Basics in Link Engineering 
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Fade Margin and Outage Prediction
Link Equation with Passive
Repeater
©
20012016, Apus Cloud Project e Luigi Moreno
_______________________________________________________________
In this
Session the Free Space radio link equation is presented, together with the
concept of Free Space Loss. Then, terrestrial radio hops are considered and a
brief summary is given of the most significant propagation impairments.We discuss the Link Budget, in order to
estimate the Fade Margin, and how to use the Fade Margin in predicting the
outage probability. Finally, the radio
link equation is revised to include the use of passive repeaters.
We approach radio link engineering by first
considering an ideal propagation environment, where transmission of radio waves
from Tx antenna to Rx antenna is free of all objects that might interact in any
way with electromagnetic (EM) energy.
This assumption is usually referred as "Free Space"
propagation.
Let us consider
a radio transmitter with power
p_{T}
coupled to a
directive
antenna
with maximum gain on the axis g
_{
T
}.
At
distance D from the transmitting antenna (sufficiently large, in order that Far
Field conditions are satisfied), the Power Density on the antenna axis is :
_{
}
Computation of Received Power in Free Space propagation
Now we imagine that, at the
distance D, a receiving antenna is installed. The
antenna "effective
aperture"
or "effective area" A_{E} gives a measure
of the antenna ability to capture a fraction of the radio energy distributed at
the receiver location. Assuming no
receiver mismatch, the power p_{R}, at the receiver antenna output
flange, is :
_{
}
Taking account
that the relation between the Rx
antenna
gain
and the antenna "effective aperture" is :
_{
}
the received power
equation becomes :
_{ }
where F is the frequency of the transmitted
signal,
lis the wavelength, and c =l
F is the propagation speed, which can be
assumed to be about 3 10^{8} m/s, with good approximation, both in the
vacuum and in the atmosphere.
This is usually
known as the "
Free
Space Radio Link Equation.
"Using logarithmic units, it can be written
as :
_{
}
where
uppercase letters are used to express power in dBm
and gains in dB, while the same letters in lowercase had been previously used
for nonlogarithmic units.
Note that frequency must be expressed in
GHz and distance in km, otherwise the 92.44 constant is to be modified
accordingly (e.g. : with distance
in miles, the constant is 96.57; with frequency in MHz, the constant is 32.44).
The above equation can be also
written as :
_{
}
where FSL is called Free Space Loss, given
by:
_{
}
If we assume to use Isotropic Antennas (G = 0 dB)
both at the transmitting and at the receiving site, then :
_{
}
so FSL is also defined as "loss
between isotropic antennas".
Free Space Loss vs. distance and frequency
Comments on
Free Space Loss
The concept of Free
Space Loss, and the related formulas, need some comments.First, the term "loss" could
suggest some similarity with losses in coaxial cables or other guided
transmission of electromagnetic (EM) energy, where we observe an interaction
and power transfer from the EM wave to the propagation medium.Here, we are talking about "Free Space
Propagation": the propagation medium is the vacuum and no interaction
exists. The Free Space Loss is just to be referred to the density of EM energy,
which follows the
inverse squarelaw
dependence versus distance
from the source.
A second problem
is the role of frequency in the
Free Space Loss formula
.
Is the Free Space a transmission medium more lossy as frequency increases?Let us consider the two equivalent forms of
the radio link equation given above :
The first
expression is probably more intuitive
and should be preferred when we try to understand the physical concept
underlying free space propagation. The
Tx antenna is described by its gain (the ability to focus the EM power toward a
given direction), while the Rx antenna is described by its equivalent aperture
(the ability to capture the EM power distributed at the receiver location).
On
the other hand, we passed to the
second
expression
, where both the Tx and Rx antenna gains appear, since it looks
attractive for its symmetric form.
The frequency dependence in this case is
due to the decreasing effective aperture of the
receiving antenna (for a given gain), as the frequency increases. It is just a
formal artifice to include frequency dependence in the socalled Free Space
Loss.
As a conclusion,
the Free Space Loss is a convenient step in evaluating the received power in a
radio link and it is useful in order to put formulas in a manageable form.However, care should be paid about the
physical concept related to it, in order to avoid misleading interpretations.
We now depart from the Free Space
assumption and we put again our feet to the earth.We consider radiowave propagation between two terrestrial radio sites,
in the context of radio hop design.
Transmitting and receiving
antennas are assumed to be installed on towers / buildings, at moderate height
above the earth surface (meters or tens of meters), so that propagation in the
lower atmosphere, close to ground, has
to be considered.
Moreover, we assume that the
radiowave frequency is in the range from UHF band (lower limit 300 MHz) up to
some tens of GHz (60 GHz can roughly be the upper limit, according to present
applications).
Compared with Free Space
Propagation, the presence of the atmosphere and the vicinity of the ground
produce a number of phenomena which may severely impact on radiowave
propagation.
The major phenomena are due to :
·
Atmospheric Refraction :
· Ray Curvature;
·
Multipath Propagation;
·
Interaction with particles/molecules in the
Atmosphere:
·
Atmospheric Absorption in the absence of
rain;
· Raindrop Absorption and Scattering;
·
Effects of the Ground :
· Diffraction through Obstacles;
· Reflections on flat terrain / water surfaces.
When one or more of the above
phenomena affect radio propagation, the resulting impairment is :
·
usually, an additional loss (with
respect to free space) in the received signal power;
·
in particular cases, also a distortion of the received signal.
Propagation impairments will be
considered in the following sessions. In most cases they can be predicted only
on a statistical basis. They are mainly
affected by :
· Frequency of operation;
· Hop Length;
·
Climatic environment and current
meteorological conditions;
·
Ground characteristics (terrain profile,
obstacles above ground, electrical parameters).
From the viewpoint of the
phenomena duration, let us consider :
·
temporary impairments, which
affect the received signal only for small percentages of time (examples are
rain, multipath propagation, ...);
·
longterm (or permanent)
propagation conditions, which affect the received signal for most of the time
(examples are atmospheric oxygen absorption, terrain diffraction, ...), even if
their impact may be variable in some measure.
In most cases, longterm
propagation impairments do not produce a significant power loss in the received
signal, compared with Free Space conditions.
So, the received power observed for long periods of time will be rather
close to that predicted by the
Free Space
Radio Link Equation
.
The most significant exception to the
above condition is experienced in radio paths with notperfect visibility.In that case, attenuation caused by terrain
diffraction results in a systematic loss, in comparison with Free Space
conditions.
Even in designing Terrestrial
Radio Links, the
Free Space Radio Link
Equation
is the basis for received power prediction.
The
equation in logarithmic units offers a very simple
and convenient tool, since
Gains and Losses, throughout the transmission chain, are added with
positive or negative sign, as in a financial budget. The result is what is
called the "Link Budget".
The
Free Space equation can be rewritten with more detail, taking account of
actual equipment structure and of systematic impairments throughout the
propagation path. An example is given in the Table below
.
Power Level
[dBm] 
Gains
[dB] 
Losses
[dB] 
Tx Power at radio eqp. output flange 




Tx branching filter
Tx feeder
Other Tx losses 
Power at ant. input 



Tx antenna gain 



Propagation losses :
Free Space
Obstruction
Atm. Absorption
Other 

Rx Antenna gain 

Poweratant. output 




Rx feeder
Rx branching filter
Other Rx losses 
Nominal Rx Power at radio eqp.input flange 


As shown in the above example, the link budget includes an estimate of the power loss due to permanent (or longterm) impairments (like atmospheric absorption and obstructions).So, the Nominal Rx Power (as computed at the last line) is expected to be observed for long periods of time.
Once the Link Budget is computed, other impairments at the receiver are taken into account as :
· a degrading effect in receiver operation ( Rx threshold degradation): this usually applies to the effect of ground reflections and interference;
· a short term attenuation (or even distortion) in the received signal, whose effect may be to fade the received signal below the Rx threshold
Power 
Threshold 
Margin 
Nominal Rx Power 



Equipment Threshold 


Threshold Degrad.
Reflections
Interference 


Hop Threshold 



Fade margin 
We summarize the final steps in Link Budget analysis with the two equations :
_{ }
Note that Threshold Degradation causes the actual Hop Threshold to be higher than the Equipment Threshold (one dB threshold increase means one dB reduction in the available Fade Margin).
Typically, pointtopoint radio
hops are designed in a way that the Nominal Rx Power (as computed in the Link Budget) is far greater than the
receiver threshold. So, rather large
Fade Margins (of the order of 3040 dB, or even greater) are usually available.
The Fade Margin is required to cope with short term attenuation and distortion in the received signal (mainly caused by rain and multipath).
A summary of various definitions
is given in the diagram below.
A summary of definitions in Received Power levels,
thresholds,
and margins, with application to Outage estimation.
The above figure suggests the following comments :
·
The Rx power may
exceed the Free Space level: the
socalled "upfading" is a rather unusual event (it may be caused by
particular refraction conditions, which create a sort of guided propagation
through the atmosphere). Care must be taken that the received power level be in
any case below the maximum level accepted by the Rx equipment (otherwise,
receiver saturation and nonlinear distortion may be observed).
· The Rx Power will be at the Nominal level (Normal propagation) for most of the time.
·
Moderate
attenuation below the Nominal Rx power does not usually produce any significant
loss in signal quality.
· The Equipment threshold may be degraded in some measure by reflections and/or interference, so that a higher Hop threshold must be considered.
· Starting from the very low Rx power, the Outage conditions are :
· below the Equipment threshold, outage is produced by the receiver thermal noise, even in the absence of any additional impairment in the received signal;
· below the Hop threshold, outage is caused by the combined effect of receiver noise and other impairments (like reflection or interference);
· in the deep fading region, above the Hop threshold, outage may be observed when the received signal is not only attenuated, but also distorted by propagation events (mainly, frequency selective multipath).
From the above discussion, the Outage time, during the observation period To (typically, one month) can be predicted as :
_{ }
if no contribution to outage is expected from signal distortion.
On the other hand, if significant distortion in the Rx signal is expected to contribute to the total outage, the prediction formula has to be completed as :
_{ }
where the second term gives the contribution to outage probability when the received signal is above the Hop threshold, but it is severely distorted (note that Prob {A/B} means probability of event A, given that event B is true) .
These formulas only help to clarify how the outage time is related to the Rx power level and to additional impairments in the received signal. They do not provide a practical means to predict outage time; this requires that suitable statistical models of propagation impairments be available: Such models will be considered in the following Sessions.
When a Passive
Repeater is used in a radio hop, we have to revise the "Basic Radio Link
Equation".
To be consistent with
the simple Free Space formula, we write the new
equation as :
_{
}
where :
FSL(D_{TOT}) is the Free Space Loss of a radio link with
path length D_{TOT} =
SD_{i};
D_{i} is the
length of each path leg;
L_{PR} is the power loss caused by the passive repeater,
in comparison with the Free Space case.
Single Reflector

We refer to the path geometry, as shown in a previous figure and to
the definition of the reflector effective area A_{E}.Then, L_{PR} is given by :
_{
}
where F is the working
frequency in GHz and D_{1}, D_{2} are the leg lengths in km.
Double Reflector

Again, we refer to the path geometry, as shown in a previous figure and to
the definition of the reflector effective area A_{E}.Then, L_{PR} is given by :
_{
}
where F is the working
frequency in GHz and D_{1}, D_{2}, D_{3} are the leg
lengths in km.
BacktoBack antenna system  The path geometry is shown in a previous figure.Then, L_{PR} is given by :
_{ }
where F is the working
frequency in GHz, D_{1}, D_{2} are the leg lengths in km, G_{1},
G_{2} are the antenna gains at the repeater site (usuallyG_{1} = G_{2}) and L_{F}
is the loss due to the feeder connecting the two antennas.
Near Field
correction

The above formulas are
correctly used when the reflectors are positioned outside the
"nearfield" region. If this
condition is not satisfied, then a correction factor (additional loss) must be
applied.
The nearfield region is
estimated as a function of the antenna and reflector dimensions and of the
signal frequency (wavelength
l
).Two normalized parameters (
a,b) are computed :
_{ } _{ }
where D_{Min} is the shortest leg from one antenna to the closest reflector, d is the antenna diameter and A _{ E } is the reflector effective area.
A rule of thumb is the following: for b in the range 0.2  1.5 (this covers most practical conditions), the near field correction factor is not negligible if a< (0.5+b ).Some examples are given in the Table below :

b= 0.2 
b= 0.6 
b= 1.0 
b= 1.4 
a= 0.25 
4.6 dB 
8.2 dB 
9.5 dB 
> 10 dB 
a= 0.40 
1.7 dB 
3.9 dB 
7.1 dB 
9.8 dB 
a= 0.60 
0.7 dB 
1.8 dB 
3.8 dB 
6.7 dB 
a= 1.00 
< 0.5 dB 
0.7 dB 
1.6 dB 
3.1 dB 
a= 1.50 
< 0.5 dB 
< 0.5 dB 
0.7 dB 
1.3 dB 
Further Readings
Doble J., Introductionto Radio Propagation for Fixed and Mobile Communications, Artech House Inc., 1996.
Anderson H.R., Fixed Broadband Wireless System Design, J. Wiley, 2002.
Ivanek F. (editor), Terrestrial Digital Microwave Communications, Artech House Inc., 1989.
Vigants A., "Microwave Radio Obstruction Fading", BSTJ, vol. 60, n.8, August 1981, 785801.
Giger A.J. and Barnett W.T., "Effects of Multipath Propagation on Digital radio", IEEE Trans. on Communications, vol. 29, n. 9, Sept. 1981, pp. 134552.
Fedi F., "Prediction of attenuation due to rainfall on Terrestrial Links", Radio Sci, vol. 16, n.5, 1981, pp. 731743.
End
of Session #2
_______________________________________________________________
©
20012016, Apus Cloud Project e Luigi Moreno