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China(People's Republic of)

A PATH SPECIFIC PREDICTION METHOD FOR POINT-TO-AREA PROPAGATION

# 1 Introduction

In this document a path specific prediction method is presented for
point-to area propagation, based on Recommendations ITU-R P. 452, 526
and 1546. The field strength can be expressed as

$E(T,L) = E(\text{50},\text{50}) + {\Delta E}_{t}(T) + {\Delta E}_{l}(L)$
(1)

Where $E(T,L)$is the field strength for $T\text{\%}$ of time and
$L\text{\%}$ of locations , $E(\text{50},\text{50})$ the median field
strength, $$${\Delta E}_{t}(T)$ the variation for $T\text{\%}$ of time,
and ${\Delta E}_{l}(L)$ the variation for $L\text{\%}$ of locations. It
is suggested that the median field strength be predicted based on
Recommendations ITU-R P. 452 and 526, and the variation with time and
locations predicted based on Recommendation ITU-R P. 1546.

# 2 Prediction of median field strength

The median field strength, $E(\text{50},\text{50})$(dB(μV)/m), can be
expressed in terms of the median basic transmission loss,
$L_{b}(\text{50},\text{50})$(dB), as follows:

$E(\text{50},\text{50}) = \text{ERP} - L_{b}(\text{50},\text{50}) + \text{20}\text{lg}f + \text{109}\text{.}4$
(2)

Where $\text{ERP}$ is the effective radiated power(dBW) and f the
frequency(MHz). Before prediction of median basic transmission loss,
input data should be clarified and followed by path profile analysis.

# 2.1 Input data

The basic input data includes the following:

$f$: frequency(MHz)

$h_{\text{tg}},h_{\text{rg}}$: antenna heights(m) above ground level

$\Delta N$: radio-refractivity lapse-rate(N-units/km) through the lowest
1 km of the atmosphere

$N_{0}$: sea level surface refractivity(N-units)

$N + 1$: terrain point number on the path profile

$d_{i}(i = 0,1,\cdots,N)$: distance(km) of the ith terrain point from
the 0th point

$h_{i}(i = 0,1,\cdots,N)$: terrain height(m) of the ith point amsl

$\text{GC}_{i}(i = 0,1,\cdots,N)$: ground-cover type of the ith point

$h_{\text{gci}}(i = 0,1,\cdots,N)$: ground-cover height(m) of the ith
point

# 2.2 Path profile analysis

Path profile is analysed based on the effective earth radius,
$a_{e}(\text{km})$:

$a_{e} = \text{ka}$

where

$k = \frac{\text{157}}{\text{157} - \Delta N}$ (3)

$a$is the true earth radius(6371km).

1)  whether the path is LOS(Line-Of-Sight) or NLOS(trans-horizon)

It is adjudged by comparison between $\theta_{\text{max}}$(mrad) and
$\theta_{\text{td}}$(mrad) where

$\theta_{\text{td}} = \frac{h_{\text{rs}} - h_{\text{ts}}}{d} - \frac{\text{10}^{3}d}{2a_{e}}$
(4)

$\theta_{\text{max}} = \underset{i = 1}{\overset{n - 1}{\text{max}}}(\theta_{i})$
(5)

$\theta_{i} = \frac{h_{i} - h_{\text{ts}}}{d_{i}} - \frac{\text{10}^{3}d_{i}}{2a_{e}}$
(6)

$h_{\text{ts}} = h_{0} + h_{\text{tg}}$ (7)

$h_{\text{rs}} = h_{n} + h_{\text{rg}}$ (8)

$d = d_{n}$ (9)

If $\theta_{\text{max}} > \theta_{\text{td}}$, the path is NLOS.
Otherwise it is LOS.

2)  Whether a LOS path has first Fresnel zone clearance or sub-path
    diffraction

It is adjudged by comparison between $\theta_{f\text{max}}$(mrad) and
$\theta_{\text{td}}$ where

$\theta_{f\text{max}} = \underset{i = 1}{\overset{n - 1}{\text{max}}}(\theta_{\text{fi}})$
(10)

$\theta_{\text{fi}} = \frac{(h_{i} + R_{i}) - h_{\text{ts}}}{d_{i}} - \frac{\text{10}^{3}d_{i}}{2a_{e}}$
(11)

$R_{i} = \text{550}\sqrt{\frac{d_{i}(d - d_{i})}{\text{fd}}}$ (12)

If $\theta_{f\text{max}} > \theta_{\text{td}}$, the LOS path has first
Fresnel zone clearance. Otherwise it has sub-path diffraction.

3)  Whether the sub-path surface is spherical or irregular

It is adjudged by $h_{m}$(m) and $\delta h$(m) where

$h_{m} = \frac{1}{2(d - d_{i0})}\sum_{i = i_{0} + 1}^{n}{(d_{i} - d_{i - 1})(h_{i} + h_{i - 1})}$
(13)

$\delta h = \underset{i = i_{0}}{\overset{n - 1}{\text{max}}}(h_{i}) - h_{m}$
(14)

$d_{i0} = \text{min}(3,0\text{.}2d)$ (15)

If $\delta h < 0\text{.}1R$ and
$\text{min}(h_{\text{ts}},h_{\text{rs}}) > h_{m}$, the sub-path surface
is spherical. Otherwise it is irregular. Where

$R = \text{275}\sqrt{\frac{f}{d}}$ (16)

4)  Whether the surface between two ends' horizons is spherical or
    irregular

It is adjudged by $h_{m}^{'}$(m) and ${\delta h}^{'}$(m) where

$h_{m}^{'} = \frac{1}{2(d_{\text{ilr}} - d_{\text{ilt}})}\sum_{i = i_{\text{lt}} + 1}^{i_{\text{lr}}}{(d_{i} - d_{i - 1})(h_{i} + h_{i - 1})}$
(17)

${\delta h}^{'} = \underset{i = i_{\text{lt}}}{\overset{i_{\text{lr}}}{\text{ma}}}x(h_{i}) - h_{m}^{i}$
(18)

$d_{\text{ilt}} = d_{i}$ for $\text{max}(\theta_{i})$ (19)

$d_{\text{ilr}} = d - d_{j}$ for $\text{max}(\theta_{j})$ (20)

$\theta_{j} = \frac{h_{j} - h_{\text{rs}}}{d - d_{j}} - \frac{\text{10}^{3}(d - d_{j})}{2a_{e}}$
(21)

If $\delta_{h}^{'} < 0\text{.}1R$ and
$\text{min}(h_{\text{ts}},h_{\text{rs}}) > h_{m}^{'}$, the surface
between two ends' horizons is spherical. Otherwise it is irregular.

# 2.3 Prediction of median basic transmission loss

The median basic transmission loss can be expressed by

$L_{b}(\text{50},\text{50}) = L_{\text{bf}} + A(\text{50},\text{50})$
(22)

where $L_{\text{bf}}$ is the free-space basic transmission loss(dB),

$L_{\text{bf}} = \text{32}\text{.}5 + \text{20}\text{lg}f + \text{20}\text{lg}d$
(23)

$A(\text{50},\text{50})$ is the median attenuation(dB) relative to
free-space. It is predicted for different path types.

1)  LOS path with first Fresnel zone clearance

$L_{b}(\text{50},\text{50}) = L_{\text{bf}} + A_{\text{cld}}$ (24)

where $A_{\text{cld}}$ is the additional clutter loss (dB) due to
diffraction.

2)  LOS path with sub-path diffraction

$L_{b}(\text{50},\text{50}) = L_{\text{bf}} + A_{\text{ds}}(\text{50},\text{50}) + A_{\text{cld}}$
(25)

where $A_{\text{ds}}(\text{50},\text{50})$ is the median sub-path
diffraction loss(dB).

If the sub-path surface is spherical, $A_{d}$ is predicted according to
Recommendation ITU-R P. 526-8, §3.2.

If the sub-path surface is irregular, $A_{d}$ is predicted according to
Recommendation ITU-R P. 526-8, §4.1.

3)  Trans-horizon path

$L_{b}(\text{50},\text{50}) = - \text{10}\text{lg}$ (26)

where $L_{\text{bd}}(\text{50},\text{50})$ and
$L_{\text{bs}}(\text{50},\text{50})$ are the median basic transmission
loss(dB) due to trans-horizon diffraction and troposcatter,
respectively, $A_{\text{cld}}$ and $A_{\text{cls}}$ the clutter loss(dB)
due to diffraction and scatter.

The median basic transmission loss due to trans-horizon diffraction can
be expressed by

$L_{\text{bd}}(\text{50},\text{50}) = L_{\text{bf}} + A_{\text{dt}}(\text{50},\text{50})$
(27)

where $A_{\text{dt}}(\text{50},\text{50})$is the median trans-horizon
diffraction loss(dB) relative to free-space.

If the surface between two ends' horizons is spherical, $A_{\text{dt}}$
is predicted according to Recommendation ITU-R P. 526-8, §3.1.1.2.

If the surface between two ends' horizons is irregular, $A_{\text{dt}}$
is predicted according to Recommendation ITU-R P. 526-8, §4.4.2.

The median basic transmission loss due to troposcatter is predicted
according to Recommendation ITU-R P. 452-12, Equation(15), taking
angular distance(mrad) as

$\theta = \frac{\text{10}^{3}d}{a_{e}} + \theta_{t} + \theta_{r}$ (28)

where

$\theta_{t} = \underset{i = 1}{\overset{n - 1}{\text{max}}}(\theta_{i})$
(29)

$\theta_{r} = \underset{j = 1}{\overset{n - 1}{\text{max}}}(\theta_{j})$
(30)

4)  Additional clutter loss

There are two basic parameters for clutter loss prediction, i.e.

$h_{a}$: clutter height(m) above local ground level

$d_{k}$: distance(km) from the clutter to the antenna.

The typical clutter data can be summarized in the following table.

Typical clutter data

  ------------------ ------------------- ---------------- ------------------
  code               clutter category    $$h_{a}(m)$$     min($d_{k}$)(km)

  0                  unknown             10.0             0.05

  1                  open/rural          0.0\~5.0         0.1

  2                  water               0.0              

  3                  trees/forest        10.0\~30.0       0.05

  4                  suburban            5.0\~15.0        0.025

  5                  urban               15.0\~25.0       0.02

  6                  dense urban         20.0\~40.0       0.02
  ------------------ ------------------- ---------------- ------------------

Concrete data might be obtained from path profile data. If the ratio of
the clutter height to the distance from the antenna attains to the
maximum at a terrain point, the relevant clutter height and distance are
taken to be $h_{a}$ and $d_{k}$, respectively.

The clutter loss due to diffraction, $A_{\text{cld}}$ is predicted as
for a knife-edge diffraction, taking the diffraction parameter as

$V_{\text{cl}} = 2\text{.}\text{582} \times \text{10}^{- 3}\theta_{\text{cl}}\sqrt{\text{fd}_{k}}$
(31)

where

$\theta_{\text{cl}} = \frac{h_{a} - h_{\text{rg}}}{d_{k}} - \theta_{\text{rf}}$
(32)

$\theta_{\text{rf}}$ is a reference elevation angle.

For a LOS path with or without first Fresnel zone clearance,

$\theta_{\text{rf}} = \frac{h_{\text{ts}} - h_{\text{rs}}}{d} - \frac{\text{10}^{3}d}{2a_{e}}$
(33)

For a trans-horizon path,

$\theta_{\text{rf}} = \theta_{r}$ (34)

The clutter loss due to troposcatter can be predicted by

$A_{\text{cls}} = \text{30}\text{lg}(1 + \frac{\theta_{\text{cl}}}{1 + \theta})$
(35)

where $\theta$ is the angular distance.

# 3 Prediction of the variation with time and locations

The variation of field strength with time can be expressed by

${\Delta E}_{t}(T) = E(T) - E(\text{50})$ (36)

where $E(T)$ is the field strength for $T\text{\%}$ of time.

The variation of field strength with locations is considered for land.
According to Recommendation ITU-R P. 1546-1, Annex 5, §12, It can be
predicted by

${\Delta E}_{l}(L) = Q_{i}(\frac{L}{\text{100}})\sigma_{L}(f)$ (37)

Where $Q_{i}(x)$ is the inverse complementary cumulative normal
distribution and $\sigma_{L}$ the standard deviation.

The prediction of $E(T)$ is briefed in the following.

# 3.1 Basic data files

The prediction of variation with time is based on Recommendation ITU-R
P. 1546 tabulated field strengths and relevant Recommendation ITU-R P.
453 climatic data files. Therefore the basic field strength data files
should be built first, and the climatic data files should be cited.
There are 24 basic field strength data files, corresponding to 24
figures in Recommendation ITU-R P. 1546, each applying a specific set of
frequency, zone and time percentage, and containing 702 basic field
strength values for 8 different effective transmitting/base antenna
height values and maximums at 78 specific distances. There are three
relevant climatic data files, i.e. DNDZ-50.TXT, DNDZ-10.TXT and
DNDZ-01.TXT, each corresponding to one of three time percentage 50, 10
and 1, and containing $\Delta N$ values at specific grid points. The
latitude grid is from +90ºN to -90ºS in 1.5º steps; the longitude grid
is from 0º to 360º in 1.5º steps.

# 3.2 Input data

The basic input data includes the following:

$\text{Lat}1,\text{lon}1$: latitude and longitude of transmitting/base
station

$\text{Lat}2,\text{lon}2$: latitude and longitude of receiving/mobile
station

$f$: frequency

$T$: percentage of time

$d$: path length

$h_{\text{tg}}$: transmitting/base antenna height above ground level

$F_{\text{sea}}$: fraction of path over sea

$N + 1$: terrain point number on a path section

$d_{i}(i = 0,1,\cdots,N)$: distance of the ith terrain point from the
transmitting/base station

$h_{i}(i = 0,1,\cdots,N)$: terrain height of the ith point

where $d_{0} = \text{min}(3,0\text{.}2d)$ and
$d_{N} = \text{min}(\text{15},d)$

If full information of path profile is available, data
$d$,$F_{\text{sea}}$,$d_{i}$ and $h_{i}$ can be replaced by
$d_{i}$,$h_{i}$ and $\text{GC}_{i}$(Ground cover) for the whole path.

# 3.3 Rough path analysis

1)  Zone analysis

If $w = 0\text{.}0$, the path is over land.

If $w = 1\text{.}0$, the path is over sea.

If $w = 1\text{.}0$ and
$\text{min}(\text{lat}1,\text{lat}2) < \text{30}^{\circ}$, the path is
over warm sea.

If $w = 1\text{.}0$ and
$\text{min}(\text{lat}1,\text{lat}2) > \text{30}^{\circ}$, the path is
over cold sea.

If $0\text{.}0 < w < 1\text{.}0$ and
$\text{min}(\text{lat}1,\text{lat}2) < \text{30}^{\circ}$, the path is
mixed with land and warm sea.

If $0\text{.}0 < w < 1\text{.}0$ and
$\text{min}(\text{lat}1,\text{lat}2) > \text{30}^{\circ}$, the path is
mixed with land and cold sea.

2)  Analysis of transmitting/base station antenna height, $h_{1}$

It is determined according to Recommendation ITU-R P. 1546-1, Annex 5,
§1.

# 3.4 Prediction of the variation with time

In time variation consideration, field strength is predicted based on
Recommendation ITU-R P. 1546-1 in a simplified form.

1)  For any one of three frequencies 100MHz, 600MHz and 2000MHz, any one
    of three zones land, cold sea and warm sea, any one of three time
    percentages 50, 10 and 1, and any distance, $d$, between 1 km and
    1000km, open the right basic field strength data file by the set of
    frequency, zone and time percentage, and draw 9 pairs of field
    strengths at two specific distances closest to the desired distance.
    The 9 pairs of field strengths correspond to 8 specific effective
    transmitting/base antenna heights and a maximum field strength.

2)  Through distance interpolation according to Recommendation ITU-R P.
    1546-1, Annex 5, §5, obtain 9 field strengths for the desired
    distance, $d$.

3)  Open the climatic data file for desired time percentage, draw the
    data by the latitude and longitude of the mid-path, and use it to
    adjust the 9 field strengths according to Recommendation ITU-R P.
    1546-1 Annex 8.

4)  For any effective transmitting/base antenna height, $h_{1}$, between
    10m and 3000m, through interpolation according to Recommendation
    ITU-R P. 1546-1, Annex 5, §4.1, obtain the desired field strength
    for the desired $h_{1}$ from the 9 field strenghts.

5)  If the effective transmitting/base antenna height is less than 10m,
    correct the field strength according to Recommendation ITU-R P.
    1546-1, Annex 5, §4.2 for $0 < h_{1} < \text{10}$m, and §4.3 for
    $h_{1} < 0$m.

6)  For any frequency between 30MHz and 3000MHz and any time percentage
    between 50 and 1, take interpolations according to Recommendation
    ITU-R P. 1546-1, Annex 5, §6 for frequency and §7 for time
    percentage.

7)  For mixed paths, take the method in Recommendation ITU-R P. 1546-1,
    Annex 5, §8.

8)  Considering what is concerned is field strength difference of two
    time percentages, other corrections independent of time, such as
    those for different receiving/mobile antenna herghts and terrain
    clearance angle, are not needed.

# 4 Software

A software for the above method has been compiled and is executable,
which can be names temporarily PSPROGCN. Its input data includes the
following:

$f$: frequency

$\text{ERP}$: effective radiated power

$\text{NPL}$: polarization

$h_{\text{tg}},h_{\text{rg}}$: antenna heights above ground level

$N_{0}$: sea level surface refractivity

$\Delta N$: radio-refractivity lapse-rate through the lowest 1km of the
atmosphere

> $d_{i},h_{i},\text{GC}_{i},h_{\text{gci}}(i = 0,1,\cdots,N)$: distance
> from transmitting/base station, terrain height amsl, ground cover type
> and its height at the ith terrain point on the path profile

$\text{lat}1,\text{lon}1$: latitude and longitude of transmitting/base
station

$\text{lat}2,\text{lon}2$: latitude and longitude of receiving/mobile
station

$T$: percentage of time

$Q$: Percentage of locations

PSPROGCN mainly consists of three functions: ALB, DETT and EVSLB.

The input data of the functions includes the following:

ALB(median basic transmission loss):

$f$: frequency

$\text{NPL}$: polarization

$h_{\text{tg}},h_{\text{rg}}$: antenna heights above ground level

$N_{0}$: sea level surface refractivity

$\Delta N$: radio-refractivity lapse-rate through the lowest 1km of the
atmosphere

> $d_{i},h_{i},\text{GC}_{i},h_{\text{gci}}(i = 0,1,\cdots,N)$: distance
> from transmitting/base station, terrain height amsl, ground cover type
> and its height at the ith terrain point on the path profile

DETT(variation with time and locations):

$f$: frequency

$T$: percentage of time

$Q$: Percentage of locations

$h_{\text{tg}}$: transmitting/base antenna height above ground level

$F_{\text{sea}}$: fraction of path over sea

$\text{lat}1,\text{lon}1$: latitude and longitude of transmitting/base
station

$\text{lat}2,\text{lon}2$: latitude and longitude of receiving/mobile
station

EVSLB(transformation from $L_{b}$ to field strength):

$f$: frequency

$\text{ERP}$: effective radiated power

$L_{b}$: basic transmission loss

PSPROGCN has been tested by the measurement data files from ITU-R
WP3K-1. The prediction errors are summarized in Tables 1 and 2.

Table 1. Prediction errors for different data sources

  -------------- -------------- -------------- -------------- --------------
  data source    path amount    data amount    mean error(dB) r.m.s
                                                              error(dB)

  BBC            38             70             7.0            12.5

  BBCL           68             68             9.8            16.2

  BBCn           274            274            5.9            12.5

  ERT            37             37             6.4            13.1

  HOL            72             73             3.5            11.3

  IRT            600            600            3.0            9.3

  IRTL           156            156            -6.2           18.7

  IRTs           11             63             2.0            9.2

  ORF            77             497            -15.5          19.0

  RAI            87             87             0.7            7.4

  S              107            107            13.3           17.2

  SUI            1083           1247           3.4            12.3

  TDF            68             72             -7.9           15.8

  YLE            100            100            -6.3           13.4

  YLEs           17             68             5.6            12.5

  TOTAL          2795           3519           0.4            13.6
  -------------- -------------- -------------- -------------- --------------

Table 2 Prediction errors for different frequency bands

  --------------- -------------- -------------- -------------- --------------
  Frequency bands path amount    data amount    mean error(dB) r.m.s
                                                               error(dB)

  below 300MHz    1670           2365           -1.3           13.4

  300\~1000MHz    913            913            5.6            12.4

  1000\~3000MHz   241            241            -1.9           18.7

  TOTAL           2824           3519           0.4            13.6
  --------------- -------------- -------------- -------------- --------------

Software PSPROGCN and its detailed output data files of the test against
ITU-R WP3K-1 input data are submitted to ITU-R WP3K-1.