# Communication Systems/Wave Propagation

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

## Electromagnetic Spectrum


:   

    :   ![](cont_emspec2.jpg "fig:cont_emspec2.jpg")

## Radio Waves

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.

:   

    :   ![](tem_wave.gif "fig:tem_wave.gif")

The relationship between wavelength and frequency is given by:

$$c = \lambda f$$

:   

    :   where c is the speed of light (approximately 300,000 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.

:   

    :   ![](electron_density_altitude.gif "fig:electron_density_altitude.gif")

### 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
  THF - Tremendously High Frequency   300 -- 3000 GHz   1 -- 0.1 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.

:   

    :   ![](surface_wave.gif "fig:surface_wave.gif")

#### 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.

:   

    :   ![](refraction_distance.gif "fig:refraction_distance.gif")

##### 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 200 MHz.
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 180^o^ out of phase with each other.

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

Vertically polarized waves generally reflect less than half of the
incident energy. If the angle of incidence is greater than 10^o^ 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 1,000 km.[^1]

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.

## Fading and Interference

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.

:   

    :   ![](direct_relected_wave.gif "fig:direct_relected_wave.gif")

```{=html}
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```

:   

    :   *p~1~* = direct wave path length

```{=html}
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```

:   

    :   *p~2~* = reflected wave path length

$$\Delta$$*p* = *p~2~ - p~1~* 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:

:   

    :   ![](vector_sum.gif "fig:vector_sum.gif")

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:

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

### Multipath Fading

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 nanosecond. This
spreading tends to limit the bit rate over RF links.

#### Rayleigh Fading

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.

:   

    :   ![](Rayleigh_fading_doppler_10Hz.gif "fig:Rayleigh_fading_doppler_10Hz.gif"){width="300"}

#### Ricean Fading

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:

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

*v~m~* is the relative motion of the transmitter with respect to the
receiver, *c* is the speed of light and *f~c~* 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 maximum in the direction of propagation and zero in the
reverse direction.

## 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.

## Diffraction

Diffraction occurs in beams of light or waves when they become spread
out as a result of passing through a narrow slit. Maximum diffraction
occurs when the slit through which the wave passes through is equal to
the wavelength of the wave. Diffraction will result in constructive and
destructive interference.

## Path Loss

## References


[^1]: <http://www.hq.nasa.gov/iwgsdi/Ionosphere.html>
