Subject: [NEXTEL-1] Inside line-of-sight propagation

From: Marcelrf <[email-masked]>
Date: Sat, 21 Feb 2004 05:18:30 -0500

Inside line-of-sight propagation

BY HAROLD KINLEY

Mobile Radio Technology, Jan 1, 2004

When a line-of-sight path exists between two antennas, the propagation
loss is equal to free-space attenuation. Free-space propagation occurs
in the far-field region. Optical line of sight does not necessarily
provide radio line-of-sight conditions. It depends on the clearance of
the Fresnel zone.  Obviously, these terms need to be defined
mathematically and literally before continuing.

Free-space attenuation

Free-space propagation loss increases by 6 decibels (dB) per octave of
distance from the transmitter antenna. Technically speaking, it is 6 dB
per octave of distance from the point where far-field propagation
begins.  Free-space attenuation is found from the formula in Equation 1,
where A is path attenuation in decibels, F is frequency in megahertz and
D is distance in miles. It is important to note that this formula
assumes that the antennas on each end are half-wave dipoles. After all,
it takes an antenna to radiate a signal and one to capture it.

Figure 1 shows a free-space link between two antennas operating at a
frequency of 800 MHz at a distance of 15 miles. The path attenuation
between the half-wave dipole antennas is 114 dB. This is the actual
attenuation between the antenna terminals.

Far-field region

The far-field region is the region in which plane-wave propagation takes
place. The beginning of the far-field region can be determined from the
formula in Equation 2, where F is the distance (in feet) from the
antenna where the far field begins, D is the largest dimension of the
antenna (in feet) and ? is the wavelength in feet. Also, F must be much
greater than both D and ?. The beginning of the far-field region should
be no less than 10 wavelengths from the antenna. In the case of Figure
1, the half-wave antenna would have a dimension of 0.62 feet and ? would
be 1.23 feet.

Plugging these figures into Equation 2 would yield a distance of 0.625
feet. Thus, the far-field region begins 0.625 feet from the antenna.
Since F is not much greater then D or ?, the distance to the beginning
of the far field should be taken as 10 wavelengths or approximately 12
feet.  Relative to the 15-mile distance between the two antennas, 12
feet is insignificant.

Fresnel zones

Radio line of sight and optical line of sight are different. Even over a
smooth earth with no obstructions, radio line of sight is limited by the
earth's curvature. Radio wave propagation extends beyond optical line of
sight. So, for radio line-of-sight calculations, the earth's radius is
taken to be 1.333 times or 4/3 the normal radius. This produces a
flatter earth between two fixed points.
In order to achieve true line-of-sight propagation (free space) the true
line-of-sight path between two fixed antennas must clear any obstruction
by more than the distance required for optical line of sight. Figure 2
shows a situation where optical line of sight exists between two
antennas. However, Fresnel zones exist around the radio wave and at
least 60 percent of the first Fresnel zone must clear any obstruction in
order to achieve minimal degradation to the radio wave for virtual
free-space propagation to exist. Figure 3 shows the first Fresnel zone
around the radio wave and 60 percent of the first Fresnel zone is shown
as the gray shaded area. Notice that the tall building penetrates the
Fresnel zone such that not even 60 percent of the first Fresnel zone is
clear. Thus, radio line of sight does not exist and the radio wave will
be degraded by the obstruction.

Equation 3 can be used to calculate the Fresnel zone around the radio
wave at any given point between the receiver and transmitter antennas.
In Equation 3, H is the height (in feet) of the first Fresnel zone above
optical line of sight. D1 is equal to or less than D2 and is measured in
miles. F is the frequency in megahertz.

Figure 4 shows the first Fresnel zone is an ellipsoid surrounding the
straight line between the two antennas. The sum of the distances between
the two antennas and a common point on the ellipsoid is one-half
wavelength greater than the straight line between the two antennas. For
example, in Figure 4 the length of A-B-C is one-half wavelength greater
than length A-C.
Suppose that the straight-line distance (A-C in Figure 4) between the
two antennas is 25 miles, D1 is 10 miles, and D2 is 15 miles, while the
operating frequency is 800 MHz. Plugging these numbers into Equation 3
yields a solution of 197.5 feet for the first Fresnel zone at distance
D1.  The wavelength at 800 MHz is 1.2303 feet. The straight-line
distance (A-C) is equal to 25 miles (132,000 feet or 107,290.9
wavelengths).

Using the Pythagorean theorem and substituting 197.5 feet for B-D, we
find that the length of A-B is 52,800.37 feet or 42,916.66 wavelengths.
Similarly, length B-C is calculated to be 79,200.25 feet or 64,374.74
wavelengths. The sum of A-B and B-C is 107,291.4 wavelengths, 0.5
wavelengths longer than A-C. This simply proves that the calculation for
the height (B-D) of the first Fresnel zone is correct.

Path profile

Figure 5 shows a path profile that was obtained using software called
Radio Mobile Deluxe.1 This software is downloadable free from the
Internet and is quite useful in running various communication scenarios
using actual terrain data.
Figure 6 shows the boundary of 60 percent of the first Fresnel zone.
Notice that 60 percent of the first Fresnel zone would not even clear
smooth earth. Smooth earth is indicated by the black curvature at the
bottom of the figure. With the hilly terrain between the two antennas,
the signal would encounter severe attenuation.

Summary

As the frequency of operation increases, the boundary of the Fresnel
zone draws in closer to the straight line. That is, at very high
frequencies the propagation approaches optical line of sight. While it
isn't always necessary to achieve a line-of-sight path between two fixed
points, it does greatly improve the probability of communication to do
so.

This is especially important in microwave links in order to achieve
maximum reliability. Using a program such as Radio Mobile Deluxe with
the proper terrain data (also free from the Internet) will allow one to
determine necessary antenna heights on each end as well as other
pertinent information for establishing a reliable communication link.
Until next time — stay tuned!

1 Radio Mobile Deluxe was written by Roger Coude of Canada and made
available as freeware.
Editor's note: The web site for Radio Mobile Deluxe is
www.cplus.org/rmw/english1.html.

http://iwce-mrt.com/ar/radio_inside_lineofsight_propagation/index.htm
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