1.3 Antennas

Antennas are devices used either for the emission or for the reception of radio waves. An emitting antenna is a device supplied by an electric power generator at a certain frequency and radiating radio waves in space. These waves are generated through the emission of a variable current along the emitting antenna. A receiving antenna is a device whose function is to transmit to a receiver the effects of the radio waves emitted by a distant source. The interaction between an antenna and an electromagnetic wave produces on the antenna a variable current identical to the current that would have been necessary for this antenna to emit the wave.

The shapes and dimensions of the emitting and receiving antennas depend on their intended use as well as on the frequency. Among the different forms of antennas we may for instance mention linear, helical, reflector, loop, horn and patch antennas. The main characteristics of antennas are their radiation pattern, the power gain, the directivity, the beamwidth, the aperture, the polarisation, the current distribution along the antennas, their effective height and their impedance.

1.1.4. Selectivity

In the presence of significant time differences between the multiple paths, the transfer function is no longer constant over the entire width of the spectrum: in these conditions, the path loss is dependent on the frequency, and accordingly the propagation channel shall be described as being frequency selective. Different selectivity parameters are deduced from the average power delays profile: among these parameters we may mentioned here the mean delay, the root-mean square delay spread, the delay interval, the delay window and the correlation bandwidth.

The correlation bandwidth is defined as the frequency at which the autocorrelation function of the transfer function, i.e. the Fourier transform of the power of the impulse response, intersects with a given threshold value, which may be equal to 50 or 90 percent compared to the peak value.

In narrow band communication, the used frequency band is lower than the correlation bandwidth. A signal in narrow band is therefore characterised by a nearly constant amplitude within this frequency band. The propagation channel cannot be studied save through the consideration of the attenuation. In order to compensate for the possible increase of attenuation, one generally resorts in analog to the use of a power margin and in digital to a frequency hopping.

In broadband communication, the used frequency band is higher than the correlation bandwidth. The presence of multiple paths leads to the temporal spreading of the received signals, revealed by presence of power peaks in the impulse response, and to a major fading in frequency domain. The different spectral components of the emitted signal are not affected in the same way over the used frequency band. This phenomenon, associated with the temporal spreading of the signal, results in the appearance of inter-symbol interferences due to the superposition of the delayed preceding symbols on the last emitted symbol. The possibility that such inter-symbol interferences may occur imposes a higher limit to the bit data rate. This limit can be improved if an equaliser is used.

1.1.5 Propagation Modelling

The propagation of radio waves is described through the modelling of the different physical mechanisms (free-space attenuation, atmospheric attenuation, vegetation and hydrometeor attenuation, attenuation by diffraction, building penetration loss, etc). This modelling is necessary for the conception of telecommunication systems and, once they have been designed, for their actual field deployment.

In the first case propagation models are implemented in software in order to simulate the transmission chain: this process allows to identify and reproduce the relevant characteristics of the propagation channel and to evaluate systems in terms of quality and error rate. These models are based on the consideration of the impulse response and its evolution in space and time, and rely on generic or typical environments rather than on geographical databases.

In the second case propagation models are implemented in engineering tools for the prediction different parameters useful for the field deployment of systems, for the study of the radio coverage (selection of the emission sites, frequency allocation, powers evaluation, antenna gains, polarisation) and for the definition of the interferences occurring between distant transmitters.

The analysis of propagation has its place in the study of the different types of links: ionospheric links, fixed links, point-to-point or microwave links, Earth-satellite links and mobile radio links. These different types of links will be successively considered in the course of this book.

1.2 Overview of the Book

This book devoted to the propagation of radio waves is aimed at complementing the excellent book written by L. Boithias Radio Wave Propagation. It results from researches conducted at France Telecom R&D by different researchers on the one hand on and from an extensive bibliographic compilation of studies in this field on the other hand. This book is organised in seven chapters and fifteen appendices.

The first and present chapter is an introduction to the propagation of radio waves, to the frequency spectrum, the different uses of models, the evolution of ideas and technologies which has led to the development of the present-day systems (radio relay systems, ionospheric links, transmission by geostationary or medium or low earth orbit satellites, mobile radio communication, etc). It defines the different notions associated with the propagation of radio waves: free-space attenuation, the different propagation mechanisms (reflection, transmission, diffraction, scattering, guiding), interferences, multipath propagation, propagation environment, coverage cells, narrow and broadband propagations, correlation bandwidth, antennas, etc.

Chapter 2 provides first a description of the structure and composition of the Earth's atmosphere. The different parameters used for its characterisation are then introduced, before considering the main weather phenomena which occur within the atmosphere.

The Earth's atmosphere is structurally divided into two main regions: the homosphere and the heterosphere. The homosphere is the layer of the atmosphere extending from the surface to the altitude of approximately 90 kilometres, while the homosphere is the region of the atmosphere extending beyond this altitude. The two main components of the homosphere, nitrogen and oxygen, are present in this layer in constant proportions. In contrast, light gases, such as nitrogen, hydrogen and helium are prevailing in the heterosphere.

The homosphere is itself subdivided into three layers differentiated by their temperature gradient with respect to the altitude: the troposphere, extending from the surface to the altitude of approximately 15 kilometres, the stratosphere, between 15 and 45 kilometres, and the mesosphere, from 45 to 80 kilometres.

The heterosphere is likewise subdivided into two layers: the thermosphere extending at altitudes between 80 and 1000 kilometres, and the exosphere, extending beyond 1000 kilometres.

The ionosphere located within thermosphere is characterised by the presence of ions and electrons resulting from an ionisation of the different atmospheric constituents by the solar radiation.

The constituents of the atmosphere vary with the altitude. They are classified into major atmospheric constituents (N2, O2, Ar, CO2, He, Kr, CH4, H2), minor atmospheric constituents (water vapour primarily) and aerosols, which are fine particles suspended in the atmosphere.

The Earth's atmosphere can be characterised through different atmospheric parameters, such as the pressure, the temperature, the humidity, the dew-point, the water vapour partial pressure, the saturation vapour pressure and the water vapour density. Each of these parameters will be defined within this chapter.

Several different weather phenomena take place in the atmosphere. After defining the various processes involved in these phenomena, like evaporation, condensation, solidification, fusion, superfusion or reverse sublimation, such weather phenomena as the wind, turbulence, advection, subsidence, meteors, fog, mist, precipitations, clouds and auroras are addressed.

Chapter 3 is entirely devoted to electromagnetic waves. These waves are the propagation mode of electromagnetic disturbances characterised by a simultaneous variation of an electric field and a magnetic field. Electromagnetic waves are transverse waves propagating at the speed of light in vacuum. Their spectrum or frequency range of these waves is very broad, and they include radio waves, used for radio communications and where the wavelength X ranges from a few tenths of millimetres to a few tens of thousands kilometres, infrared rays (0.8 ^m < X < 300 ^m), visible rays (0.4 ^m < X < 0.8^m), ultraviolet rays (0.001^m < X < 0.4 ^m), X-rays (0.1 A < X < 100 A) and gamma rays (1 < 0.1 A).

The first section of this chapter is devoted to the fundamental properties of electromagnetic waves and approaches the following topics : the electromagnetic parameters, the electric and magnetic fields, the electric and magnetic induction, Maxwell's equations, the propagation velocity of a wave, the wavelength, the frequency, the characteristic impedance of the propagation medium, the Poynting vector, the refractive index, polarisation, cross-polarisation, depolarisation, the cross-polarisation discrimination or decoupling ratio and the cross-polarisation isolation.

Different mechanisms of propagation, which depend on the environment where the wave propagates, are considered in the second section: reflection, either specular or diffuse, transmission, diffraction, scattering and guiding, as well as the models associated with these phenomena.

The third section of this chapter defines the different parameters used for the study of propagation both in narrowband, where the signal has a nearly constant amplitude in the used frequency band, and in broadband, where due to the presence of multiple paths the signal has no longer a constant amplitude but is affected by major fading effects in the frequency domain. The following topics are approached in this section : the different paths that a wave may follow between an emitter and a receiver (line-of-sight, reflected, transmitted, diffracted and scattered paths), the study of Fresnel ellipsoids for the characterisation of radio visibility, the main characteristics of the signal (attenuation, variability, selectivity), the different representations of the channel (time - delay representation, delay -Doppler shift representation, Doppler shift - frequency representation, temporal attenuation representation) and the broadband representation of the radio channel (average delay profile, average delay, delay spread, delay interval, delay window, correlation bandwidth).

The next four chapters consider the propagation of radio waves for different types of links: ionospheric links, terrestrial fixed links, Earth-satellite links and radio mobile links.

Chapter 4 is devoted to the propagation of waves over long distances by ionospheric refraction and reflection in the high frequency range (3-30 MHz).

The study of ionospheric refraction is developed on the basis of the magneto-ionic theory developed by Appelton and Hartree: the equations for the refractive index and the polarisation ratio are presented in this context. Approximations are then introduced for different conditions of propagation, in quasi longitudinal propagation with respect to the magnetic field, in quasi transverse propagation and in the general case. A definition of the different parameters involved in the propagation of radio waves in the ionosphere, like the absorption, the phase velocity, the group velocity, the ordinary and extraordinary critical frequencies or the real and virtual reflection heights, is provided.

When a radio wave penetrates inside the ionosphere, the presence in this medium of electrified particles combined with the influence of the magnetic field, causes different modifications affecting the essential characteristics of the wave, its trajectory, its frequency and the absorption it is submitted to. The problems associated with the calculation of trajectories are also considered in this chapter.

Finally, since the conditions of propagation in the ionosphere are greatly variable in time and space, it is essential, in order to maintain an ionospheric link under satisfactory conditions, to develop forecasts predicting the usable frequency band. Different methods of forecast have therefore been developed depending on the duration chosen for the forecast. Forecasts are classified as short-term, medium-term or long-term forecasts depending on whether they are established over twenty-four hours, over a week or over more than a month. These different types of forecasts will be described in this chapter.

Although the last decades have seen a remarkable development of satellite transmissions, ionospheric links still play an important part in radio communications, where they find privileged fields of application in maritime communications and broadcasting services.

Chapter 5 is devoted to the propagation mechanisms involved in point-to-point fixed links, and more specifically in terrestrial fixed links, also known as radio relay systems. A definition of the different radio atmospheric parameters, such as the refractive index, the modified refractive index, the standard atmosphere for refraction or the variability of the refractive index is first provided, before considering such topics as the phenomenon of refraction, the trajectory of radio waves, the radius of curvature of the paths and the effects of the variations of the refractivity index in the subrefraction and superrefraction cases.

Experimental results of interest for the study of the refractive index, of the refractivity gradient and of the cumulative distribution of the refractivity gradient are then described. A modelling of the cumulative distribution of the refractivity gradient, based on the evaluation of the median and on the percentage of time at which the gradient is lower or higher than median, is also proposed.

The main propagation mechanisms are described in the course of this chapter: line-of-sight propagation, duct propagation, reflection at elevated layers, diffraction and tropospheric scatter. The fluctuations of the scattered field, the scatter geometry and the models for the path loss due to tropospheric scatter are more particularly examined in this context.

The results of a forward-scatter terrestrial link experiment are then presented: these results concern such phenomena as tropospheric scatter, tropospheric radio duct, reflection at elevated layers, spherical diffraction, spherical superrefraction and the dynamic and statistical characteristics of the path loss. A comparison with a forward-scatter maritime link is also undertaken.

The influence of rain on a horizontal 800 metre link at four different frequencies (30, 50, 60 and 94 GHz) is also examined: after describing the experimental setup, theoretical and statistics results are presented concerning the precipitation rates, the path loss, the frequency scaling, the dynamic characteristics of rain attenuation and the distributions for the rain intensity and for the attenuation due to rain.

Chapter 6 addresses the propagation of radio waves between the Earth and a satellite. In this context, the atmospheric paths and the influence of the ground can be neglected: the study of the propagation of radio waves between the Earth and a satellite is therefore reduced, besides free-space attenuation, to the study of phenomena related to the refractive indices inside the troposphere and the ionosphere, to the absorption due to atmospheric gases, in particular oxygen and water vapour, and to the attenuation induced by hydrometeors like clouds, rain, fog, snow or ice.

The following topics are considered in the course of this chapter: free-space attenuation, the different phenomena associated with the refractive indices in the troposphere and in the ionosphere, in the case of either an absorbing or a non-absorbing medium and either in the presence or the absence of a magnetic field, refraction, delay and propagation time distortion, directions of arrival and scintillations. The different types of attenuation affecting the propagation of radio waves in this context are also examined: atmospheric attenuation, attenuation due to hydrometeors like clouds, fog or rain, attenuation due to cross-polarisation, building penetration loss, attenuation due to vegetation.

Chapter 7 is devoted to mobile radio links. Compared with the three previously mentioned links (ionospheric, terrestrial and Earth-satellite links), mobile radio links are based on the concept of a non line-of-sight propagation between the transmitter, i.e. the base station and a mobile receiver. The propagation of radio waves is generally achieved through a variety of propagation mechanisms: reflection, for instance at mountainsides or at walls, diffraction at edges, either horizontal (roofs) or vertical (corners of buildings), scattering by vegetation or guiding in street canyons. This results in the existence of a multitude of elementary paths at the reception, each such path being characterised by an attenuation, a delay and a phase difference leading to constructive or destructive interferences.

In this chapter, the modelling of the propagation in different environments (rural, suburban and urban) will be more particularly emphasised: the different types of theoretical, empirical, statistical and semi-empirical models are presented, as well as the different uses of these models. The following models are then considered: macrocell models used in rural or mountainous environments, microcell models, small cell models, ray launching models, building penetration loss models, indoor propagation models, broadband models, for instance path models and representation models (deterministic propagation models, either with or without frequency hopping), ray tracing models and geometrical models.

The use of simulation software for broadband models is also approached in this chapter. These software tools can be used for proceeding to the evaluation of the quality of service (QoS) of a digital transmission where the distortions induced by propagation play an essential part.

In addition to the chapters described above, this book includes fifteen appendices aimed at addressing in more depth certain specific topics.

Appendix A provides a detailed description of the Sun and of the solar activity. The atmosphere of the Sun is divided into three main layers: the photosphere, which delimits its visible contour, the chromosphere and the corona. The sunspots present in the photosphere are associated with strong magnetic fields and therefore play an important part in solar activity and in the disturbances affecting the relations between the Earth and the Sun. The solar wind plays an important part in the configuration of the magnetosphere, i.e. the region of the circumterrestrial space subjected to the influence of the Earth's magnetic field. The solar activity is commonly characterised either by the Wolf number or by the radio flux at the 10.7 centimetre wavelength (2800 MHz).

The microphysical properties of hydrometeors, like rain, drizzle, snow, hail and fog, are addressed in Appendix B. For each of these hydrometeors, different models are presented for the determination of some of their characteristics, like their density, form, size or fall speed.

Appendix C is entirely devoted to the frequency spectrum and describes successively the different frequency bands are: for each band, the atmospheric and terrestrial influence, as well as the system considerations and the associated services are indicated (Hall 1989). The frequency allocation for UMTS by the IMT-2000 is then given for the different geographical areas (ITU, Europe, United States and Japan), before listing the frequency bands used in satellite communications. At last, additional information concerning the P, L, S, X, K, Q, V and W bands is provided.

The phenomenon of cross-polarisation induced by the atmosphere will be considered in Appendix D. Indeed, while orthogonal polarisations are used in order to increase the line capacity of a given link without increasing the bandwidth, the presence for instance of asymmetrical raindrops or ice crystals in the atmosphere where the waves propagate causes a part of the energy emitted with a given polarisation to become orthogonally polarised, thereby causing interferences between the two communication channels. Different parameters, like the cross-polarisation discrimination and the cross-polarisation isolation are considered for the characterisation of this phenomenon. Special attention is given to the models which have been developed for the determination of the cross-polarisation discrimination due to rain, to snow and in clear atmosphere respectively.

A description of Fresnel equations used in the evaluation of the reflection and transmission coefficients, either simple or multiple, is provided in Appendix E for different types of polarisations: horizontal, vertical and unspecified polarisations.

Appendix F is aimed at complementing Chapter 4 on the propagation of electromagnetic waves in the ionosphere. Different types of disturbances observed within the Earth's atmosphere after a solar flare are described in this appendix. These disturbances may be either radio electric like sudden ionospheric disturbances or polar cap absorption events, geomagnetic like magnetic storms, ionospheric like ionospheric storms or atmospheric like polar auroras.

Appendix G is devoted to the sounding methods of the ionosphere used for determining the characteristics of the ionospheric propagation medium, like for instance the critical frequencies and the heights of the different layers, the Doppler frequencies, the diffusion function or the angles of arrival. These methods include bottomside vertical or oblique soundings of the ionosphere, topside vertical soundings of the ionosphere, backscatter soundings and incoherent scatter soundings. A description of riometers as well as of low frequency and very low frequency receivers is also presented in this appendix.

Appendix H provides a brief description of the terrestrial magnetic field. The different magnetic indices K, Kp, Ap, Aa, Dst and AE used for characterising the terrestrial magnetic field are then defined.

The attenuation due to rain is one of the most important factors to consider for the design of telecommunication systems, and more particularly for the design of satellite telecommunication systems. This subject is considered in Appendix I, and different statistical models of rain attenuation are presented.

Different models that have been developed in order to determine the attenuation due to vegetation are then described in Appendix J. These models include the exponential decay model, the modified exponential decay model, the Rice model, the ITU-R model, the Al Nuaimi Hammoudeh model and the Stephens model, as well as radiative transfer models like the MIMICS model or the Karam-Fung model. The results of two experiments conducted in the UHF band are presented. In the first experiment, a 2270 metre fixed link with a 160 metre length inside the vegetation, was considered in order to investigate the daily and seasonal influence of vegetation depending on the meteorological parameters. In the second experiment, mobile links were set up in a wooded area along a 52 kilometre long route in order to investigate the effects of the penetration distance inside the foliage, depending on the period of the day and the season, and for vegetation depths ranging from a few meters and 6 kilometers.

Appendix K is devoted to a survey of different diffraction models, either for the diffraction by a single or multiples knife edges, or for the diffraction by a rounded obstacle. The Millington method, the Vogler method, the Epstein-Peterson method, the Shibuya method, the Deygout method and the Giovanelli method for the calculation of the attenuation due to diffraction by multiple knife edges are introduced. The Wait method and the ITU-R method for the diffraction by a rounded obstacle are then described.

The measurements of the field strength, of the impulse response and of the directions of arrival for mobile radio links are addressed in Appendix L. These measurements are necessary for the development, the optimisation and the validation of propagation models, which are then implemented in engineering tools in order to define, design and set up communication systems. The main features of the propagation channel sounder AMERICC defined and developed at France Telecom R&D are then briefly described. This channel sounder can be used in particular for obtaining a precise characterisation of the radio propagation channel over a bandwidth ranging from 0 to 250 MHz around a carrier frequency fixed between 1.9 and 60 GHz.

The experimental determination and the mathematical modelling of directions of arrival are more particularly addressed in Appendix M. Different determination methods of the angles of arrival are presented in this appendix: linear methods like Fourier analysis or phase reconstruction, as well as non-linear or high-resolution methods, like the MUSIC method or the method based on the estimate of the maximum probability.

Appendix N is devoted more specifically to geographical databases. These databases allow the description of propagation environments. They generally include data relating to the topography, the vegetation and the land use, the streets axes and the buildings.

At last, different methods for the determination of the electromagnetic field after its interaction with a structure, a half-plane or a dihedron for instance, either metallic or dielectric, are presented in Appendix O. These methods include the geometric optical method, the geometrical theory of diffraction, the uniform theory of diffraction, the finite difference in time domain method, the moment method and parabolic equation methods.

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  • erica
    What are meant by subrefraction and superrefraction in case of radio wave propagation?
    2 years ago

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