# Communication Systems/Wave Propagation

This page will discuss some of the fundamental basics of EM wave propagation.

## Electromagnetic Spectrum

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Maxwell first predicted the existence of electromagnetic waves in the 19th century. He came to this conclusion by careful examination of the equations describing electric and magnetic phenomenon. It was left up to Hertz to create these waves, and Marconi to exploit them.

In spite of one hundred years of study, exactly what radio waves are and why they exist, remain somewhat of a mystery.

Electromagnetic waves in free space, or TEM waves, consist of electric and magnetic fields, each at right angles to each other and the direction of propagation.

The relationship between wavelength and frequency is give by:

$c = \lambda f$
where c is the speed of light (approximately 300,000,000 m/s in vacuum), f is the frequency of the wave, and λ is the wavelength of the wave.

Radio waves can be reflected and refracted in a manner similar to light. They are affected by the ground terrain, atmosphere and other objects.

Maxwell’s equations state that a time varying magnetic field produces an electric field and a time varying electric field produces a magnetic field. This is kind of a chicken and egg situation.

Radio waves propagate outward from an antenna, at the speed of light. The exact nature of these waves is determined by the transmission medium. In free space, they travel in straight lines, whereas in the atmosphere, they generally travel in a curved path. In a confined or guided medium, radio waves do not propagate in the TEM mode, but rather in a TE or TM mode.

Radio waves interact with objects in three principle ways:

Reflection – A radio wave bounces off an object larger than its wavelength.
Diffraction – Waves bend around objects.
Scattering – A radiowave bounces off an object smaller than its wavelength.

Because of these complex interactions, radio wave propagation is often examined in three distinct regions in order to simplify the analysis:

Surface (or ground) waves are located very near the earth’s surface.
Space waves occur in the lower atmosphere (troposphere).
Sky waves occur in the upper atmosphere (ionosphere).

The boundaries between these regions are somewhat fuzzy. In many cases, it is not possible to examine surface waves without considering space waves.

### Common RF Band Designations

Frequency band name Frequency Wavelength
ELF - Extremely Low Frequency 3 – 30 Hz 100000 – 10000 km
SLF - Super Low Frequency 30 – 300 Hz 10000 – 1000 km
ULF - Ultra Low Frequency 300 – 3000 Hz 1000 – 100 km
VLF - Very Low Frequency 3 – 30 kHz 100 – 10 km
LF - Low Frequency 30 – 300 kHz 10 – 1 km
MF - Medium Frequency 300 – 3000 kHz 1000 – 100 m
HF - High Frequency 3 – 30 MHz 100 – 10 m
VHF - Very High Frequency 30 – 300 MHz 10 – 1 m
UHF - Ultra High Frequency 300 – 3000 MHz 1000 – 100 mm
SHF - Super High Frequency 3 – 30 GHz 100 – 10 mm
EHF - Extremely High Frequency 30 – 300 GHz 10 – 1 mm

### Surface Waves

These are the principle waves used in AM, FM and TV broadcast. Objects such as buildings, hills, ground conductivity, etc. have a significant impact on their strength. Surface waves are usually vertically polarized with the electric field lines in contact with the earth.

#### Refraction

Because of refraction, the radio horizon is larger than the optical horizon by about 4/3. The typical maximum direct wave transmission distance (in km) is dependent on the height of the transmitting and receiving antennas (in meters):

$d_{\max } \approx \sqrt {17h_t } + \sqrt {17h_r } \quad {\rm{km}}$

However, the atmospheric conditions can have a dramatic effect on the amount of refraction.

##### Super Refraction

In super refraction, the rays bend more than normal thus shortening the radio horizon. This phenomenon occurs when temperature increases but moisture decreases with height. Paradoxically, in some cases, the radio wave can travel over enormous distances. It can be reflected by the earth, rebroadcast and super refracted again.

##### Sub refraction

In sub refraction, the rays bend less than normal. This phenomenon occurs when temperature decreases but moisture increases with height. In extreme cases, the radio signal may be refracted out into space.

### Space Waves

These waves occur within the lower 20 km of the atmosphere, and are comprised of a direct and reflected wave. The radio waves having high frequencies are basically called as space waves. These waves have the ability to propagate through atmosphere, from transmitter antenna to receiver antenna. These waves can travel directly or can travel after reflecting from earth’s surface to the troposphere surface of earth. So, it is also called as Tropospherical Propagation. In the diagram of medium wave propagation, c shows the space wave propagation. Basically the technique of space wave propagation is used in bands having very high frequencies. E.g. V.H.F. band, U.H.F band etc. At such higher frequencies the other wave propagation techniques like sky wave propagation, ground wave propagation can’t work. Only space wave propagation is left which can handle frequency waves of higher frequencies. The other name of space wave propagation is line of sight propagation. There are some limitations of space wave propagation.

1. These waves are limited to the curvature of the earth.
2. These waves have line of sight propagation, means their propagation is along the line of sight distance.

The line of sight distance is that exact distance at which both the sender and receiver antenna are in sight of each other. So, from the above line it is clear that if we want to increase the transmission distance then this can be done by simply extending the heights of both the sender as well as the receiver antenna. This type of propagation is used basically in radar and television communication.

The frequency range for television signals is nearly 80 to 200MHz. These waves are not reflected by the ionosphere of the earth. The property of following the earth’s curvature is also missing in these waves. So, for the propagation of television signal, geostationary satellites are used. The satellites complete the task of reflecting television signals towards earth. If we need greater transmission then we have to build extremely tall antennas.

#### Direct Wave

This is generally a line of sight transmission, however, because of atmospheric refraction the range extends slightly beyond the horizon.

#### Ground Reflected Wave

Radio waves may strike the earth, and bounce off. The strength of the reflection depends on local conditions. The received radio signal can cancel out if the direct and reflected waves arrive with the same relative strength and 180o out of phase with each other.

Horizontally polarized waves are reflected with almost the same intensity but with a 180o phase reversal.

Vertically polarized waves generally reflect less than half of the incident energy. If the angle of incidence is greater than 10o there is very little change in phase angle.

### Sky Waves

These waves head out to space but are reflected or refracted back by the ionosphere. The height of the ionosphere ranges from 50 to 600 km.

Radio waves are refracted by the ionized gas created by solar radiation. The amount of ionization depends on the time of day, season and the position in the 11-year sun spot cycle. The specific radio frequency refracted is a function of electron density and launch angle.

A communication channel thousands of kilometers long can be established by successive reflections at the earth’s surface and in the upper atmosphere. This ionospheric propagation takes place mainly in the HF band.

The ionosphere is composed of several layers, which vary according to the time of day. Each layer has different propagation characteristics:

D layer – This layer occurs only during the day at altitudes of 60 to 90 km. High absorption takes place at frequencies up to 7 MHz.
E layer – This layer occurs at altitudes of 100 to 125 km. In the summer, dense ionization clouds can form for short periods. These clouds called sporadic E can refract radio signals in the VHF spectrum. This phenomenon allows amateur radio operators to communicate over enormous distances.
F layer - This single nighttime layer splits into two layers (F1 and F2) during the day. The F1 layer forms at about 200 km and F2 at about 400 km. The F2 layer propagates most HF short-wave transmissions.

Because radio signals can take many paths to the receiver, multipath fading can occur. If the signals arrive in phase, the result is a stronger signal. If they arrive out of phase with each other, they tend to cancel.

Deep fading, lasting from minutes to hours over a wide frequency range, can occur when solar flares increase the ionization in the D layer.

The useful transmission band ranges between the LUF (lowest usable frequency) and MUF (maximum usable frequency). Frequencies above the MUF are refracted into space. Below the LUF, radio frequencies suffer severe absorption. If a signal is near either of these two extremes, it may be subject to fading.

Meteors create ionization trails that reflect radio waves. Although these trails exist for only a few seconds, they have been successfully used in communications systems spanning 1500 km.

The Aurora Borealis or Northern Lights cause random reflection in the 3 - 5 MHz region. Aurora causes signal flutter at 100 Hz to 2000 Hz thus making voice transmission impossible.

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Radio signals may vary in intensity for many reasons.

### Flat Earth Reflections (Horizontal Polarization)

There are at least two possible paths for radio waves to travel when the antennas are near the earth: direct path and reflected path. These two signals interact in a very complex manner. However, ignoring polarization and assuming a flat earth can produce some interesting mathematical descriptions.

p1 = direct wave path length
p2 = reflected wave path length
$\Delta$p = p2 - p1 difference in path lengths
d = distance

From the geometry we can observe:

$p_1^2 = \left( {h_r - h_t } \right)^2 + d^2$
$p_2^2 = \left( {h_r + h_t } \right)^2 + d^2$
$p_2^2 - p_1^2 = \left( {h_r - h_t } \right)^2 + d^2 - \left( {h_r + h_t } \right)^2 - d^2 = 4h_r h_t$
$\left( {p_2 - p_1 } \right)\left( {p_2 + p_1 } \right) = 4h_r h_t$

But$\Delta p = \left( {p_2 - p_1 } \right)$ and $d \approx p_1 \approx p_2$

$\Delta p2d \approx 4h_r h_t$ therefore $\Delta p \approx \frac{{2h_r h_t }}{d}$

If the difference in the two paths $\Delta$p, is 1/2 $\lambda$ long, the two signals tend to cancel. If $\Delta$p is equal to $\lambda$, the two signals tend to reinforce. The path difference $\Delta$p therefore corresponds to a phase angle change of:

$\varphi _p = \frac{{2\pi }}{\lambda }\Delta p = \frac{{4\pi h_r h_t }}{{\lambda d}}$

The resultant received signal is the sum of the two components. The situation is unfortunately made more complex by the fact that the phase integrity of the reflected wave is not maintained at the point of reflection.

If we limit the examination of reflected waves to the horizontally polarized situation, we obtain the following geometry:

Applying the cosine rule to this diagram, we obtain a resultant signal of:

$E_r = E_1 \sqrt {2\left( {1 - \cos \varphi _p } \right)} = 2E_1 \sin \left( {\frac{{\varphi _p }}{2}} \right)$

The signal strength of the direct wave is the unit distance value divided by the distance: $E_r = \frac{{E_0 }}{d}$ Therefore, the received signal can be written as:

$E_r = \frac{{2E_0 }}{d}\sin \left( {\frac{{2\pi h_r h_t }}{{\lambda d}}} \right)$

For small angles this can be approximated by:

$E_r \approx \frac{{2E_0 }}{d}\frac{{2\pi h_r h_t }}{{\lambda d}} = E_0 \frac{{4\pi h_r h_t }}{{\lambda d^2 }}$

The received signal is generally a combination of many signals, each coming over a different path. The phase and amplitude of each component are related to the nature of the path. These signals combine in a very complex manner. Some multipath fading effects are characterized by delay spread, Rayleigh and Ricean fading, doppler shifting, etc. Fading is the most significant phenomenon causing signal degradation. There are several different categories of fading:

• Flat fading: the entire pass band of interest is affected equally (also known as narrow or amplitude varying channels).
• Frequency selective fading: certain frequency components are affected more than others (also known as wideband channels). This phenomenon tends to introduce inter-symbol interference.
• Slow fading: the channel characteristics vary at less than the baud rate.
• Fast fading: the channel characteristics vary faster than the baud rate.

#### Time Dispersion

Time dispersion occurs when signals arrive at different times. Signals traveling at the speed of light move about 1 foot in 1 Sec. This spreading tends to limit the bit rate over RF links.

The Rayleigh distribution can be used to describe the statistical variations of a flat fading channel. Generally, the strength of the received signal falls off as the inverse square of the distance between the transmitter and receiver. However, in cellular systems, the antennas are pointed slightly down and the signal falls of more quickly.

The Ricean distribution is used to describe the statistical variations of signals with a strong direct or line-of-sight component and numerous weaker reflected ones. This can happen in any multipath environment such as inside buildings or in an urban center.

A received signal is generally comprised of several signals, each taking a slightly different path. Since some may add constructively in-phase and others out of phase, the overall signal strength may vary by 40 dB or more if the receiver is moved even a very short distance.

#### Doppler Shift

A frequency shift is caused by the relative motion of the transmitter and receiver, or any object that reflects/refracts signal. This movement creates random frequency modulation. Doppler frequency shift is either positive or negative depending on whether the transmitter is moving towards or away from the receiver.

This Doppler frequency shift is given by:

$f_d = \frac{{v_m }}{c}f_c$

vm is the relative motion of the transmitter with respect to the receiver, c is the speed of light and fc is the transmitted frequency. In the multipath environment, the relative movement of each path is generally different. Thus, the signal is spread over a band of frequencies. This is known as the Doppler spread.

### Atmospheric Diffraction

Radio waves cannot penetrate very far into most objects. Consequently, there is often a shadow zone behind objects such as buildings, hills, etc.

The radio shadow zone does not have a very sharp cutoff due to spherical spreading, also called Huygens’ principle. Each point on a wavefront acts as it were a point source radiating along the propagation path. The overall wavefront is the vector sum of all the point sources or wavelets. The wavelet magnitude is proportional to $1 + \cos \theta$ where $\theta$ is measured from the direction of propagation. The amplitude is a maximum in the direction of propagation and zero in the reverse direction.

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## Reflection

Reflection normally occurs due to the surface of earth or building & hills which have large dimension relative to the wavelength of the propagation waves. The reflected wave changes the incident angle.

There is similarity b/w the reflection of light by a conducting medium. In both cases, angle of reflection is equal to angle of incidence. The equality of the angles of reflection & incidence follows the second law of reflection for light.

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## Diffraction

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## Path Loss

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## Doppler Shift

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