broadband propagation models v4

Propagation models

Alcatel-Lucent File Reference Date Edition Page Propagation models ed4.doc 06/2007 04 1

All rights reserved. Passing on and copying of this document, use and communication of its contents not permitted without written authorisation.

Propagation Models for BroadBand Wireless Systems

Propagation models



CONTENTS

1. SCOPE ..................................................................................................................... 3

2. LOS PROPAGATION MODELS ............................................................................. 3

2.1 Freespace ............................................................................................................................................3

2.2 Two slopes model ..............................................................................................................................3

2.3 Availability ..........................................................................................................................................4

2.4 Diffraction other obstacles and irregular terrain .......................................................................7 2.4.1 Single knife-edge obstacle ....................................................................................................................8 2.4.2 Multiple Knife-edge................................................................................................................................9 2.4.3 Radio network planning tool A9155 LOS model..................................................................................10

2.5 Earth curvature..................................................................................................................................12

3. NLOS PROPAGATION MODELS ........................................................................ 13

3.1 Shadowing effect .............................................................................................................................13

3.2 Erceg models ....................................................................................................................................14

3.3 Modified Cost-Hata model.............................................................................................................14

3.4 SPM model ........................................................................................................................................15

3.5 Comparison of statistical models at 3,5 GHz .............................................................................16

3.6 Indoor penetration..........................................................................................................................18

3.7 Indoor propagation models ..........................................................................................................19

Propagation models



1. SCOPE

This document analyzes the different propagation models used when designing wireless broadband

networks. Depending on the deployement scenario, LOS or NLOS models must be considered. In the

first part, LOS / near LOS models are examined. Then, NLOS models and indoor penetration are

described. Finally, indoor models (mainly for WiFi) are presented.

2. LOS PROPAGATION MODELS

LOS or Near LOS models are employed when the wireless system to be deployed is a fixed system with

antennas of the base station and the terminal being located on top of the roof. This deployment type

concerns mainly Alcatel WiMAX A7387 product (a.k.a. release W1), which uses fixed CPE with outdoor

antennas. Several LOS/Near LOS models can be used depending whether a direct link exists between

the base station and the terminal.

2.1 Freespace

This model considers a straight propagation path between the terminal (or CPE, Customer Premises

Equipment) and the BS (Base Station). It takes into account the propagation losses in the atmosphere, but

no reflected path nor diffraction. It simply depends on distance between the CPE and the BS, and on the

frequency. The pathloss PL (in dB) is expressed considering the distance D (in Km) and the frequency F

(in MHz).

)(20)(2045,32 FLogDLogPL ++=

Freespace model is valid for any carrier frequency F.

2.2 Two slopes model

The freespace approach is limited to cases without multipath (usually created by signal reflection on

ground or a construction) or diffraction. The Fresnel zone, which gives the area where the signal has Pi/2

phase compare to direct signal, indicates diffraction over an obstacle when this zone is engaged. The

engagement is given by a breakpoint (Dk, when the Fresnel zone encounters obstacles). In this model,

freespace propagation is assumed up to the breakpoint, and propagation in D-3.3 after.

Figure 1: Illustration of interception of Fresnel zone in a point to (multi-)point connection

The breakpoint is computed using relative BS antenna height he (in m) over the clutter height (average

height of the environment), and the relative CPE antenna height hr (in m) over the clutter height.

Propagation models



( )λ2

2hrheDk

+=

If D < Dk then

)(20)(2045,32 FLogDLogPL ++=

Else

)(20)/(33)(2045,32 FLogDkDLogDkLogPL +++=

Two slopes model gives result for LOS deployment taking into account the effect of the ground, and is valid for any frequency.

2.3 Availability

In addition to the propagation losses described in the previous sections, an additional margin needs to

be considered for point to multi-point types of deployment. This margin refers to the link availability

expressed in percentage of time, typically between 99,95% and 99,999%. For LOS / Near LOS designs

the availability margin is computed following ITU-R P.530-9 §2.3.2 recommendation. The parameters

influencing the range are therefore:

- The BS antenna height,

- The SU (Station Unit) antenna height,

- The clutter height (including building height, terrain elevation and earth curvature effect),and,

- The geoclimatic factors (longitude / latitude, rain, …).

The algorithm for computing the availability function is provided below. Following parameters are used:

- K being the geoclimatic factor for the average worst month from fading data for the geographic

area of interest (depends on longitude and latitude),

- d being the distance between the BS and the SU (in m),

- )(dPathlossSysgainA −= ,

- he being the base station antenna height over the clutter (in m),

- hr the CPE antenna height over the clutter and (in m),

- hasl the height of the clutter above sea level (in m).

The 2 slopes propagation model is used to compute the maximum cell range with breaking point Dk :

( )λ2

2hrheDk

+=

The propagation factor is 2 for d < Dk and 3.3 for d ≥ DK

The geoclimatic factor is:

10029,02,410 dNK −−=

Propagation models



with dN1 is the point of refractivity gradient in the lowest 65 m of the atmosphere not exceeded for 1% of

an average in the year. It is provided on a 1,5° grid in latitude and longitude in recommendation ITU-R

P453.

Step 1: Calculate the multipath occurrence factor, p0 (i.e., the intercept of the deep-fading distribution

with the percentage of time-axis):

( ) LhfpO Kdp 001,0033,02,10,3 10.1 −−

+= ε [%]

Where:

- hehrdp −= 1ε

- f is the frequency in GHz,

- And if he ≥ hr

Then aslrL hhh +=

Else asleL hhh +=

Step 2: Calculate the value of fade depth, At, at which the transition occurs between the deep-fading

distribution and the shallow-fading distribution as predicted by the empirical interpolation procedure:

)log(2.125 0pAt += [dB]

The procedure now depends on whether A is greater or less than At.

Step 3a: If the required fade depth, A, is equal to or greater than At: calculate the percentage of time

that A is exceeded in the average worst month.

100 10.

A

w pp−

= [%]

Step 3b: If the required fade depth, A, is less than At: calculate the percentage of time, pt, that At is

exceeded in the average worst month.

100 10.

tA

t pp−

=

Calculate aq′ from the transition fade At and transition percentage time pt:

Atpt

qa /100

100lnlog20

−−−=′

Calculate qt from aq′ and the transition fade At:

Propagation models



+−

+

−′=

−

−− 800103.4

10*10*3.01

220

016.020

tA

AtA

at

Aqq

t

t

Calculate qa from the required fade A:

[ ]

++

++=

−−−

800103.41010*3.012 20016.020 A

qqA

tA

A

a

Calculate the percentage of time, pw, that the fade depth A (dB) is exceeded in the average worst month:

−−=

−2010exp1100

Aq

w

a

p [%]

Then the availability is:

100

100 wptyAvailabili

−=

Example of availability vs range

99,5

99,55

99,6

99,65

99,7

99,75

99,8

99,85

99,9

99,95

100

1 2 3 4 5 6 7 8

Range (Km)

Ava

ilab

ilit

y (%

)

Figure 2: Example availability margin versus range

Propagation models



Figure 3: Percentage of time, Pw, fade depth A is exceeded in the average worst month

The availability is a typical parameter of fixed LOS deployment, the CPE and BS being above the rooftop.

2.4 Diffraction other obstacles and irregular terrain

It may happen that the propagation paths (First Fresnel zone) encounter one or several obstacles. In that

case, it is necessary to evaluate the additional losses caused by those obsctale. In that case, the path is in

near LOS. For simple computations, the obstacles are idealized as knife-edge with negligible thickness. It

is then possible to evaluate the extra losses for a single knife-edge or multiple knife edges.

). The methods described hereafter are are based on ITU 526-5 recommendations.

Propagation models



2.4.1 Single knife-edge obstacle

Tx Rx h

d1 d2

In the computation of the height of the obstacle, the Earth curvature should be taken into account, using

the effective Earth radius Re = 8500000 m.

The height correction ∆h of the obstacle due to earth curvature, depends on d1 is the distance (in m) from

the BS to the obstacle, d2 the distance (in m) from the obstacle to the CPE and on the effective Earth

radius Re.

eR

ddh

4

22

21 +

=∆

The relative height hrel (in m) of the obstacle over the BS to CPE axis, He is the BS antenna height (in m)

above ground level and Hr the CPE antenna height (in m). h is the height (in m) of the obstacle above

ground level.

++

−∆+=21

12

dd

dHdHhhh re

rel

Propagation models



The radius of the nth Fresnel zone (in m) is computed using light speed 0c (in ms-1) and frequency f (in

Hz).

)(2 21

210

ddf

ddncRn +

=

The dimensionless obstruction parameter v (also called Fresnel-Kirshoff diffraction parameter) is the

basis to evaluate the knife-edge effect since it combines in a single parameter all the geometrical

parameters:

1R

hv rel= The diffraction loss J(ν) (in dB) is:

If 7.0−>v then

( ) ( )

−++−+= 1.011.0log.209,6 2 νννJ

Else

0)( =vJ

The Knife-edge loss J(ν) is then added to the pathloss.

Knife-edge can be used to consider masking by an obstacle close to the CPE.

2.4.2 Multiple Knife-edge

When multiple edges are considered, Deygout method limited to a maximum of three edges plus an

empirical correction is used (as recommended in ITU-R P.526-5). The Deygout’s construction is based on

a hierarchical knife-edge sorting used to distinguish the main edge, which induce the largest losses, and

secondary edges, which have a lesser effect. The edge hierarchy depends on the obstruction parameter

(ν) value.

The normailized obstruction parameter ν is evaluated independently for each edge. The point with the

highest ν value is termed the principal edge, p, and the corresponding loss is J(νp).

Then, the principal edge is considered as a secondary transmitter or receiver. Therefore, the profile is

divided in two parts: one half profile, between the transmitter and the knife-edge section, another half,

constituted by the knife-edge receiver portion.

The same procedure is repeated on each half profile to determine the edge with the higher Fresnel-

Kirshoff parameter ν. The two obstacles found, (points t and r), are called “secondary edges”. Losses

induced by the secondary edges, J(νt) and J(νr), are then calculated.

Propagation models



Point t

Point r

Point p

Rx

Tx h p

h r

h t

Sea level

If νp > -0.78, the diffraction loss L is:

( ) ( ) ( )[ ]CJJTJL rtp +++= ννν .

Where,

= 1,

6

)( pvJMinT

Otherwise, L= 0

The Knife-edge loss L is then added to the pathloss.

Multiple Knife-edges method is used with digital terrain maps to compute losses due to clutter height or denivelation (see part 2.4.3).

2.4.3 Radio network planning tool A9155 LOS model

A9155 is the Alcatel radio network design tool for cellular systems, which enables to take into account

for the propagation evaluation the terrain databases (digital terrain model, clutter, roads, …). The LOS

model in A9155 is called WLL. This method relies on freespace propagation losses with additional

diffraction losses. The path loss computed by A9155 is then:

PL = freespace loss + Diffraction loss

A9155 calculates diffraction losses along the transmitter-receiver profile (in a vertical plane) built from

DTM and clutter maps. Therefore, losses due to clutter height are taken into account in the diffraction

losses. A9155 takes clutter height information from the clutter heights file if available in the .atl

document. Otherwise, it considers average clutter height specified for each clutter class in the clutter

classes file description. The Deygout’s construction (considering up to 3 obstacles) is used. Clutter height

information is accurate enough to be used directly without additional information such as clearance

(A9155 can locate streets).

The receiver height is entered per clutter class, enabling A9155 to consider the fact that receivers are

fixed and located on the roofs. It has to be noted that in A9155V6.2 the entered receiver height is above

the ground level, not above the clutter height (as indicated in the RNP user manual).

Propagation models



Tx

Rx

clearance

clutter

DEM

There is also the possibility to compute LOS area, i.e. where there are direct sight between the BS and

the CPE (propagation between BS and CPE is not necessarily freespace because the Fresnel zone can be

obstructed, see part 2.2).

Figure 4: Example of LOS area

Propagation models



WLL model of RNP A9155 allows study of roof top deployment coverage, and LOS backhauling possibilities.

2.5 Earth curvature

Terrain loss due to diffraction over a spherical earth is calculated using following ITU-R formulas:

Re = 8500 Km equivalent earth radius from ITU-Rec 310-8

dRfX e3/23/12.2 −=

13/13/2

1 0096.0 HRfY e−=

23/13/2

2 0096.0 HRfY e−=

With f in MHz, d in Km and H1 and H2 antenna height in m above the ground

If Y1 > 2 Then

8)1.1(5)1.1(6.17 12/1

11 −−−−= YLogYY

Else

)1.0log(20 3111 YYY +=

End If

If Y2> 2 Then

8)1.1(5)1.1(6.17 22/1

22 −−−−= YLogYY

Else

)1.0log(20 3222 YYY +=

End If

)6.17log1011( 21 YYXXLoss ++−+−=

Propagation models



3. NLOS PROPAGATION MODELS

NLOS type of deployment concerns both Alcatel W1 and W2 solutions. In that case, the BS is situated

above the rooftops and the terminals are located well below the rooftop level. Using those models, a

target coverage probability can be achieved considering a given shadowing effect, which accounts for

the statistical distribution of the obstacles in the coverage area.

3.1 Shadowing effect

NLOS models are statistical models; hence the coverage is provided as coverage probability. The

coverage probability is linked to the shadowing effect, which accounts for the statistical distribution of the

obstacles in the coverage area. Shadowing is modelled by a lognormal distribution. The standard

deviation (σ) of this distribution is one the main network design parameter. The other input influencing

the coverage is the coverage requirement (% of surface covered). The coverage can be expressed by the

probability at cell edge or the probability for the whole area. This last approach is the most convenient to

understand directly the coverage probability but the cell edge value may be used when making

prediction with RNP tool

A safe approach is to use the shadowing standard deviation and the coverage target to derive a global

shadowing margin, ensuring that the solution is operational in x% of the cell area (x being the coverage

target). This margin is computed using the “Jack” formula.

Considering that the NLOS propagation model can be expressed as:

)(21 dLogKKPl +=

The formula is the following:

2

1

Stda =

=2

2Std

eLogKb

+−++=+

2

**arg*21

))**arg1

(1()*arg(12

1 b

bainm

Cov eb

bainmerfainmerfP

Where dtezerfZ

t Z

∫−=

0

2)(

π

Depending on K2 propagation parameter, the shadowing margin depends on the BS antenna height.

Coverage target is a criterion of quality; typical values are 90 or 95%. A fixed NLOS deployment typically requires a higher coverage than a mobile one.

Propagation models



3.2 Erceg models

Erceg models are based upon experimental data in the US. AT&T Wireless Services collected the data

across the US in 95 existing macrocells at 1.9 GHz. Erceg models are mainly for North American

suburban / rural environments:

• ErcegA propagation model is for hilly/moderate-to-heavy tree density,

• ErcegB propagation model is for hilly/light tree density or flat/moderate-to-heavy tree density,

• ErcegC propagation model is for flat/light tree density.

The different models are defined by 3 parameters, a, b, c.

Model parameter ErcegA ErcegB ErcegC

a 4.6 4 3.6

b 0.0075 0.0065 0.005

c 12.6 17.1 20

For Erceg A and Erceg B:

−

+

+−+

=2

8.102000

6104

200

0 HCPELog

fLog

d

dLog

HBS

cbHBSa

dLogPL

λπ

For Erceg C:

−

+

+−+

=2

202000

6104

200

0 HCPELog

fLog

d

dLog

HBS

cbHBSa

dLogPL

λπ

Where d0 = 100m, f the frequency in MHz, HBS the BS antenna height in m and HCPE the CPE height in

m.

Erceg models are typicals of US suburban environments; they are valid from 1800 to 2700MHz. Validity at 3.5GHz as not been clearly established but this model is used by some WiMAX manufacturers.

3.3 Modified Cost-Hata model

The Cost-Hata model has been calibrated using measurements results at 3.5 GHz. It is an extension of

Hata model. The different terrain environments are differentiated using a clutter correction factor Kc.

Typical values are:

Propagation models



Environment agressivedense urban -3dense urban skyscrapers 0lower urban -8medium urban -5rural - agriculture -24rural - forest -10rural - low tree density -20rural - open area -25sub-urban industrial zone -15sub-urban residential -10water -27

Table 1: Typical Kc values

( ) aKcDLogHBSLogHBSLogF

LogLogPl −+−+−

++= )()(55.69.44)(82.131850

20)1850(9.333.46

Where If Kc > -5 Then

97.4))75.11((2.3 2 −= HCPELoga

Else

( ) ( )8.0)(56.17.0)(1.1 −−−= FLogHCPEFLoga

3.4 SPM model

The SPM model has been calibrated using measurements results at 3.5GHz. It is an extension of Cost-

Hata model, and it is used in Alcatel A9155 propagation tool. Typical values are the same than for

Cost-Hata.

( ) ( ) ( ) ( ) ( ) ( )clutterfKHKHdKlossnDiffractioKHKdKKL clutterRxeffTxeffTxeffel ++×+×+++= 654321mod loglog loglog

K1: constant offset (dB).

K2: multiplying factor for log(d).

d: distance between the receiver and the transmitter (m).

K3: multiplying factor for log(HTxeff).

HTxeff: effective height of the transmitter antenna (m).

K4: multiplying factor for diffraction calculation. K4 has to be a positive number.

Diffraction loss: loss due to diffraction over an obstructed path (dB).

K5: multiplying factor for log(HTxeff)log(d).

K6: multiplying factor for RxeffH.

RxeffH: effective mobile antenna height (m).

Kclutter: multiplying factor for f(clutter) (usually 1)

Propagation models



f(clutter): average of weighted losses due to clutter (Kc parameter)

SPM

Parameter

Value

calibrated

at 3.5GHz

K1 27.8

K2 44.9

K3 5.83

K4 1

K5 -6.55

K6 0

In A9155, the diffraction losses due to clutter height and DTM are taken into account (using Deygout

method (see part 2.4.2), Deygout with correction, Epstein-Peterson or Millington method). By default,

CPE and BS antenna height are not considered from the ground level but computed using the terrain

slope.

( ) ( ) dKHHHHH RxRxTxTxTxeff ×++−+= 00

where,

RxH is the receiver antenna height above the ground (m).

RxH0 is the ground height (ground elevation) above sea level at receiver (m).

K is the ground slope calculated over a user-defined distance (Distance min). In this case, Distance min

is a distance from receiver.

Moreover, two sets of K1 and K2 parameters can be defined far and close to the BS, ensuring calibration

of SPM model close to the BS (Cost-Hata model is not valid less than 1000m from the BS).

SPM standard model and has been calibrated at 3.5GHz. The model is valid with CPE below 10m and BS above 20m.

3.5 Comparison of statistical models at 3,5 GHz

Erceg models have been evaluated using measurements in typical suburban US area. Scope of Erceg

models is more “limited” than SPM model, which covers more morpho types. A comparison between the

propagation models is as follows:

Propagation models



Urban area

110,00

120,00

130,00

140,00

150,00

160,00

170,00

0 0,5 1 1,5 2 2,5

Distance (Km)

Pat

hlo

ss (

dB

)

SPM Dense Urban Skyscraper

SPM Dense Urban

ErcegA

ErcegA model is not adapted to dense urban environment.

SubUrban area

110,00

120,00

130,00

140,00

150,00

160,00

170,00

0 1 2 3 4 5 6

Distance (Km)

Pat

hlo

ss (d

B)

ErcegA

SPM Suburban

ErcegB

ErcegC

Erceg models are somehow representative of different kind of suburban environments.

Propagation models



Rural area

110,00

120,00

130,00

140,00

150,00

160,00

170,00

0 2 4 6 8 10 12 14

Distance (Km)

Pat

hlo

ss (d

B)

SPM Low Tree Density

SPM Agriculture

ErcegC

As for dense urban, Erceg models are not adapted to rural environments.

SPM standard model and has been calibrated at 3.5GHz. The model is valid far to the BS (>1000m), with CPE below 10m and BS above 20m.

3.6 Indoor penetration

As soon as indoor penetration is desired, NLOS radio conditions are encountered. Measurements have

been made for different materials, at different frequencies. Attenuation due to indoor penetration

depends on material type, angle of incidence, and frequency. However, there are no clear statements or

absolute law that gives the indoor penetration (see technical memo from PCS on “First Wall Penetration

losses”).

Different materials are not affected in the same way by the frequency; attenuation may have peaks in

some frequency bands.

Propagation models



Figure 5: Brick-masonry block wall with a peak at 1.8GHz

Usual values go from 12dB (in car rural area) to 22 or 25dB for deep indoor in dense urban area. In

case of multi-techno comparison, an additional margin between 7Log(F2/F1) and 15Log(F2/F1) could

be applied to the indoor penetration at F2 frequency.

Typical values of indoor penetration represent the first wall penetration; values could be different depending on the carrier frequency.

3.7 Indoor propagation models

Indoor propagation models are mainly used for WiFi hotspots. In case a database of the building is

available, a ray tracing propagation model can be used with A9155 and WinProp module.

In order to determine hotspot BoQ, an analytical model is used. General expression of the model,

function of distance d (in m):

)(104

20 dnLogLPi

LogPL ++

=λ

Recommended model in 802.11-00/162 for indoor propagation (offices with partitions and 1 wall) is:

)(333,184

20 dLogPi

LogPL ++

=λ

It has to be noted that typical 802.11g range with this model is around 25m, typical 802.11a range is

around 10m in the same conditions.

Some general parameters for WiFi propagation models:

Propagation models



Indoor propagation models are used in case the transmitter is close to the BS (8m< <300m), usually with low power transmissions.

End of DOCUMENT

broadband propagation models v4

Documents