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Essentials of Radio Wave Propagation

Javier Leonardo Araque QuijanoAssociate Professor

Electric and Electronics Engineering DepartmentUniversidad Nacional de Colombia

jlaraqueq@unal.edu.coEdif. 453 � Of.204

Ext 14083

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(Very Short) History of Wireless Communications

A. Antoniou, �On the Roots of Wireless Communications�, IEEE Circuits and Systems Magazine, 1st Quarter 2011, pp.14-25.

� Michael Faraday (1831)

� Lord Kelvin (1845)

� James Clerk Maxwell (1862)

� Heinrich Rudolf Hertz (1887)

� Nikola Tesla (1897)

� Guglielmo Marconi (1896)

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Review of Electromagnetic Waves

� Maxwell's equations � Time-domain Vs. Frequency domain

� Wave types

� Wave properties:

� Polarization

� Velocity

� Wavelength

� Power transmission and loss

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Generation of EM Waves: Radiation

� Accelerated charges cause radiation

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The Communications Link

� Antennas perform the key step of transforming voltage/current into a free-space wave and viceversa

� From the Tx/Rx viewpoint antennas make part of channel!

� Thus the need to account for their behavior when analyzing communication links

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Antenna Pattern types

� Isotropic: not physically realizable

� Omnidirectional: non-directional in one plane and directional in any perpendicular plane.

� pencil beam: considerable radiation only in a small neighborhood of a unique direction.

� contoured beam: considerable radiation only in a shaped portion of solid angle.

08/12/11 7

Field regionsReactive near-field:

R<

Fields are mostly reactive.

Radiating near-field

<R<

Fields are mostly radiating but angular distribution depends on distance.

Far field (Fraunhofer)

R>

Angular distribution is essentially independent on distance, fields are transverse.

08/12/11 8

Far Field

In the far field, dependence on r and spherical angles theta, phi are separable, the wavefront is spherical and fields are transverse:

Universal spherical wave, complex scalar

Antenna-specific pattern, vector with negligible radial component

In Far Field, E and H are transverse and are related by the usual impedance relations. P is a unit vector along the observation direction.

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Antenna Parameters (Tx - Rx)� Gain (Tx): ratio between the antenna's

radiation intensity and that due to an isotropic lossless radiator with the same input power in a given direction:

� Effective area (Rx): Ratio between power available at antenna terminals and the incident power density (depends on the incidence direction):

� Those parameters are linearly related for any antenna:

Plane

wav

e

RX Antenna: aperture collecting power from impinging waves

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Propagation in Free-SpaceFriis equation

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Example

A GSM circular cell with a maximum diameter of 17km is covered by three identical antennas working at 1850MHz. These antennas cover 120° non-overlapping portions of the horizon and have an input power of 15W each. The transversal dimensions of each antenna are 25cm x 1m, consider an aperture efficiency of 0.7.

Considering as receiver a handset equipped with an antenna having G=-1dB and maximum polarization mismatch of -3dB, compute the power received in the worst case.

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Wave Interaction with Matter

Reflection/transmission: occurs in presence of large material discontinuities.

� For plane waves/interfaces, the Fresnel relate Et, Er with Ei.

� According to interface roughness, reflection may be specular or diffuse.

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Reflection/Transmission (Smooth Interface)

� Reflected wave amplitude depends on:

� Incidence angle

� Media impedance

� Separate cases for analysis: TE (perpendicular) and TM (parallel)

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Example

� Reflection from a lossy brick wall (epsr=4-j0.1) with 30cm thickness

See ref [2], sec. 3.3 for the computation details

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Example

� A TE wave with amplitude 1V/m going through free-space impinges on a dielectric interface with theta_i = 20°. The dielectric half space has epsilon_r = 3- j0.2. Compute the amplitude of the wave transmitted into the medium and the propagation constant therein.

er

ki

kt

krz

y

qi

qi

qt

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Solution� Using Snell's law:

sin(theta_t) = 0.1971 + 0.0066i

why is this complex? In medium 2, phase increase and attenuation must occur in different directions in order to satisfy the boundary conditions, see k later.

�

� Using 4th eq in slide 13 (note that cos^2+sin^2=1 works also in the complex field):

Et = 0.7119 + 0.0159i

This has only x component (TE wave)

E = x^ Et

� Compute wave vector (complex):

k = wsqrt(me)( - � sin(qt) + �cos(qt))

k = k0[ -� 0.34 + � (1.7 � j5.9e-2)]

re phase / im attenuation� �

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Diffuse Reflection

Tx Rx

W

D

H

Occurs when: Lambert model

Phong model:

R power�

�r Reflection coefficient

rd �Diffusion ratio

qi

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Wave Diffraction

� Occurs when the radio path is obstructed by a surface with sharp irregularities. Shadow is not perfect, some energy actually reaches the region behind the obstruction.

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The Canonical Obstruction Problem:knife-edge diffraction

� When h << min(d1,d2), the difference between the direct and broken path lengths is approximately:

Tx Rx

b g

a

h

d1 d2

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Knife-edge Diffraction: solution

� Canonical problem can be solved in terms of special functions:

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Fresnel Ellipsoids� These are a family of surfaces giving constant

phase difference between direct and broken paths in multiples of lambda/2:

n=0

n=3n=2n=1

For acceptable attenuation obstacles must remain out of the first Fresnel obstacle.

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Example

� For the situation in figure, compute the total power at the receiver.

Tx Rx

h_o

h_Rx

h_Tx

d_Tx d_Rx

EIRP = 100W, G_Rx = 0dB, f=1.85GHz

H_Tx = 30m, H_Rx = 2m

H_o = 50m

d_Tx = 400m, d_Rx = 200m

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Propagation in Atmosphere

� Bending in troposphere

� Ducting

� Troposphere scattering

� Ionospheric propagation

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Ray Bending for Tropospheric Links

� Troposphere extends to about 10km above earth surface and presents a refraction coefficient that decreases with height EM waves bend �

towards ground allowing LoS communication beyond the horizon.

� By applying an earth scaling procedure and maintaining the path-to-ground distance all over the link one may consider rectilinear propagation.

� The maximum range attainable by such a link considers a larger earth to include this effect: (in average Re = 8500km)

Dmax is given here in km, while h_tx and h_rx are in m

Varyng atomosphere eps_R with height �

curved path

Enlarged earth allows considering a rectilinear path

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Ducting

� When the gradient of n is too small rays bend considerably towards earth and bounce back again and again, possibly reaching long distances.

� Generation of an inversion layer (exceptional atmospheric conditions create a local maximum of n at some height above the ground) may trap rays and allow long-range propagation.

� These phenomena cannot are difficult the predict, thus cannot be consistently exploited. On the other hand, increased range may result in harmful interference.

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Ionospheric Propagation

� Ionosphere is located in the range 50km -1000km above earth surface: solar and cosmic radiation cause ionization wide availability of free �

electrons and atom nuclei (plasma state).

� Depending on frequency and angle of incidence, absorption, reflection or transmission (with polarization rotation- the Faraday effect) may take place.

The allowed band for reflection is limited by the LUF and the MUF, at which the plasma becomes absorbing and transparent respectively. These vary along the day and from day to day.

freq

Day hour

Transparent

Reflective

Absorbing

Fc in MHz, ne in electr /m^3

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Ionospheric Communication Multi-hop Link

� Ground/iononsphere bouncing allows long-range links (in figure, Florida � South Pacific Islands, extracted from [3])

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Multi-Path Propagation

Interference between approximately plane waves arriving from different directions creates a standing wave pattern in space �strong amplitude variations at

the l scale

Observed effects:- Fast fading- Doppler spread- Slow fading- Cross-polarization coupling

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A Simple Situation

V

q

V(x) = A exp(-i x 2p/l) � B exp(i w x cos(q) 2p/l)

Relative Tx/Rx velocity causes Doppler shift:

Df1 = -v/l

Df2 = v cosq/l

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References

[1] Balanis, C. �Antenna Theory: Analysis and Design� 3rd Ed. John Wiley, 2007.

[2] Bertoni, H. �Radio Propagation for Modern Wireless Systems�, Prentice Hall, 2000.

[3] Siwiak, K. and Bahreini, Y. �Radiowave Propagation and

Antennas for Personal Communications� 3rd Ed. Artech House, 2007.

[4] Sizun, H. �Radio Wave Propagation for Telecommunication Applications�. Springer, 2005.