Atoll RF Planning & Optimisation Software

Measurements and ModelCalibration Guide

v e r s i o n 2.8.2

AT282_MCG_E0~~

Contact Information

Atoll 2.8.2 Measurements and Model Calibration Guide Release AT282_MCG_E0

Copyright 1997 - 2010 by Forsk

The software described in this document is provided under a licence agreement. The software may only be used/copiedunder the terms and conditions of the licence agreement. No part of this document may be copied, reproduced ordistributed in any form without prior authorisation from Forsk.

The product or brand names mentioned in this document are trademarks or registered trademarks of their respectiveregistering parties.

IntroductionTo find an accurate propagation model for determining path losses is a leading issue when planning a mobile radionetwork. Two strategies for predicting propagation losses are in use these days. One of these strategies is to derive anempirical propagation model from measurement data, and the other is to use a deterministic propagation model. AtollsStandard Propagation Model is a macrocell propagation model based on empirical formulas and a set of parameters.

When Atoll is installed, the SPM and Hata model parameters are set to their default values. However, they can be adjustedto tune the propagation model according to actual propagation conditions. This calibration process of the StandardPropagation and Hata Models facilitates improving the reliability of path loss and, hence, coverage predictions.

This guide describes the way to import and manage the necessary measurement data. It also indicates the calibrationmethod and the steps to calibrating the SPM and Hata models, from planning the CW measurement surveys to obtainingthe final propagation model. The resulting tuned propagation model is directly usable in Atoll as an additional model.

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Table of ContentsTable of Contents

1 Introduction ..................................................................................... 11

2 Standard Propagation Model .......................................................... 152.1 SPM Formula.................................................................................................................................. 152.2 The Correspondence Between the SPM and Hata ..................................................... 15

2.2.1 Hata Formula.................................................................................................................................... 152.2.2 Correspondence Between Hata and SPM Parameters .................................................................... 16

2.2.2.1 Reducing the Hata and SPM Equations ..................................................................................... 162.2.2.2 Equating the Coefficients ............................................................................................................ 16

2.2.3 Typical SPM Parameter Values ....................................................................................................... 162.3 Making Calculations in Atoll .................................................................................................... 17

2.3.1 Visibility and Distance Between Transmitter and Receiver .............................................................. 172.3.2 Effective Transmitter Antenna Height............................................................................................... 17

2.3.2.1 Height Above Ground ................................................................................................................. 172.3.2.2 Height Above Average Profile..................................................................................................... 172.3.2.3 Slope at Receiver Between 0 and Minimum Distance ................................................................ 182.3.2.4 Spot Ht........................................................................................................................................ 182.3.2.5 Absolute Spot Ht......................................................................................................................... 182.3.2.6 Enhanced Slope at Receiver ...................................................................................................... 18

2.3.3 Effective Receiver Antenna Height................................................................................................... 202.3.4 Correction for Hilly Regions in Case of LOS .................................................................................... 212.3.5 Diffraction ......................................................................................................................................... 212.3.6 Losses Due to Clutter ....................................................................................................................... 212.3.7 Recommendations for Using Clutter with the SPM .......................................................................... 22

3 Collecting CW Measurement Data.................................................. 293.1 Before You Start............................................................................................................................ 29

3.1.1 Geographic Data .............................................................................................................................. 293.1.2 Measurement Data ........................................................................................................................... 29

3.2 Guidelines for CW Measurement Surveys ....................................................................... 303.2.1 Selecting Base Stations ................................................................................................................... 303.2.2 Planning the Survey Routes ............................................................................................................. 303.2.3 Radio Criteria ................................................................................................................................... 313.2.4 Additional Deliverable Data .............................................................................................................. 31

4 The Model Calibration Process....................................................... 354.1 Setting Up Your Calibration Project..................................................................................... 35

4.1.1 Creating an Atoll Calibration Document ........................................................................................... 354.1.1.1 Setting Coordinates .................................................................................................................... 364.1.1.2 Importing Geo Data .................................................................................................................... 36

4.1.2 Importing CW Measurements........................................................................................................... 364.1.2.1 Importing a CW Measurement Path ........................................................................................... 374.1.2.2 Importing Several CW Measurement Paths ............................................................................... 384.1.2.3 Creating a CW Measurement Import Configuration.................................................................... 404.1.2.4 Defining the Display of CW Measurements ................................................................................ 41

4.1.3 Verifying the Correspondence Between Geo and Measurement Data ............................................ 434.1.4 Filtering Measurement Data ............................................................................................................. 44

4.1.4.1 Filtering on Clutter Classes......................................................................................................... 454.1.4.2 Signal and Distance Filtering ...................................................................................................... 46

4.1.4.2.1 Typical Values....................................................................................................................... 464.1.4.2.2 Using Manual Filtering on CW Points ................................................................................... 464.1.4.2.3 Creating an Advanced Filter.................................................................................................. 474.1.4.2.4 Using the Filtering Assistant on CW Measurement Points.................................................... 48

4.1.4.3 Filtering by Geo Data Conditions................................................................................................ 504.1.4.3.1 About Diffraction ................................................................................................................... 504.1.4.3.2 About Specific Sections ........................................................................................................ 504.1.4.3.3 About Potentially Invalid Measurement Levels ..................................................................... 51 Forsk 2010 Unauthorized reproduction or distribution of this document is prohibited 5

Atoll User Manual4.1.4.3.4 Deleting a Selection of Measurement Points .........................................................................534.1.4.3.5 Using Filtering Zones on CW Measurement Points ...............................................................544.1.4.3.6 Filtering by Angle ...................................................................................................................54

4.1.5 Selecting Base Stations for Calibration and for Verification..............................................................554.2 Calibrating the SPM .....................................................................................................................55

4.2.1 Quality Targets..................................................................................................................................554.2.2 Setting Initial Parameters in the SPM ...............................................................................................56

4.2.2.1 Parameters Tab...........................................................................................................................564.2.2.2 Clutter Tab...................................................................................................................................57

4.2.3 Running the SPM Calibration Process..............................................................................................594.2.3.1 The Automatic Calibration Wizard ...............................................................................................604.2.3.2 The Assisted Calibration Wizard .................................................................................................61

4.3 Calibrating Hata Models.............................................................................................................624.3.1 Quality Targets..................................................................................................................................624.3.2 Setting Initial Parameters in the Hata Models ...................................................................................63

4.3.2.1 Defining General Settings ...........................................................................................................634.3.2.2 Selecting an Environment Formula .............................................................................................634.3.2.3 Creating or Modifying Environment Formulas .............................................................................64

4.3.3 Running the Hata Calibration Process ..............................................................................................644.4 Analysing the Calibrated Model .............................................................................................664.5 Finalising the Settings of the Calibrated SPM.................................................................714.6 Deploying the Calibrated Model .............................................................................................73

4.6.1 Copying a Calibrated Model to Another Document...........................................................................734.6.2 Deploying a Calibrated Model to Transmitters ..................................................................................74

5 Additional CW Measurement Functions ..........................................775.1 Creating a CW Measurement Path ......................................................................................775.2 Drawing a CW Measurement Path .......................................................................................785.3 Merging Measurement Paths for a Same Transmitter................................................785.4 Smoothing Measurements to Reduce the Fading Effect ...........................................785.5 Calculating Best Servers Along a CW Measurement Path ......................................79

5.5.1 Adding Transmitters to a CW Measurement Path.............................................................................795.5.2 Selecting the Propagation Model ......................................................................................................795.5.3 Setting the Display to Best Server ....................................................................................................805.5.4 Calculating Signal Levels ..................................................................................................................805.5.5 Displaying Statistics Over a Measurement Path ...............................................................................805.5.6 Displaying Statistics Over Several Measurement Paths ...................................................................80

6 Survey Site Form.............................................................................856 Unauthorized reproduction or distribution of this document is prohibited Forsk 2010

List of FiguresList of Figures

Figure 2.1 Enhanced Slope at Receiver ..................................................................................................................... 18Figure 2.2 Losses due to Clutter................................................................................................................................. 22Figure 2.3 Setting losses per clutter class .................................................................................................................. 23Figure 2.4 Tx-Rx profile .............................................................................................................................................. 23Figure 2.5 Settings when using clutter heights set per class ...................................................................................... 24Figure 2.6 Diffraction caused by surrounding buildings when the receiver is indoors ................................................ 24Figure 2.7 Clutter class settings when using a clutter height file ................................................................................ 25Figure 4.1 The Setup tab of the Import of Measurement Files dialogue..................................................................... 37Figure 4.2 Defined thresholds as they will appear in the Legend ............................................................................... 43Figure 4.3 Distribution of the Measured Signal Strength around a station ................................................................. 44Figure 4.4 Point distribution in the different clutter classes......................................................................................... 45Figure 4.5 Filtering Assistant Launching..................................................................................................................... 48Figure 4.6 Point Selection Tool in the Filtering Assistant............................................................................................ 49Figure 4.7 Point Exclusion Tool in the Filtering Assistant ........................................................................................... 49Figure 4.8 Point Analysis Tool window showing diffraction peaks.............................................................................. 50Figure 4.9 Distribution of the point positions around a station .................................................................................... 51Figure 4.10 The CW Measurement Analysis Tool window ........................................................................................... 52Figure 4.11 Simultaneous display of measurement path and table .............................................................................. 53Figure 4.12 Angular Filter around a station................................................................................................................... 55Figure 4.13 SPM Transmitter effective height method selection .................................................................................. 56Figure 4.14 Calculating the total clutter loss between the transmitter and the receiver................................................ 58Figure 4.15 Comparative behaviour of the clutter weighting functions in the SPM....................................................... 58Figure 4.16 Calibration launching on SPM model......................................................................................................... 59Figure 4.17 Path and Calibration method selection for SPM Calibration...................................................................... 60Figure 4.18 Range definition for SPM parameters during calibration ........................................................................... 60Figure 4.19 SPM Comparative Calibration Results ...................................................................................................... 61Figure 4.20 Table listing the correlation of the SPM variables to the global error ........................................................ 62Figure 4.21 Calibration launching on Hata models ....................................................................................................... 65Figure 4.22 Path and Calibration method selection for SPM Calibration...................................................................... 65Figure 4.23 Range definition for SPM parameters during calibration ........................................................................... 66Figure 4.24 Hata Models Comparative Calibration Results .......................................................................................... 66Figure 4.25 Selecting the calibrated model for all CW measurement paths ................................................................. 67Figure 4.26 Calculating the signal levels on all CW measurement paths ..................................................................... 67Figure 4.27 Selecting on of the verification stations for the statistics ........................................................................... 68Figure 4.28 Comparative statistics of the verification stations ...................................................................................... 68Figure 4.29 Distribution of error around a verification station ....................................................................................... 69Figure 4.30 Opening the CW Measurement Analysis tool ............................................................................................ 70Figure 4.31 CW Measurement Analysis ....................................................................................................................... 71Figure 4.32 Description of the available clutter classes................................................................................................ 73Figure 5.1 The New CW Measurement Path dialogue ............................................................................................... 77Figure 5.2 Sliding Window Property Dialogue ............................................................................................................ 79 Forsk 2010 Unauthorized reproduction or distribution of this document is prohibited 7

Atoll User Manual8 Unauthorized reproduction or distribution of this document is prohibited Forsk 2010

Chapter 1

AtollRF Planning & Optimisation Software

Introduction

10 Unauthorized reproduction or distribution of this document is prohibited

Measurements and Model Calibration Guide

Chapter 1: Introduction1 IntroductionThe Model Calibration Guide is intended for project managers or anyone else responsible for calibrating the StandardPropagation Model (SPM) or Hata Models (Okumura-Hata and Cost-Hata) using continuous wave (CW) measurements.To that end, the Model Calibration Guide presents you with detailed information on the SPM and guides you through thecalibration process of both types of models.

It is not the intention of this guide to explain in detail how to use Atoll, nor to provide detailed technical information aboutAtoll projects. For information on using Atoll, see the User Manual and the Administrator Manual. For detailed technicalinformation about Atoll projects, see the Technical Reference Guide.

The Model Calibration Guide follows the calibration process from planning the CW survey, to incorporating the CW meas-urements into Atoll, to using the CW measurements to calibrate the SPM.

If this is the first time you are calibrating Atolls SPM, you might want to read though the entire Model Calibration Guide.Or, you can go directly to the chapter that interests you:

The Standard Propagation Model: This chapter describes the Atoll SPM, including the SPM formula and theHata formula on which the SPM is based. Other aspects described include, typical SPM parameter values, makingcalculations using the SPM, and recommendations for using the SPM.

CW Measurements: This chapter explains the role of CW measurements in calibrating the SPM. It also gives youinformation that will help you successfully plan and carry out a CW survey.

The Model Calibration Process: This chapter explains the entire calibration process for any model type:

- Creating an Atoll document that to use to calibrate a propagation model.- Importing the measurements from the CW survey into the new Atoll document.- Filtering the imported CW measurements to ensure that you are using only the most relevant data.- Calibrating the SPM or Hata Models, using either the automatic or the assisted method (SPM only).- Finalising and deploying the calibrated model.

This guide also contains an appendix with additional information on using CW measurements in Atoll.Unauthorized reproduction or distribution of this document is prohibited 11

Measurements and Model Calibration Guide12 Unauthorized reproduction or distribution of this document is prohibited

Chapter 2

AtollRF Planning & Optimisation Software

Standard Propagation Model

14 Unauthorized reproduction or distribution of this document is prohibited

Technical Reference Guide

Chapter 2: Standard Propagation Model2 Standard Propagation ModelThe Standard Propagation Model is a propagation model based on the Hata formulas and is suited for predictions in the150 to 3500 MHz band over long distances (from one to 20 km). It is best suited to GSM 900/1800, UMTS, CDMA2000,WiMAX, and LTE radio technologies.

2.1 SPM FormulaThe Standard Propagation Model is based on the following formula:

where:

received power (dBm)

transmitted power (EIRP) (dBm)

constant offset (dB)

multiplying factor for

distance between the receiver and the transmitter (m) multiplying factor for

effective height of the transmitter antenna (m)

multiplying factor for diffraction calculation. must be a positive number.

losses due to diffraction over an obstructed path (dB) multiplying factor for

multiplying factor for

multiplying factor for

effective height of the receiver antenna (i.e., mobile antenna height) (m)

multiplying factor for

average of weighted losses due to clutter corrective factor for hilly regions (=0 in case of NLOS)

2.2 The Correspondence Between the SPM and HataIn this section, the Hata formula on which the SPM is based is described. The correspondence between the SPM and theHata formula is also described.

2.2.1 Hata FormulaThe SPM formula is derived from the basic Hata formula, which is:

where,

, , , , , Hata parameters

Frequency in MHz Effective BS antenna height in metres

Distance in kilometres Mobile antenna height correction function

Clutter correction function

Typical values for Hata model parameters are:

A1 = 69.55 for 900 MHz, A1 = 46.30 for 1800 MHz

PR PTxK1 K2 Log d( ) K3 Log HTxeff( ) K4 DiffractionLoss K5 Log d( ) Log HTxeff( ) + + + + +K6 HRxeff K7 Log HRxeff( ) Kclutter f clutter( ) Khill LOS,+ + + =

PRPTxK1K2 Log d( )dK3 Log HTxeff( )HTxeffK4 K4DiffractionLossK5 Log d( ) Log HTxeff( )K6 HRxeffK7 Log HRxeff( )HRxeffKclutter f clutter( )f clutter( )Khill LOS,

Note: The distance in this equation is given in kilometres as opposed to the SPM, where the distance is given in metres.

L A1 A2 flog A3 hBSlog B1 B2 hBSlog B3hBS+ +( ) dlog a hm( ) Cclutter+ + +=

A1 A2 A3 B1 B2 B3fhBSda hm( )CclutterUnauthorized reproduction or distribution of this document is prohibited 15

Technical Reference Guide A2 = 26.16 for 900 MHz, A2 = 33.90 for 1800 MHz A3 = 13.82 B1 = 44.90 B2 = 6.55 B3 = 0

2.2.2 Correspondence Between Hata and SPM ParametersIn this section, the Hata and SPM parameters are compared.

2.2.2.1 Reducing the Hata and SPM EquationsBecause you are only dealing with standard formulas, you can ignore the influence of diffraction and clutter correction. Itis understood that, with appropriate settings of A1 and K1, and taking only one clutter class into consideration, you can setthe clutter correction factor to zero without reducing the validity of the following equations.

The correction function for mobile antenna height can also be ignored. The mobile antenna height correction factor is zerowhen hm=1.5 m, and has negligible values for realistic mobile antenna heights. The B3 parameter is usually not used andcan be considered to be 0.

The Hata formula can now be simplified to:

where:

, , , , , Hata parameters

Frequency in MHz Effective BS antenna height in metres

Distance in kilometres

The SPM formula can be simplified to:

If you rewrite the Hata equation using with the distance in metres as in the SPM formula, you get:

This leads to the following equation:

2.2.2.2 Equating the CoefficientsIf you compare the simplified Hata and SPM equations, you see the following correspondence between the coefficients:

2.2.3 Typical SPM Parameter ValuesBy referring to typical Hata parameters, typical SPM parameters can be determined as the following:

K1 depends on the frequency, some examples are:

L A1 A2 flog A3 hBSlog B1 B2 hBSlog+( ) dlog+ + +=

A1 A2 A3 B1 B2fhBSd

L K1 K2 dlog K3 hBSlog K5 dlog hBSlog K6hmeff K7Log hmeff( )+ + + + +=

L A1 A2 flog A3 hBSlog B1 B2 hBSlog+( ) d1000-------------log+ + +=

L A1 A2 flog 3 B1 A3 3 B2( ) hBSlog B1 dlog B2 hBSlog dlog++ + +=

K1 A1 A2 flog 3 B1+=K2 B1=

K3 A3 3 B2=K5 B2=

K6 0=K7 0=

Project type Frequency (MHz) K1GSM 900 935 12.5

GSM 1800 1805 22GSM 1900 1930 23

UMTS 2110 23.8

K2 44.90=K3 5.83=K5 6.55=16 Unauthorized reproduction or distribution of this document is prohibited

Chapter 2: Standard Propagation Model2.3 Making Calculations in AtollIn this section, the different aspects of making calculations using the SPM are explained in detail:

"Visibility and Distance Between Transmitter and Receiver" on page 17 "Effective Transmitter Antenna Height" on page 17 "Effective Receiver Antenna Height" on page 20 "Correction for Hilly Regions in Case of LOS" on page 21 "Diffraction" on page 21 "Losses Due to Clutter" on page 21 "Recommendations for Using Clutter with the SPM" on page 22.

2.3.1 Visibility and Distance Between Transmitter and ReceiverFor each calculation pixel, Atoll determines:

The distance between the transmitter and the receiver.

- If the transmitter-receiver distance is less than the maximum user-defined distance (the break distance), thereceiver is considered to be near the transmitter. Atoll will use the set of values called Near transmitter.

- If the transmitter-receiver distance is greater than the maximum distance, the receiver is considered far fromthe transmitter. Atoll will use the set of values called Far from transmitter.

Whether the receiver is in the transmitter line of sight or not.

- If the receiver is in the transmitter line of sight, Atoll will take into account the set of values (K1, K2)LOS. TheLOS is defined by no obstruction along the direct ray between the transmitter and the receiver.

- If the receiver is not in the transmitter line of sight, Atoll will use the set of values (K1, K2)NLOS.

2.3.2 Effective Transmitter Antenna HeightThe effective transmitter antenna height (HTxeff) can be calculated using one of six different methods:

"Height Above Ground" on page 17 "Height Above Average Profile" on page 17 "Slope at Receiver Between 0 and Minimum Distance" on page 18 "Spot Ht" on page 18 "Absolute Spot Ht" on page 18 "Enhanced Slope at Receiver" on page 18.

2.3.2.1 Height Above GroundThe transmitter antenna height is its height above the ground (HTx in metres).

2.3.2.2 Height Above Average ProfileThe transmitter antenna height is determined relative to an average ground height calculated along the profile between atransmitter and a receiver. The profile length depends on the minimum distance and maximum distance values and islimited by the transmitter and receiver locations. Distance min. and Distance max are minimum and maximum distancesfrom the transmitter respectively.

where,

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

is the average ground height above sea level along the profile (m).

1xRTT 1900 23

WiMAX

2300 24.7

2500 25.4

2700 26.1

3300 27.8

3500 28.3

HTxeff HTx=

Note: If the profile is not located between the transmitter and the receiver, HTxeff equals HTx only.

HTxeff HTx H0Tx H0( )+=

H0TxH0Unauthorized reproduction or distribution of this document is prohibited 17

Technical Reference Guide2.3.2.3 Slope at Receiver Between 0 and Minimum DistanceThe transmitter antenna height is calculated using the ground slope at the receiver.

where,

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

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

2.3.2.4 Spot HtIf then,

If then,

2.3.2.5 Absolute Spot Ht

These values are only used in the last two methods and have different meanings for each method.

2.3.2.6 Enhanced Slope at ReceiverAtoll offers a new method called Enhanced slope at receiver to evaluate the effective transmitter antenna height.

The X-axis and Y-axis represent positions and heights respectively. It is assumed that the X-axis is oriented from the trans-mitter (origin) towards the receiver.

This calculation is made in several steps:

1. Atoll determines line of sight between the transmitter and the receiver.

The LOS line equation is:

where,

Notes:

If , Atoll uses 20 m in calculations.

If , Atoll takes 200 m.

HTxeff HTx H0Tx+( ) H0Rx K d+=

H0RxK

HTxeff 20m

H0Tx H0Rx> HTxeff HTx H0Tx H0Rx( )+=H0Tx H0Rx HTxeff HTx=

Note: Distance min. and distance max are set to 3000 and 15000 m following ITU recommendations (low frequency broadcast f < 500 Mhz) and to 0 and 15000 m following Okumura recommendations (high frequency mobile telephony).

HTxeff HTx H0Tx H0Rx+=

Figure 2.1Enhanced Slope at Receiver

Los i( ) H0Tx HTx+( )H0Tx HTx+( ) H0Rx HRx+( )( )

d-------------------------------------------------------------------------------Res i( )=18 Unauthorized reproduction or distribution of this document is prohibited

Chapter 2: Standard Propagation Model- is the receiver antenna height above the ground (m).- i is the point index.- Res is the profile resolution (distance between two points).

2. Atoll extracts the transmitter-receiver terrain profile.

3. Hills and mountains are already taken into account in diffraction calculations. Therefore, in order for them not tonegatively influence the regression line calculation, Atoll filters the terrain profile.

Atoll calculates two filtered terrain profiles; one established from the transmitter and another from the receiver. Itdetermines the filtered height of every profile point. Profile points are evenly spaced on the basis of the profile reso-lution. To determine the filtered terrain height at a point, Atoll evaluates the ground slope between two points andcompares it with a threshold set to 0.05; where three cases are possible.

Some notations defined hereafter are used in next part.

- is the filtered height.

- is the original height. The original terrain height is determined from extracted ground profile.

When filtering starts from the transmitter:

Let us assume that

For each point, there are three different possibilities:

a. If and ,

Then,

b. If and

Then,

c. If

Then,

If, as well,

Then,

When filtering starts from the receiver:

Let us assume that

For each point, there are three different possibilities:

a. If and ,

Then,

b. If and

Then,

c. If

Then,

If, as well,

Then,

Then, for every point of profile, Atoll compares the two filtered heights and chooses the higher one.

4. Atoll determines the influence area, R. It corresponds to the distance from receiver at which the original terrainprofile plus 30 metres intersects the LOS for the first time (when beginning from transmitter).

The influence area must satisfy additional conditions:

- ,- ,

HRx

HfiltHorig

Hfilt Tx Tx( ) Horig Tx( )=

Horig i( ) Horig i 1( )>Horig i( ) Horig i 1( )

Res------------------------------------------------------ 0.05

Hfilt Tx i( ) Hfilt Tx i 1( ) Horig i( ) Horig i 1( )( )+=

Horig i( ) Horig i 1( )>Horig i( ) Horig i 1( )

Res------------------------------------------------------ 0.05>

Hfilt Tx i( ) Hfilt Tx i 1( )=

Horig i( ) Horig i 1( )Hfilt Tx i( ) Hfilt Tx i 1( )=

Hfilt i( ) Horig i( )>

Hfilt Tx i( ) Horig i( )=

Hfilt Rx( ) Horig Rx( )=

Horig i( ) Horig i 1+( )>Horig i( ) Horig i 1+( )

Res------------------------------------------------------- 0.05

Hfilt Rx i( ) Hfilt Rx i 1+( ) Horig i( ) Horig i 1+( )( )+=

Horig i( ) Horig i 1+( )>Horig i( ) Horig i 1+( )

Res------------------------------------------------------- 0.05>

Hfilt Rx i( ) Hfilt Rx i 1+( )=

Horig i( ) Horig i 1+( )Hfilt Rx i( ) Hfilt Rx i 1+( )=

Hfilt i( ) Horig i( )>

Hfilt Rx i( ) Horig i( )=

Hfilt i( ) max Hfilt Tx i( ) Hfilt Rx i( ),( )=

R 3000mR 0.01 dUnauthorized reproduction or distribution of this document is prohibited 19

Technical Reference Guide- R must contain at least three pixels.

5. Atoll performs a linear regression on the filtered profile within R in order to determine a regression line.

The regression line equation is:

and

where,

i is the point index. Only points within R are taken into account.

d(i) is the distance between i and the transmitter (m).

Then, Atoll extends the regression line to the transmitter location. Its equation is:

6. Then, Atoll calculates the effective transmitter antenna height, (m).

If HTxeff is less than 20 m, Atoll recalculates it with a new influence area, which begins at the transmitter.

7. If is less than 20 m (or negative), Atoll evaluates the path loss using and applies a cor-rection factor.

Therefore, if ,

where,

2.3.3 Effective Receiver Antenna Height

where,

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

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

Notes:

When several influence areas are possible, Atoll chooses the highest one. If d < 3000m, R = d.

Notes:

If , 1000m will be used in calculations.

If is less than 20 m, an additional correction is taken into account (step 7).

y ax b+=

a

d i( ) dm( ) Hfilt i( ) Hm( )i

d i( ) dm( )2i

------------------------------------------------------------------------=

b Hm adm=

Hm1n--- Hfilt i( )

i=

dm dR2----=

regr i( ) a i Res( ) b+=HTxeff

HTxeffH0Tx HTx b+

1 a2+--------------------------------------=

HTxeff 1000m>HTxeff

HTxeff HTxeff 20m=

HTxeff 20m