##### DETERMINISTIC PATH SPECIFIC PROPAGATION PREDICTION MODEL FOR TERRESTRIAL BROADCASTING SERVICES IN THE FREQUENCY RANGE 30 MHz TO 3000 MHz

(Revised February 25, 2007)

**1. Introduction**

Congestion of the radio-frequency spectrum has made necessary the
sharing of many frequency bands between the different operators of
broadcasting services. In order to ensure the satisfactory coexistence
of the terrestrial broadcasting stations involved, it is important to be
able to predict with reasonable accuracy the interference potential
between them, using prediction procedures and models which are
acceptable to all parties concerned, and which have demonstrated
accuracy and reliability.

Path general methods such as Recommendation ITU-R P.1546 are good for
general planning and determination of coordination requirements. They
can be used with the minimum of information about the propagation path
and can be agreed easily between countries. Averaged over a large number
of transmission paths, such methods can be very accurate. However, as
they take little account of terrain there can be significant prediction
errors on individual paths. Thus, for detailed planning and coordination
of specific transmitter locations there are considerable benefits in
using "deterministic" prediction methods that take account of the
terrain.

Many types of interference path may exist between terrestrial
broadcasting stations, and prediction methods are required for each
situation. This method addresses the problems where there is a potential
for interference between terrestrial broadcasting stations.

The prediction procedure, based on ITU-R Recommendations P.452, P.526,
P.1546, is appropriate to broadcasting stations operating in the
frequency range of about 30 MHz[^1] to 3000 MHz. The method includes a
complementary set of propagation models, which ensure that the
predictions embrace all the significant interference propagation
mechanisms that can arise. Methods for analysing the
radio-meteorological and topographical features of the path are provided
so that predictions can be prepared for any practical interference path
falling within the scope of the procedure.

**2. Field strength prediction**

**2.1 General comments**

The procedure calculates six propagation mechanisms. These are as
follows:

*-- free space,*

*-- diffraction loss* (embracing irregular terrain and sub-path cases),

*-- tropospheric* *scatter loss*;

*-- anomalous* *propagation* (ducting) *field strength*,

*-- signal-variation with receiving antenna height in the presence of
ground cover,*

*-- building penetration loss.*

Depending on the type of path, as determined by a path profile analysis,
one or more of these propagation mechanisms are used in order to provide
the required prediction of basic transmission loss.

**2.2 Deriving a prediction**

**2.2.1 Outline of the procedure**

The steps required to achieve a prediction are as follows:

***Step 1: Input data***

The basic input data required for the procedure are given in Table 1.
All other information required is derived from these basic data during
the execution of the procedure.

TABLE 1

Basic input data

  -------------------- --------------------------------------------------
  Parameter            Description

  *f*                  Frequency (MHz)

                       Required time percentage(s) for which the
                       calculated basic trans­mission loss is not exceeded

  φ*~t~*, φ*~r~*       Latitude of transmitter and receiver (degrees)

  *~t~*, *~r~*         Longitude of transmitter and receiver (degrees)

  *h~tg~*, *h~rg~*     transmitter and receiver antenna centre height
                       above ground level (m)

  *h~ts~, h~rs~*       transmitter and receiver antenna centre height
                       above mean sea level (m)

  *G~t~*, *G~r~*       transmitter and receiver antenna gain (relative to
                       half wave dipole) in the direction of the horizon
                       along the great-circle interference path (dB)
  -------------------- --------------------------------------------------

# 

**Step 2: Radiometeorological data**

The prediction procedure employs three radio-meteorological parameters
to describe the variability of background and anomalous propagation
conditions at the different locations around the world.

--  N, the average radio-refractive index lapse-rate through the lowest
1 km of the atmosphere, provides the data upon which the appropriate
effective Earth radius can be calculated for path profile and
diffraction obstacle analysis. In Appendix 1, Figure A1.1 provides a
world map of average annual  N values. Note that  N is a positive
quantity in this procedure. The value of N to be used is that
corresponding to the path centre.

-- , the time percentage for which refractive index lapse-rates
exceeding\
100 N‑units/km can be expected in the first 100 m of the lower
atmosphere, is used to estimate the relative incidence of fully
developed anomalous propagation at the latitude under consideration. The
value of 0 to be used is that corresponding to the path centre latitude.

-- N~0~, the sea-level surface refractivity, is used only by the
troposcatter model as a measure of location variability of the
troposcatter scatter mechanism. Figure A1.2 provides annual values of
N~0~. The value of N~0~ is the path-centre sea-level surface
refractivity.

Point incidence of anomalous propagation,  (%), for the path centre
latitude is determined using:

> ![](media/image1.wmf){width="3.2368055555555557in"
> height="0.5423611111111111in"} (1)

where:

 : path centre latitude (degrees).

The parameter ~1~ depends on the longest continuous land section of the
path, and is given by:

> ![](media/image2.wmf){width="2.036111111111111in" height="0.50625in"}
> (2)

where the value of shall be limited to 1,

with:

![](media/image3.wmf){width="1.586111111111111in"
height="0.31527777777777777in"} (2a)

where:

d~lm~ : longest continuous land section of the great-circle path (km)

Note: A \'continuous land section\' is a segment of a propagation path
between a transmitter and receiver, along a great-circle path, which
contains no continuous water segment (i.e., a segment\
of the path passing entirely over water) [exceeding]{.underline} 2 km.

![](media/image4.wmf){width="2.7375in" height="0.5354166666666667in"}
(3)

**Step 2.1 Effective Earth radius**

Assuming a true Earth radius of 6371 km, the effective earth radius for
any time percentage, p, can be calculated from the following:

![](media/image5.wmf){width="1.3465277777777778in"
height="0.2638888888888889in"} (4)

where:

![](media/image6.wmf){width="1.875in" height="0.34652777777777777in"}
(5a)

and where the median effective Earth radius factor k~50~ for the path is

![](media/image7.wmf){width="1.1388888888888888in"
height="0.4722222222222222in"} (5b)

where ∆N is given in N-units/km

and

> ![](media/image8.wmf){width="1.9722222222222223in"
> height="1.2777777777777777in"} (5c)

In particular, for 50% of the time, the median value of effective Earth
radius in equation (4) simplifies to:

> ![](media/image9.wmf){width="1.4166666666666667in"
> height="0.2638888888888889in"} (5d)

Step 3: Path profile analysis

Values for a number of path-related parameters necessary for the
calculations, as indicated in Table 2, must be derived via an initial
analysis of the path profile based on the value of a~ep~ given by
equation (4). Information on the derivation, construction and analysis
of the path profile is given in Appendix 2. Having thus analysed the
profile, the path will also have been classified into one of the
geometrical categories indicated in Table 3.

NOTE -- The determination of values for additional profile-related
parameters required specifically for diffraction calculations is
described in Appendices 3 and 4.

**Step 4: Propagation predictions**

Table 3 indicates, for each type of path, the propagation models that
are appropriate. The necessary equations for these individual
propagation mechanism predictions are to be found in the text sections
indicated in the table. In order to build an overall prediction, the
predictions for the individual propagation mechanisms must be calculated
and combined in the manner shown in Table 4. Once this has been achieved
for each of the required time percentages, the prediction is complete.

TABLE 2

Parameter values to be derived from the path profile analysis

  --------------- --------------- ------------------------------------------------
  **Path type**   **Parameter**   Description

  Trans-horizon   d               Great-circle path distance (km)

  Trans-horizon   d*~lt~*,        Distance from the transmit and receive antennas
                  d*~lr~*         to their respective horizons (km)

  Trans-horizon   θ*~t~*, θ*~r~*  Transmit and receive horizon elevation angles
                                  respectively (mrad)

  Trans-horizon   θ               Path angular distance (mrad)

  All             h*~ts~*,        Antenna centre height above mean sea level (m)
                  h*~rs~*         

                                  
  --------------- --------------- ------------------------------------------------

TABLE 3

Interference path classifications and propagation model requirements

+----------------------------+-----------------------------------------+
| **Classification**         | **Models required**                     |
+----------------------------+-----------------------------------------+
| Line-of-sight with first   | Relative ground cover and receiving     |
| Fresnel zone clearance     | antenna height loss (§ 3.6)             |
|                            |                                         |
|                            | Building penetration loss (§3.8, where  |
|                            | appropriate)                            |
+----------------------------+-----------------------------------------+
| Line-of-sight with         | Diffraction loss(§ 3.3)                 |
| sub-path diffraction, i.e. |                                         |
| terrain incursion into the | Relative ground cover and receiving     |
| first Fresnel zone         | antenna height loss (§ 3.6)             |
|                            |                                         |
|                            | Building penetration loss (§3.8, where  |
|                            | appropriate)                            |
+----------------------------+-----------------------------------------+
| Trans-horizon              | Diffraction loss(§ 3.3)                 |
|                            |                                         |
|                            | Troposcatter loss(§ 3.4)                |
|                            |                                         |
|                            | Ducting field strength(§ 3.5, where     |
|                            | appropriate)                            |
|                            |                                         |
|                            | Relative ground cover and receiving     |
|                            | antenna height loss (§ 3.6)             |
|                            |                                         |
|                            | Building penetration loss (§3.8, where  |
|                            | appropriate)                            |
+----------------------------+-----------------------------------------+

TABLE 4

Methods for deriving Basic Transmission Loss

+--------+-------------------------------------------------------------+
| **Path | **Action required**                                         |
| type** |                                                             |
+--------+-------------------------------------------------------------+
| L      | The prediction is obtained by subtracting the losses given  |
| ine-of | by the ground cover and building loss models from the free  |
| -sight | space field strength, i.e.:                                 |
|        |                                                             |
|        | E~b~  = 106.9 - 20 log d - ( A~hr~ +  A~bl~  )   dB (6a)    |
|        |                                                             |
|        | where:                                                      |
|        |                                                             |
|        | A~hr~  : appropriate additional ground cover and receiving  |
|        | antenna height loss(see section 3.6)                        |
|        |                                                             |
|        | A~bl~ : appropriate additional losses due to building       |
|        | penetration loss (see section 3.8)                          |
+--------+-------------------------------------------------------------+
| L      | The prediction is obtained by subtracting the losses given  |
| ine-of | by the (sub‑path) diffraction, ground cover and building    |
| -sight | penetration loss models from the free space field strength, |
| with   | i.e.:                                                       |
| su     |                                                             |
| b-path | E~b~  = 106.9 - 20 log d - (  L~d~ + A~hr~  + A~bl~  )  dB  |
| diffr  | (6b)                                                        |
| action |                                                             |
|        | where:                                                      |
|        |                                                             |
|        | L~d~ : prediction for p % of time given by the sub-path     |
|        | diffraction loss element of the diffraction model (see      |
|        | section 3.3)                                                |
+--------+-------------------------------------------------------------+
| T      | The overall prediction can be obtained by applying the      |
| rans-h | following ancillary algorithm:                              |
| orizon |                                                             |
|        | $E_{b} = \                                                  |
|        | text{10}\text{log}(\text{10}^{\frac{E_{s}}{\text{10}}} + \t |
|        | ext{10}^{\frac{E_{d}}{\text{10}}} + \text{10}^{\frac{E_{a}} |
|        | {\text{10}}}) - (A_{\text{hr}} + A_{\text{bl}})\ \text{dB}$ |
|        | (6c)                                                        |
|        |                                                             |
|        | where:                                                      |
|        |                                                             |
|        | E~d~ = 106.9 - 20 log d - L~d~                              |
|        |                                                             |
|        | L~d~ : prediction for p % of time given by the diffraction  |
|        | model (see section 3.3)                                     |
|        |                                                             |
|        | E~s~ = 106.9 - 20 log d - L~s~                              |
|        |                                                             |
|        | L~s~ : predicted loss for p % of time given by the          |
|        | troposcatter model (see section 3.4)                        |
|        |                                                             |
|        | E~a~ : the field strength resulting from ducting (see       |
|        | section 3.5)                                                |
+--------+-------------------------------------------------------------+

**2.3 Calculating the electric field strength**

Taking into account location variability of the signals, the
corresponding electric field strength at *q* % of the locations, E~q~,
is given by:

![](media/image10.wmf){width="0.8888888888888888in"
height="0.2638888888888889in"} (7)

where C~q~ is the correction defined in sections 3.7 and 3.9. (Note, for
q = 50, C~q~= 0 and thus E~50 ~= E~b~.)

**3. Propagation losses**

**3.1 General**

The procedure given above invokes one or more separate propagation
models to provide the components of the overall prediction. These
propagation models are provided in this section.

**3.2 Basic transmission loss**

Where needed, the basic transmission loss, L~b~, is given by:

L~b~ = 139.3 - E~b~ + 20 log f (8)

*f* : frequency (MHz)

**3.3 Diffraction loss**

The time variability of the additional loss due to the diffraction
mechanism is assumed to be the result of changes in bulk atmospheric
radio refractivity lapse rate, i.e. as the time percentage *p* reduces,
the effective Earth radius factor *k~p~*  is assumed to increase.

The additional loss due to diffraction, *L~d~* (dB), not exceeded for
any time percentage, *p*, below 50%, is calculated by the method
described in Appendix 4.

**3.4 Tropospheric scatter loss (Notes 1 and 2)**

NOTE 1 -- At time percentages much below 50%, it is difficult to
separate the true tropospheric scatter mode from other secondary
propagation phenomena which give rise to similar propagation effects.
The "tropospheric scatter" model adopted here is therefore an empirical
generalization of the concept of tropospheric scatter which also
embraces these secondary propagation effects. This allows a continuous
consistent prediction of basic transmission loss over the range of time
percentages *p* from 1% to 50%, thus linking the ducting and layer
reflection model at the small time percentages with the true "scatter
mode" appropriate to the weak residual field exceeded for the largest
time percentage.

NOTE 2 -- This troposcatter prediction model has been derived for
interference prediction purposes and should not be used for the
calculation of propagation conditions above 50% of time.

The excess loss due to troposcatter, *L~s~*  (dB) not exceeded for any
time percentage, *p*, from 1 to 50%, is given by:

![](media/image11.wmf){width="4.990277777777778in"
height="0.49444444444444446in"} (9)

where:

*L~f~*  : frequency dependent loss:

![](media/image12.wmf){width="2.6527777777777777in"
height="0.2916666666666667in"} (9a)

d : path length (km)

f : frequency (MHz)

*N~0~* : path centre sea-level surface refractivity (N-units) derived
from Fig. A1.2

: path angular distance (mrad), see appendix 2, section 4.5

**3.5 Ducting mechanism**

For time percentages less than , signal levels are dominated by
anomalous propagation mechanisms rather than by the bulk refractivity
characteristics of the atmosphere. Thus for values of *p* less than the
value of *k* is evaluated for %. In this situation, the field strength
resulting from ducting is calculated as:

> E~a~ = 20 log f - 0.4 - 30 log p -10 (p/)^3^ (10)

where:

f : frequency (MHz)

: path angular distance (mrad), see appendix 2, section 4.5.

For paths where the principal diffraction edge is on land, E~a~ = -900.

**3.6 Relative ground cover and receiving antenna height loss**

The relative ground cover loss takes account of losses due to the
environment in the vicinity of the receiving site. As well as being
frequency dependent, it is a function of receiving antenna height above
ground level. Thus the relative ground cover and receiving antenna
height loss is the total loss due to height gain effects in local ground
cover.

The category of ground cover type at the receiving location, the
receiving antenna height, and the frequency are used to determine the
relative ground cover loss.

**Table 5** shows the relative ground cover and receiving antenna height
loss as a function of antenna height above ground level in various
environments and for three nominal frequencies and for thirteen nominal
receiving antenna heights.

The relative ground cover and receiving antenna height loss values,
*A~hr~*, for a given frequency (MHz) and receiving antenna height should
be obtained by interpolating between (or extrapolating[^2] beyond) the
values for the nominal frequency values of 100 MHz, 1000 MHz and 3 000
MHz, and between the values for the nominal receiving antenna height
values, 1 m, 2 m, \... 60 m as given in Table 5. Double interpolation
for log (frequency) and log(height) is used.

![](media/image13.wmf){width="5.596527777777778in"
height="0.9722222222222222in"} (11)

where:

> *f *: frequency for which the prediction is required (MHz)
>
> *h *: receiver antenna height above ground level for which the
> prediction is required (m)
>
> *f~I~ *: lower nominal frequency (MHz) = 100 if the required frequency
> is less than (or equal to) 1000 MHz and 1000 MHz otherwise,
>
> *f~S~ *: higher nominal frequency (MHz) = 1000 if the required
> frequency is less than (or equal to) 1000 MHz and 3000 MHz otherwise
>
> *h~I~ *: lower nominal receiving antenna height above ground level (m)
>
> *h~S~ *: higher nominal receiving antenna height above ground level
> (m)
>
> *A~S,S~ *: ground cover loss value for *f~S~ , h~S~ *
>
> *A~S,I~ *: ground cover loss value for *f~S~ , h~I~ *
>
> *A~I,S~ *: ground cover loss value for *f~I~ , h~S~ *
>
> *A~I,I~ *: ground cover loss value for *f~I~ , h~I~ *

For receiving antenna heights greater than 60 m, relative ground cover
loss is set equal to the value at 60 m.

TABLE 5

Relative ground cover and receiving antenna height loss, A~hr~(f,h), as
a function of nominal receiving antenna height above ground level and
nominal frequency\*

<table>
<colgroup>
<col style="width: 10%" />
<col style="width: 12%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 9%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
</colgroup>
<tbody>
<tr class="odd">
<td><p>Nominal Antenna<br />
height</p>
<p><strong>(m)<br />
(a.g.l.)</strong></p></td>
<td><strong>Open/ Rural/ Water</strong></td>
<td colspan="3">Suburban**</td>
<td colspan="3">Urban/Trees/Forest</td>
<td colspan="3">Dense urban</td>
</tr>
<tr class="even">
<td></td>
<td><strong>Nominal frequency</strong></td>
<td colspan="3"><strong>Nominal frequency</strong></td>
<td colspan="3"><strong>Nominal frequency</strong></td>
<td colspan="3"><strong>Nominal frequency</strong></td>
</tr>
<tr class="odd">
<td></td>
<td>100-3 000 MHz</td>
<td>100 MHz</td>
<td>1000 MHz</td>
<td>3 000 MHz</td>
<td>100 MHz</td>
<td>1 000 MHz</td>
<td>3 000 MHz</td>
<td>100 MHz</td>
<td>1 000 MHz</td>
<td>3 000 MHz</td>
</tr>
<tr class="even">
<td>1</td>
<td>20</td>
<td>22</td>
<td>22</td>
<td>29</td>
<td>18</td>
<td>28</td>
<td>40</td>
<td>28</td>
<td>34</td>
<td>46</td>
</tr>
<tr class="odd">
<td>2</td>
<td>14</td>
<td>12</td>
<td>17</td>
<td>25</td>
<td>16</td>
<td>25</td>
<td>38</td>
<td>24</td>
<td>30</td>
<td>43</td>
</tr>
<tr class="even">
<td>3</td>
<td>11</td>
<td>11</td>
<td>16</td>
<td>25</td>
<td>15</td>
<td>23</td>
<td>36</td>
<td>21</td>
<td>29</td>
<td>41</td>
</tr>
<tr class="odd">
<td>4</td>
<td>8</td>
<td>8</td>
<td>13</td>
<td>22</td>
<td>11</td>
<td>20</td>
<td>34</td>
<td>18</td>
<td>26</td>
<td>40</td>
</tr>
<tr class="even">
<td>5</td>
<td>6</td>
<td>6</td>
<td>10</td>
<td>18</td>
<td>10</td>
<td>19</td>
<td>32</td>
<td>16</td>
<td>24</td>
<td>37</td>
</tr>
<tr class="odd">
<td>6</td>
<td>4</td>
<td>4</td>
<td>8</td>
<td>16</td>
<td>8</td>
<td>16</td>
<td>30</td>
<td>14</td>
<td>22</td>
<td>35</td>
</tr>
<tr class="even">
<td>7</td>
<td>3</td>
<td>3</td>
<td>6</td>
<td>13</td>
<td>7</td>
<td>14</td>
<td>28</td>
<td>12</td>
<td>22</td>
<td>34</td>
</tr>
<tr class="odd">
<td>8</td>
<td>2</td>
<td>2</td>
<td>4</td>
<td>11</td>
<td>5</td>
<td>13</td>
<td>25</td>
<td>11</td>
<td>20</td>
<td>32</td>
</tr>
<tr class="even">
<td>9</td>
<td>1</td>
<td>1</td>
<td>2</td>
<td>8</td>
<td>4</td>
<td>10</td>
<td>22</td>
<td>10</td>
<td>18</td>
<td>30</td>
</tr>
<tr class="odd">
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>3</td>
<td>8</td>
<td>19</td>
<td>8</td>
<td>16</td>
<td>28</td>
</tr>
<tr class="even">
<td>15</td>
<td>-4</td>
<td>-5</td>
<td>-7</td>
<td>-2</td>
<td>-2</td>
<td>1</td>
<td>12</td>
<td>4</td>
<td>12</td>
<td>21</td>
</tr>
<tr class="odd">
<td>30</td>
<td>-10</td>
<td>-12</td>
<td>-14</td>
<td>-9</td>
<td>-10</td>
<td>-10</td>
<td>-2</td>
<td>-4</td>
<td>-4</td>
<td>5</td>
</tr>
<tr class="even">
<td>60</td>
<td>-16</td>
<td>-16</td>
<td>-16</td>
<td>-16</td>
<td>-16</td>
<td>-16</td>
<td>-16</td>
<td>-16</td>
<td>-16</td>
<td>-16</td>
</tr>
</tbody>
</table>

\* For values of frequency, and receiving antenna height, other than the
nominal values indicated in the Table, it is necessary to interpolate
according to Equation (11).

\*\* If no ground cover information is provided, \'suburban ground
cover\' will be assumed

**3.7 Location variability in land area-coverage prediction**

Area-coverage prediction methods are intended to provide the statistics
of reception conditions over a given area, rather than at any particular
point. The interpretation of such statistics will depend on the size of
the area considered.

When one terminal of a radio path is stationary, and the other terminal
is moved, path loss will vary continuously with location, according to
the totality of influences affecting it. It is convenient to classify
these influences into three main categories:

Multipath variations

> Signal variations will occur over distances of the order of a few
> wavelengths due to phasor addition of multipath effects,
> e.g. reflections from the ground, buildings, etc.

-- Local ground cover variations

> Signal variations will occur due to obstruction by ground cover in the
> local vicinity, e.g. buildings, trees, etc., over distances of the
> order of the sizes of such objects. The distance over which these
> variations occur will normally be significantly larger than that for
> multipath variations.

-- Path variations

> Signal variations will also occur due to changes in the geometry of
> the entire propagation path e.g. the presence of hills, etc. The
> distance over which these variations occur will be significantly
> larger than that for local ground cover variations.

In this method, location variability refers to the spatial statistics of
local ground cover variations including multipath variations. This is a
useful result over distances substantially larger than the ground cover
variations, and over which path variations are insignificant. This may
be an impracticable condition for an area over which path geometry is
changing rapidly, such as sloping ground.

At VHF and UHF, location variability is typically quoted for an area
represented by a square with a side of 100 to 200 m, sometimes with the
additional requirement that the area is flat. The important issue is
whether path geometry significantly affects variations over the area
concerned.

Extensive data analysis suggests that the distribution of median field
strength due to ground cover variations over such an area in urban and
suburban environments is approximately lognormal.

It should also be noted that multipath fading is frequency selective.
Thus a knowledge of effective radio system bandwidth becomes important.

Thus for a receiving/mobile antenna location on land the field strength
*E* which will be exceeded for *q*% of locations is given by:

![](media/image14.wmf){width="1.9027777777777777in"
height="0.2638888888888889in"} (12)

![](media/image15.wmf){width="2.4027777777777777in"
height="0.2638888888888889in"} (12a)

where

> *E~50~* is the value of the field strength exceeded at 50% of the
> locations,
>
> *Q~i~(x)* is the inverse complementary cumulative normal distribution
> as a function of probability,
>
> *~L~* is the standard deviation of the Gaussian distribution of the
> local means in the study area as a function of frequency.

Values of standard deviation for digital systems having a bandwidth less
than 1 MHz and for analogue systems are given as a function of frequency
by:

*~L~* = 5.1 + 1.6 log(*f*) dB (13)

where:

> *f* is the frequency in MHz.

For digital systems having a bandwidth of 1 MHz or greater, a standard
deviation of 5.5 dB should be used at all frequencies.

Percentage location *q* can vary between 1 and 99. This method should
not be used for percentage locations less than 1% or greater than 99%.

**An approximation to the inverse complementary cumulative normal
distribution function**

The following approximation to the inverse complementary cumulative
normal distribution function, *Q~i~*(*x*), is valid for 0.01 *x* 0.99:

Q~i~(x) = T(x) -- (x) if x 0.5 (14a)

Q~i~(x) = - T(1-x) + (1 -- x) if x \> 0.5 (14b)

where:

![](media/image16.wmf){width="1.25in" height="0.2777777777777778in"}
(14c)

![](media/image17.wmf){width="2.986111111111111in"
height="0.4722222222222222in"} (14d)

C~0~ = 2.515517

C~1~ = 0.802853

C~2~ = 0.010328

D~1~ = 1.432788

D~2~ = 0.189269

D~3~ = 0.001308

Values given by the above formulas are given in Table 6.

TABLE 6

Approximate inverse complementary cumulative normal distribution values

  ------ ------------ ------ ------------ ------ ---------------------------------------- ------ ------------
  *q*%   *Q~i~*       *q*%   *Q~i~*       *Q*%   *Q~i~* (*q*/100)                         *q*%   *Q~i~*
         (*q*/100)           (*q*/100)                                                           (*q*/100)

  1      2.327        26     0.643        51     0.025                                    76     0.706

  2      2.054        27     0.612        52     ![](media/image18.wmf){width="0.125in"   77     0.739
                                                 height="0.2361111111111111in"}0.050             

  3      1.881        28     0.582        53     0.075                                    78     0.772

  4      1.751        29     0.553        54     0.100                                    79     0.806

  5      1.645        30     0.524        55     0.125                                    80     0.841

  6      1.555        31     0.495        56     0.151                                    81     0.878

  7      1.476        32     0.467        57     0.176                                    82     0.915

  8      1.405        33     0.439        58     0.202                                    83     0.954

  9      1.341        34     0.412        59     0.227                                    84     0.994

  10     1.282        35     0.385        60     0.253                                    85     1.036

  11     1.227        36     0.358        61     0.279                                    86     1.080

  12     1.175        37     0.331        62     0.305                                    87     1.126

  13     1.126        38     0.305        63     0.331                                    88     1.175

  14     1.080        39     0.279        64     0.358                                    89     1.227

  15     1.036        40     0.253        65     0.385                                    90     1.282

  16     0.994        41     0.227        66     0.412                                    91     1.341

  17     0.954        42     0.202        67     0.439                                    92     1.405

  18     0.915        43     0.176        68     0.467                                    93     1.476

  19     0.878        44     0.151        69     0.495                                    94     1.555

  20     0.841        45     0.125        70     0.524                                    95     1.645

  21     0.806        46     0.100        71     0.553                                    96     1.751

  22     0.772        47     0.075        72     0.582                                    97     1.881

  23     0.739        48     0.050        73     0.612                                    98     2.054

  24     0.706        49     0.025        74     0.643                                    99     2.327

  25     0.674        50     0.000        75     0.674                                           
  ------ ------------ ------ ------------ ------ ---------------------------------------- ------ ------------

## 

**3.8 Indoor portable reception**

For indoor portable reception two important parameters have to be taken
into account. The first one is the building penetration loss and the
second one the variation of the building penetration loss due to
different building materials.

The main building penetration loss is the difference in dB between the
mean field strength inside a building at a given height above ground
level and the mean field strength outside the same building at the same
height above ground level. The standard deviation takes into account a
large spread of building penetration losses but does not include
variation within different buildings.

Building penetration loss values are given in Table 7 below.

TABLE 7

Building penetration loss, Abl

  ----------------------- ----------------------- -----------------------
  Band                    Median value            Standard deviation

  VHF                     8 dB                    3 dB

  UHF                     7 dB                    6 dB
  ----------------------- ----------------------- -----------------------

**3.9 Signal variations at indoor locations**

The field-strength variation at indoor locations is the combined result
of the outdoor variation and the variation due to building attenuation.
These variations are likely to be uncorrelated. The standard deviation
of the indoor field strength distribution can therefore be calculated by
taking the square root of the sum of the squares of the individual
standard deviations.

For example, for digital emissions with bandwidth greater than 1 MHz, at
VHF, where the signal standard deviations are 5.5 dB and 3 dB
respectively, the combined value is 6.3 dB. At UHF, where the signal
standard deviations are both 5.5 dB, the combined value is 7.8 dB.

APPENDIX 1

Radio-meteorological data required for the prediction procedure

# **1 Introduction**

The prediction procedures rely on radio-meteorological data to provide
the basic location variability for the predictions. These data are
provided in the form of maps which are contained in this Appendix.

**2 Maps of vertical variation of radio refractivity data**

For the global procedure, the radio-meteorology of the path is
characterised for the continuous (long‑term) interference mechanisms by
the average annual value of *N* (the refractive index lapse-rate over
the first 1 km of the atmosphere). For anomalous (short-term) mechanisms
it is characterised by the time percentage, , for which the refractive
index lapse-rate over the first 100 metres of the lower atmosphere can
be expected to exceed 100 N-units/km. These parameters provide a
reasonable basis upon which to model the propagation mechanisms
described in § 2 of the main text. For some of these quantities, data
are provided in this Appendix: Figure A1.1 provides average year *N*
data.

![](media/image19.wmf){width="6.972222222222222in"
height="5.170138888888889in"}

3 Map of surface refractivity, N~0~

Figure A1.2 provides a map of average sea-level surface refractivity,
*N~0~*, for the troposcatter model.

**4 Implementation of maps in computer database form**

For computer implementation of the procedures, it is convenient to
capture these maps in digital form and to convert them into simple
databases that can be accessed by the software.

For the global refractive index maps, the contours have been converted
into two‑dimensional arrays of 0.5° x 0.5° latitude and longitude.

![](media/image20.wmf){width="6.075in" height="4.815277777777778in"}

APPENDIX 2

Path profile analysis

**1 Introduction**

For path profile analysis, a path profile of terrain heights above mean
sea level is required. The parameters that need to be derived from the
path profile analysis for the purposes of the propagation models are
given in Table A2.1.

**2 Construction of path profile**

Based on the geographical coordinates of the transmitter (*t*, *t*) and
receiver (*r*, *r*) stations, terrain heights (above mean sea level)
along the great-circle path should be derived from a topographical
database or from appropriate large‑scale contour maps. The profile
should include the ground heights at the transmitter and receiver
locations as the start and end points. To the heights along the path
should be added

\- the necessary Earth's curvature, based on the value of *a~ep~* found
in equation (4), and also

\- the ground cover heights, except at the start point, and within 1 km
of the end point.

For the purposes of this method the point of the path profile at the
transmitter is considered as point *0*, and the point at the receiver is
considered as point *n*. The path profile therefore consists of *n + 1*
points. Figure A2.1 gives an example of a path profile of terrain
heights above mean sea level, showing the various parameters related to
the actual terrain.

> ![](media/image21.wmf){width="5.614583333333333in"
> height="5.177083333333333in"}

Table A2.1 defines parameters used or derived during the path profile
analysis.

TABLE A2.1

Basic path profile parameter definitions

**4. Derivation of trans-horizon path parameters from the path profile**

The parameters for trans-horizon paths to be derived from the path
profile are those contained in Table A2.1 and defined below.

**4.1 Transmitter antenna horizon elevation angle, ~t~**

The transmitting antenna horizon elevation angle, *t*, is the maximum
elevation angle derived from the *n* -- 1 terrain profile heights, that
is, excluding the points at the transmitter and receiver sites.

![](media/image22.wmf){width="0.9027777777777778in"
height="0.4166666666666667in"}            mrad (A2.3)

*~i~* : elevation angle to the *i*th terrain point

> ![](media/image23.wmf){width="2.263888888888889in"
> height="0.5138888888888888in"} (A2.4)

**4.2 Transmitter antenna horizon distance, *d~lt~***

The transmitter antenna horizon distance is the distance from the
transmitter at which the maximum transmitter horizon elevation angle,
*~t~*, is derived from equation (A2.3).

*d~lt~* = *d~i~*               km               for max (θ~i~) (A2.5)

**4.3 Receiver antenna horizon elevation angle, θ*~r~***

The receiving antenna horizon elevation angle, ~r~, is the maximum
horizon elevation angle derived from the *n* -- 1 terrain profile
heights:

![](media/image24.wmf){width="0.9861111111111112in"
height="0.5277777777777778in"}              mrad (A2.6)

*~j~* : elevation angle to the *j*th terrain point

![](media/image25.wmf){width="1.9027777777777777in"
height="0.5277777777777778in"} (A2.7)

**4.4 Receiver antenna horizon distance, *d~lr~***

The receiver antenna horizon distance is the distance from the receiver
at which the maximum receiving horizon elevation angle, *r*, is derived
from equation (A2.6).

*d~lr~* = *d* -- *d~j~*               km               for max (*θ~j~*)
(A2.8)

**4.5** **Angular distance (mrad)**

![](media/image26.wmf){width="1.3194444444444444in"
height="0.5138888888888888in"} mrad (A2.9)

**5 Path classification**

The path profile must next be used to classify the path into one of
three geometrical categories based on an effective Earth's radius of
*a~ep~*. The path classifications are as indicated in Table 3.

**5.1 Classification Step 1: Test for a trans-horizon path**

A path is trans-horizon if the physical horizon elevation angle as seen
by the transmitter antenna (relative to the local horizontal), *~t~*, is
greater than the angle (again relative to the transmitter's local
horizontal), *~tr~* , subtended by the receiver antenna (See Figure A
2.2).

![](media/image27.wmf){width="5.614583333333333in"
height="5.177083333333333in"}

The test for the trans-horizon path condition is thus:

θ*~t~* \> θ*~tr~*               mrad (A2.10)

where:

![](media/image28.wmf){width="2.3194444444444446in"
height="0.5138888888888888in"} (A2.11)

where:

*h~rs~* : receiver antenna height (m) amsl

*d* : total great-circle path distance between transmitter and receiver
(km)

If the condition of equation (A2.10) is met, then the remaining path
profile analysis required for trans‑horizon paths can be undertaken.
Under these conditions Step 2 of the path classification is not needed.

If the condition of equation (A2.10) is not fulfilled, the path is
line-of-sight, with or without incursion by the terrain of the first
Fresnel zone.

**5.2 *Step 2: Test for line-of-sight with sub-path diffraction (i.e.
without full first Fresnel zone clearance)***

A non trans-horizon path is line-of-sight with sub-path diffraction, if
the first Fresnel ellipsoid is obstructed at any point by the terrain.
The appropriate test is illustrated in Figure A2.3. An 'elevated'
terrain is constructed by adding a clearance equal to the first Fresnel
ellipsoid radius at each point along the path. The addition of the
radius Ri for the i-th terrain point is illustrated, with the
corresponding elevation angle, *~Fi~* , as seen by the transmitter
antenna (relative to the local horizontal). The path is line-of-sight
with sub-path diffraction if the elevation angle over the horizon, *~F~*
, (the maximum value of *~Fi~*), is greater than the angle (again
relative to the transmitter's local horizontal), *~tr~* subtended by the
receiver antenna. Note that all the elevation angles are signed values.
As drawn in Figure A2.3 they are negative so that *~F~* is greater than
*~Fi~*.

> ![](media/image29.wmf){width="5.541666666666667in"
> height="5.034722222222222in"}

The path has sub-path diffraction if:

![](media/image30.wmf){width="0.5555555555555556in"
height="0.25in"}           mrad (A2.12)

where:

![](media/image31.wmf){width="1.0138888888888888in"
height="0.4166666666666667in"} (A2.13)

To complete this test an extra term is therefore required in equation
(A2.15) to allow for the first Fresnel ellipsoid. Recommendation ITU‑R
P.526, § 2, gives the radius of this ellipsoid, *Ri* (m), at any point
along the path:

![](media/image32.wmf){width="1.7222222222222223in"
height="0.5277777777777778in"} m (A2.14)

where *f* is the frequency (MHz) and the distances are in km.

The appropriate radius, *Ri* (m), is added to each terrain height, *hi*
(m), in equation (A.4) yielding equation (A2.15). Allowing for first
Fresnel zone clearance, *~Fi~*, the terminal antenna elevation angle
(rad) to the *i*th terrain point is obtained from the following
equation:

![](media/image33.wmf){width="1.94375in" height="0.5138888888888888in"}
mrad (A2.15)

where:

*h~ts~* : transmitter antenna height (m) amsl

*d~i~:* distance to the ith terrain point from the transmitter (km)

If the condition of equation (A2.12) is met, then the remaining path
profile analysis required for sub‑path diffraction cases can be
undertaken.

If the condition of equation (A2.12) is not fulfilled, the path is
line-of-sight and no further path profile analysis is needed.

APPENDIX 3

Single knife-edge obstacle

> ![](media/image34.wmf)

In this extremely idealized case (Figs. A3.1a) and (A3.1b), all the
geometrical parameters are combined together in a single dimensionless
parameter normally denoted by which may assume a variety of equivalent
forms according to the geometrical parameters selected:

![](media/image35.wmf){width="1.65in" height="0.5625in"} (A3.1)

![](media/image36.wmf){width="1.6805555555555556in"
height="0.7916666666666666in"} (A3.2)

![](media/image37.wmf){width="2.7916666666666665in"
height="0.4861111111111111in"} (A3.3)

![](media/image38.wmf){width="3.4722222222222223in"
height="0.4861111111111111in"} (A3.4)

where:

> *h* : height of the top of the obstacle above the straight line
> joining the two ends of the path. If the height is below this line,
> *h* is negative

*d~1~* and *d~2~* : distances of the two ends of the path from the top
of the obstacle

*d* : length of the path

> *θ* : angle of diffraction (rad); its sign is the same as that of *h*.
> The angle *θ* is assumed to be less than about 0.2 rad, or roughly 12°

*α~1~* and *α~2~* : angles between the top of the obstacle and one end
as seen from the other end. *α~1~* and *α~2~* are of the sign of *h* in
the above equations.

NOTE 1 -- In the four equations above, *h*, *d*, *d~1~*, *d~2~* and *λ*
should be in self-consistent units.

Figure A3.2 gives, as a function of , the loss (dB) caused by the
presence of the obstacle. For greater than -- 0.78 an approximate value
can be obtained from the expression:

![](media/image39.wmf){width="4.930555555555555in"
height="0.5555555555555556in"} (A3.5)

![](media/image40.wmf){width="6.174305555555556in"
height="6.250694444444444in"}

APPENDIX 4

General method for one or more obstacles

The following method is recommended for the diffraction loss over
irregular terrain which forms one or more obstacles to line-of-sight
propagation. The calculation takes Earth curvature into account via the
concept of an effective Earth radius (see equation (4) of the main
text). This method is suitable in cases where a single general procedure
is required for terrestrial paths over land or sea and for both
line-of-sight and trans-horizon.

A profile of the radio path should be available consisting of a set of
samples of ground height above sea level ordered at intervals along the
path the first and last being the heights of the transmitter and
receiver sites above mean sea level, and a corresponding set of
horizontal distances from the transmitter. Each height and distance
pair, *h~i~* and *d~i~*, are referred to as a profile point and given an
index, *i*, with indices incrementing from the transmitter (*0*) to the
receiver (*n*) point.

It is preferable but not essential for the profile samples to be equally
spaced horizontally. Further input variables are: transmitter and
receiver antenna heights (m) above mean sea level, *h~ts~* and *h~rs~* ,
effective Earth radius (km), *a~ep~*, and wavelength (m), .

For trans-horizon paths, this procedure is based on the Deygout method
limited to a maximum of 3 edges.

That point with the highest value of the geometrical parameter *i*
(equation A.4.1) is defined as the principal edge, denoted *P*. The
obstacle containing the principal edge is termed principal obstacle. The
other diffracting edges should not be part of the principal obstacle.
The Steps 1 to 5 outline the procedure to isolate the principal obstacle
from other secondary obstacles that contribute to diffraction loss. For
background information regarding the derivation of the parameter *~i~* ,
the reader is referred to Appendix 3 above.

**Step 1: Position of the principal edge**

![](media/image41.wmf){width="6.614583333333333in"
height="4.104166666666667in"}

The profile to be considered is defined from the transmitter point index
*0* to the receiver point index *n* (Fig. A4.1). If n = *1* there is no
intermediate point and the diffraction loss of the path is considered to
be zero.

The construction of Fig. A4.1 is applied by evaluating the geometrical
parameter *i* (*0*  \<  *i * \< *n*)

![](media/image42.wmf){width="1.4583333333333333in"
height="0.5277777777777778in"} (A4.1)

where:

![](media/image43.wmf){width="2.763888888888889in"
height="0.5555555555555556in"} (A4.1a)

*h~i~* : vertical heights as shown in Fig. A4.1 taken from a terrain
profile (m)

> *h~0~*, *h~n~*  : vertical heights as shown in Fig. A4.1 taken from a
> terrain profile plus antenna height of transmitter and receiver
> respectively (m)

*d~0i~*, *d~in~*,*d~0n~* : horizontal distances as shown in Fig. A4.1
(km)

*a~ep~* : effective Earth radius for *p*% of time (km)

> *λ* : wavelength (m)

The reference line for calculation of *h* (Equation A4.1a) extends from
point *0* to point *n*, i.e. from Tx to Rx antenna.

Note that equation (A4.1) is derived directly from equation (A3.1). The
geometry of equation (A4.1a) is illustrated in Fig. A4.1. The second
term in equation (A4.1a) is a good approximation to the additional
height at point i due to Earth curvature.

The diffraction loss of the principal edge (situated at point P) is then
given as the knife-edge loss *J*(~P~) (equation A3.5). In case ~P~  ≤ --
0.78 the excess diffraction loss of the path is zero.

![](media/image44.wmf){width="5.388888888888889in"
height="0.5555555555555556in"} (A4.1b)

In line-of-sight cases no contribution from secondary edges is taken
into account.

**Step 2: Horizontal exclusion zone of the principal obstacle**

The horizontal exclusion zone of the principal obstacle is estimated to
be ± 1 km from the position of the principal edge, i.e., no secondary
obstacles should be considered if they lie within one km (horizontally)
of the main obstacle. This is done in order to avoid the same, single,
obstacle being included several times and thus having its loss
over-estimated.

**Step 3: ~t~ and *J*(~t~) at the Tx side of the principal obstacle**

The construction principles of Fig. A4.1 are applied between transmitter
and the principal edge (point *P*). The reference line for calculation
of *h* (equation A4.1a) extends from point *0* to point *P*. The point
with the highest value of , between the principal edge *P* (excluding
the principal obstacle) and point *1*, is denoted *~t~* and hence
*J(~t~ )* can be calculated.

**Step 4: ~r~ and *J*(~r~* *) at the Rx side of the principal obstacle**

The construction principles of Fig. A4.1 are applied between receiver
and the principal edge.

The reference line for calculation of *h* (equation A4.1a) extends from
point *P* to point *n*. The point with the highest value of , between
the principal point *P* (excluding the principal obstacle) and point *n*
-- 1, is denoted *~r~* and hence *J(~r~ )* can be calculated.

**Step 5: Excess diffraction loss of the path**

The excess diffraction loss for the path is then given by:

*L~d~*  =  *J*(*~P~* )  + 
![](media/image45.wmf){width="1.0694444444444444in"
height="0.6111111111111112in"}\[ *J*(*~t~* )  +  *J*(*~r~* )  +  *C* \]
dB for *~P~*  \>  -- 0.78 (A4.2a)

*L~d~*  =  0 dB for *~P~*  ≤  -- 0.78 (A4.2b)

where:

*C*  =    3.0 + 0.04 *d* (A4.3)

*C* : empirical correction value

*d* : total path length (km)

The method is applicable to predict diffraction loss for different
values of effective Earth radius.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

**[Intercomparison input data format]{.underline}**

**[(Updated February 2007)]{.underline}**

**[Transmitter information]{.underline}**

Line 1: Free format, available for identification, comment and any
additional remarks. Organization must be identified as the 1st three
characters on 1st line but remainder of line may be blank.

Line 2: First six characters blank if median or spot-point measurements,
or else \'MOBILE\' or \'INDOOR\' when mobile or indoor measurements is
to be indicated, respectively, + free format for other information

Line 3\*: Transmitting site name (up to 20 characters) \<A20\>\*\*.

Line 4\*\*\*: Transmitting site latitude and longitude (i.e. degrees,
N/S, minutes, seconds; and degrees, E/W, minutes, seconds)

> \<I2, A1, I2,I2,2X, I3, A1, I2,I2\>.

Line 5: Transmitting antenna height in m above ground, as integer plus
polarization as V or H or U (\'unknown\') \<I4, T6, A1\>.

Line 6: Maximum erp in dBW, as real \<F5.1\>.

Line 7: Hrp [reduction]{.underline} along profile, as real \<F5.1\>.

Line 8: Number of lines, N, of vrp information \<I2\>. If no vrp
information is available, the value 0 is to be entered.

If N \> 0

Lines 9 to 9+N Angle from horizontal through transmitting antenna and
vrp reduction as integer plus real \<I3, T5, F4.1\>. (Angles below
horizontal are negative, those above the horizontal are positive).

\_\_\_\_\_\_

\* All fixed format information starts in column 1.

\*\* Fortran-type formatting information

\*\*\* The coordinates of the older profiles don\'t have the accuracy
specified in this format and therefore should not be used to generate
profiles. Nevertheless, it is desirable to specify these coordinates to
the required accuracy.

**[Receiver information]{.underline}**

For simplicity, the first line of this information is M where:

M = 9+N (that is M = 9 if N = 0)

Line M Receiving site name (up to 20 characters) \<A20\>

Line M+1\*\*\*: Receiving site latitude and longitude (i.e. degrees,
N/S, minutes, seconds; and degrees, E/W, minutes, seconds)

\<I2, A1, I2,I2,2X, I3, A1, I2,I2\>.

Line M+2 Receiving antenna height above ground level, used for check
purposes only, as real \<F5.1\>

Line M+3 Number of measured values, L, as integer \<I2\>.

Lines M+4 to M+4+L Frequency in MHz, measured value in dBV/m, time
percentage and receiving antenna height

> as real, real, integer, real
>
> \<F6.1, T8, F5.1, T14, I2, T17, F4.1\>

Line M+5+L Number of profile points.

Remaining lines: Profile distance\*, ground height\*\*, ground cover
classification (see Annex) and ground cover height as real, real,
integer, real

\<F6.2, T8, F6.1, T15 ,I2, T18, F5.1\>

Note that the profile must extend to the receiver site.

**Final Line contains \<END OF PROFILE\> starting in column 1.**

\* All distances are in km

\*\* All heights are in m.

\*\*\* The coordinates of the older profiles don\'t have the accuracy
specified in this format and therefore should not be used to generate
profiles. Nevertheless, it is desirable to specify these coordinates to
the required accuracy.

[^1]: NOTE - this method does not include ionospheric propagation
    effects.

[^2]: For example, for a frequency, f, less than 100 MHz, use \'100
    MHz\' for f~I~ and \'1 000 MHz\' for f~S~, and extrapolate to f
    using the same equation.