GSM Static Simulations

8/10/2019 GSM Static Simulations

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GSMSTATIC SIMULATIONS

V8.1

ALGORITHMS AND OUTPUTS RELATING TO THE

SIMULATOR


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GSM Static SimulationsV 8.1

Copyright 2013 AIRCOM International Ltd.2

Copyright 2013 AIRCOM International Ltd

All rights reserved

This document is supplementary to the User Reference Guides, and is protected by copyright and

contains proprietary and confidential information. No part of the contents of this documentation may be

disclosed, used or reproduced in any form, or by any means, without the prior written consent of

AIRCOM International.Although AIRCOM International has collated this documentation to reflect the features and capabilities

supported in the software products, the company makes no warranty or representation, either expressedor implied, about this documentation, its quality or fitness for particular customer purpose. Users are

solely responsible for the proper use of ENTERPRISE software and the application of the results

obtained.

AIRCOM International Ltd

Cassini CourtRandalls Research Park

Randalls Way

Leatherhead

Surrey KT22 7TW

ENGLAND

Telephone: +44 (0) 1932 442000

Support Hotline: +44 (0) 1932 442345

Fax: +44 (0) 1932 442005

Web: http://www.aircominternational.com

VERSION HISTORY

Version Date Author Comments1.0 28/09/2007 A. Panman First version.

1.1 18/01/2007 A. Lodhi Corrected DL RSS equation.1.2 12/10/2011 A. Lawrow Version 8.0.

1.3 14/06/2013 V. Kontogeorgos Version 8.1

Added Coverage Probability OK arrayUpdated Nth DL Loss array description

Added Composite Tech arrays

Added Terminal Info Tech Type arrays


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Copyright 2013 AIRCOM International Ltd. 3

CONTENTS

1 What Is A Snapshot?........................................................................................................... ........ 41.1 Randomness in a Cellular Network .................................................................................. 41.2

Time-averaging in Coverage Evaluations........................ ................................................. 7

1.3

Time-averaging in Capacity Evaluations ....................................................... ................... 7

1.4

Why Produce Snapshots? .............................................................. ...................................... 7

1.5 Activity Factors..................................................................................................................... 82 Formulae ...................................................... .............................................................. ................... 9

2.1 Notation ........................................................... .............................................................. ........ 92.2

List of Principal Symbols .................................................................................................... 9

2.3 Downlink Power Formulae .................................... .......................................................... 113 Snapshot Overview.......................................................................................... ......................... 15

3.1

Random Terminal Distribution ............................................................... ......................... 15

3.2 Time-Slot Iterations ............................................................. ............................................... 163.3 Convergence Test ...................................................................................... ......................... 163.4

Gathering Of Results ............................................... .......................................................... 16

4 Connection Evaluation in a Snapshot .......................................................... ......................... 174.1

Connection Scenario Prioritisation ................................................................. ................. 17

4.2

GSM Downlink Evaluation ........................................................... .................................... 17

4.3 Failure Reasons ......................................................... .......................................................... 185 Output Arrays ........................................................ .............................................................. ...... 19

5.1

Array dependencies ..................................................................................................... ...... 19

Pathloss Arrays .................................................................................................... ............................ 205.2

Coverage and Data Rate Arrays .............................................................. ......................... 20

5.3 Composite Tech Arrays ............................................................................................... ...... 215.4 Terminal Info Arrays ............................................................................. ............................ 21

6 Coverage Array Calculations ...................................................................... ............................ 236.1

Notation ........................................................... .............................................................. ...... 23

6.2 Fades in the Simulation Snapshots ......................................................... ......................... 236.3

Fades in Arrays for Mean Values ............................................................ ......................... 24

6.4 Fades in Coverage Array Calculations .............................................................. .............. 24


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1 WHAT IS ASNAPSHOT?

1.1 RANDOMNESS IN A CELLULAR NETWORK

In a simulation of a cellular network there are two main types of randomness that one needs to

consider.

Spatial randomness in the location of terminals.

Temporal randomness in the activity of terminals.

We shall consider the spatial domain to be discrete and consisting of a large number of pixels (bins)

some of which will contain terminals. Each possible pattern of terminal locations has an associatedprobability of occurrence. We can label these spatial patterns X1, X2, etc and represent the

corresponding probabilities of occurrence by P(X1),P(X2), etc. An example of two spatial patternsX1andX2 is shown below.

X1 X2

Each spatial pattern has many possible configurations of transmitting and non-transmitting terminals.

Two such configurations for the spatial patterns X1 and X2 are shown below, with 1 representing a

transmitting terminal, and 0 a non-transmitting terminal.

(X1,T1) (X2,T1)

(X1,T2) (X2,T2)

X

X

X

X

X

X XX

X

X

X

X

X

1

1

0

0

0

1 10

1

0

1

0

1

1

0

1

0

0

1 01

0

1

0

0

0


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We call each of these patterns a spatio-temporal pattern to highlight the fact that we have specified

spatial locations of terminals and also their temporal state (transmitting/non-transmitting). We can

label the spatio-temporal patterns for spatial pattern X1 as follows (X1,T1), (X1,T2), etc and their

probabilites of occurrenceP(X1,T1),P(X1,T2), etc. Note that the probability of occurrence of a spatio-

temporal pattern (Xi,Tj) is proportional to the probability of occurrence of the spatial pattern Xi:

P(Xi,Tj)= P(Xi) P(Tj| Xi).

One can think of a spatio-temporal pattern as being a picture of a real network at a random instant intime. This is what most people have in mind when one mentions a simulation snapshot, but a

snapshot in our simulator represents something slightly different, as explained below.

The idealstatic simulation would calculate an average quantity (e.g. the average traffic load on a cell)

by performing a weighted sum over the set of all possible spatio-temporal patterns (Xi,Tj), with the

weight for a pattern being its probability of occurrence. So the average of some quantity F would begiven by

ji TX

jiji TXPTXFF

,

),(),( . (1a)

We can split this into separate spatial and temporal sums:

i jX

ij

T

jii XTPTXFXPF )|(),()( . (1b)

The summations in (1a) and in (1b) are over every conceivable pattern of terminal locations and

activities, including the unlikely ones, so clearly some simplifications are necessary in any practical

static simulator.

Simplification 1: Model spatialrandomnessexplicitl yby sampling.

This simplification is the most common one made in static simulations, and it is used universally.

Instead of considering allspatial patterns, we consider a set of Nsample spatial patterns drawn from

the distribution of all spatial patterns. The first weighted sum in (1b) can then be approximated by a

simple average over the set of Nsample spatial patterns:

i jX

ij

T

ji XTPTXFN

F )|(),(1

.

Spatial randomness is therefore handled explicitlyby considering a set of sample spatial patterns that

have been selected in a random and unbiased way. There is still the issue of how to handle the

different temporal states for each sample spatial pattern. There are two main approaches we can use:

Model temporal randomness explicitlyby sampling. (Simplification 2).

Model temporal randomness implicitlywith time-averages. (Simplification 3).

Simplification 2: Model temporalrandomnessexplicitl yby sampling.

This simplification is fairly common but has some drawbacks as explained below. Firstly, as in theprevious simplification, one selects a sample spatial pattern from the set of all possible spatial patterns,

making sure that the selection is made in a random and unbiased way. One then assigns a random

activity flag (1 or 0) to each terminal in the pattern, to indicate if the terminal is transmitting or not.

The probability of assigning a 1 to a terminal is just the service activity factor for that terminal. This

ensures that activity flags are assigned in a random and unbiased way. The weighted sum over the set

of all spatio-temporal patterns in (1a) can be approximated by a simple average over the set of N

sample spatio-temporal patterns:


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ji TX

ji TXFN

F

,

),(1

.

If we called a spatio-temporal pattern a snapshot then the above formula simply says that we can

approximate F by performing a simple average over the snapshots. This simple average worksbecause the sample spatio-temporal patterns are selected in a random and unbiased way. Also note that

this averaging explicitly accounts for spatial randomness and explicitly accounts for temporal

randomness.

There are problems with assigning activity flags to terminals however.

For low activity services, the user can do 100s of snapshots and never set an activity flag, and

therefore certain outputs may not have any results. For example, a simulation report may say

that many users are served on a cell but that there is no throughput on the cell. Forcing theuser to run 1000s of snapshots is unacceptable in a commercial tool, so we either have to

remove the problem outputs or calculate them some other way.

Activity flags are set when the terminals are created. For multi-rate packet-switched (PS)services, different bearers can have different activity factors. Since we do not know which

bearer a multi-rate terminal will ultimately use, we have to define a setof activity flags, one

flag for every bearer that the terminal may use. This is conceptually horrible, and can lead to

convergence issues during iterations.

For the above reasons, we do notuse Simplification 2 and use the following simplification instead.

Simplification 3: Model temporalrandomnessimplicitlywith time-averages.

As before, one selects a sample spatial pattern from the set of all possible spatial patterns, but now we

completely remove the activity flags from the randomly scattered terminals. Each terminal is therefore

neither instantaneously active nor instantaneously inactive, but rather represents a sort of time -averaged entity. Essentially, this means that when we examine the interference that the terminal

produces, or the resources it consumes, we use the time-averages for these quantities, and we calculate

these time-averages implicitlyby using activity factors to scale things.

So in our simulator, a snapshot does not represent a random instant in time for a random distribution

of terminals, but rather the average instant in time for a random distributi on of terminals. The

snapshot represents the average instant because all the measures of system load (i.e. DL interference,

time-slot usage and throughput) are time-averages.

It is still valid to perform simple averages of quantities over our snapshots. However, averaging over

the snapshots now explicitly accounts for spatial randomness only. The temporal randomness is now

handled implicitly within each snapshot through the use of time-averages in our calculations. Time-

averages feature in the evaluation of both coverage and capacity as described below.


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1.2 TIME-AVERAGING IN COVERAGE EVALUATIONS

All our link budgets (in SI units, not dB) are essentially of the form

E = (P / L ) /N,

where

E= signal to interference ratio for the link in a period ofactivity,

P= TX power in a period ofactivity,L= linkloss,

N= time-averageRX interference on the link.

To check for coverage, we set P to the maximum allowed link power and check that E meets

requirements. In other words we examine the link assuming it is active. The time-averaging affects the

coverage evaluation only because we use the time-average interferenceNin the link-budget.

1.3 TIME-AVERAGING IN CAPACITY EVALUATIONS

When evaluating capacity, we use time-average quantities only.

The downlink capacity constraint is that the time-averagenumber of time-slots consumed on the sub-

cell must not exceed the number of time-slots available on the sub-cell.

Time-averages are calculated by scaling time-slots by activity factors. (Note that the activity factor for

a circuit switched (CS) resource is always 100%, regardless of the service activity factor.)

The snapshot contains no information about the instants of time at which links are active. Only two

things are known about each link:

The time-slots required to service the link in a period of activity.

The time-average interference and time-average time-slot consumption that the link produces

in the system.

1.4 WHY PRODUCE SNAPSHOTS?

The main purpose of a snapshot is to provide us with measures of system load. In particular, each

snapshot tells us:

The total number of time-slots consumed on each sub-cell.

The total DL interference power on each sub-cell.

By running many snapshots, we obtain values for these quantities for different spatial distributions ofterminals, and can then proceed to analyse DL coverage for the system.


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1.5 ACTIVITY FACTORS

As explained in previous sections, activity factors are used to calculate implicit time-averages for

bearers in a simulation snapshot.

The time-slot activity factor is used to calculate the time-average time-slot consumption for a

packet-switched link.

Time-average Time-Slots = Bearer Activity x Time-Slots when Active.

Circuit-switched (CS) services consume time slots even during periods of inactivity. Therefore CS

connections are assumed to have an activity factor of 100%. A CS connection can use either a full-rate

or half-rate bearer corresponding to one time-slot or half a time-slot respectively. Which bearer is

selected depends on the achieved traffic C/I, whether the bearer supports half-rate connections and the

sub-cell traffic load.

PS Activity Factor Calculation

For a PS service, the tool automatically calculates the power-activity factor from the PS parameters in

the service definition:

userR User bitrate (bps).

bytesN Number of bytes per packet.

packetsN Number of packets per packet call.

callsN Number of packet calls per session.

readT Reading time (s).

interT Inter-arrival time between packets (s).

BLER-1

BLERr Retransmission factor ( 10 r ) in terms of BLER.

Active time: usercallspacketsbytesactive /)1(8 RrNNNT

Inactive time: )1()1(1)-( interpacketscallsreadcallsinactive rTNNTNT

Session time: inactiveactivesession TTT

Activity factor:session

active

T

T


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2 FORMULAE

2.1 NOTATION

Symbols in subsequent sections use the following notation.

A lowercase Greek subscript always indexes a carrier.

indicates a sum over all carriers.

An uppercase Roman subscript always indexes a sub-cell.

J

indicates a sum over all sub-cells.

A lowercase Roman subscript always indexes a terminal.

k

indicates a sum over all terminals.

Jk

indicates a sum over all terminals in sub-cellJ.

Unless stated otherwise, all quantities and formulae are in standard SI units, not in dB.

2.2 LIST OF PRINCIPAL SYMBOLS

B Bandwidth (Hz).hop

SkE Bit-Error-Rate of the average hopping carrier.hop-non

SkE Bit-Error-Rate of the average non-hopping carrier.

controlCINR Sk Averaged control CINR.

controlCINR Sk Control CINR for a single carrier.

traffCINR Sk Averaged traffic CINR.

traffCINR Sk Traffic CINR for a single carrier.diversity

G Diversity gain.antenna

SG Sub-cell antenna gain.

k Boltzmanns constant.pathloss

SkL Pathloss between sub-cell and terminal.antenna

SkL Antenna masking loss.

feederSL Feeder loss.equipSL Cell equipment loss

correctionantennaSL Antenna correction factor

correctioncellSL Cell correction factorindoorkL Indoor loss (= 1 for outdoor terminals).

hop

Sn Number of hopping carriers.hop-non

Sn Number of non-hopping carriers.thermal

kN Thermal noise power for terminal k.EIRP

SP EIRP for sub-cell S.output

SP Output power for sub-cell S.


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received

SkP Received signal strength for sub-cell Sand terminal k.hopTRX

SN Number of hopping transmitters.

hop-nonTRX

SN Number of non-hopping transmitters ( =hop-non

Sn ).

T Temperature in Kelvin.

slotST Number of timeslots in use on sub-cell S.FR

ST Number of full rate time slots.

CS

ST Number of circuit-switched time slots available on sub-cell S.

GPRS

ST Number of GPRS time slots available on sub-cell S.DTX

S Discontinuous transmission factor.

adj Adjacent carrier interference factor (from the array settings dialog).traff

S Traffic loading factor.frac

S Fractional loading factor.

k Noise figure for terminal k.


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2.3 DOWNLINK POWER FORMULAE

DL Received Signal Strength

The received signal strength for sub-cell Sand terminal kis calculated as:

indoorantennapathloss

EIRPreceived 11

kSkSk

SSkLLL

PP (2)

where

correctioncellcorrectionantennaequipfeeder

antennaoutputEIRP

SSSS

SSS

LLLL

GPP

The productantennapathloss

SkSk LL is read from the prediction file. The received signal strength must meet the

receiver sensitivity requirement on the terminal for a connection to be possible.

DL Thermal Noise

kk BTkN thermal

. (3)

DL Traffic CINR

hop-nonTRXhopTRX

hop-nonhop-nonTRXhophopTRX1traff BERCINR

SS

SkSSkSSk

NN

ENEN. (4)

WhereBER-1

is a function which maps bit error rates to values in decibels via the C/I BER conversion

table. For the purposes of the GSM simulator this is a CINR BER conversion table.

Figure 1

Hence, the CINR BER table is used as a means of averaging values in decibels during the CINR

calculation. However, the BER table has a minimum CINR value of -10dB and a maxiumum of 27dB.

The default BER values are plotted in Figure 1.


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The highest possible CINR value is achieved with a strong signal and no carrier interference. Assume

the maximum received signal strength is 1W and that there is minimal thermal noise. This gives a

maximum CINR value of:

dB15010200.293.1038.1

11CINR

323

traff

kTB

Sk .

Therefore an equation is required to calculate new BER default values up to 150dB. An assumption is

made that the line between 25 and 26dB can be extrapolated with the same gradient. This gives agradient of -2 and an intercept of 42 which yields an equation for BER:

42CINRlog20)BER(log 1010 .

This results in a graph as shown inFigure 2.

-60

-50

-40

-30

-20

-10

0

-20 -10 0 10 20 30 40 50

C/I (dB)

log(BER)

Figure 2

Bit Error Rate for the Average Hopping Carrier

hop

11diversityho p

hop

CINRBER

BERBERs

n

Sk

Skn

GE

s

(5)

The summation is restricted to the hopping carriers on sub-cell S. The diversity gain is read from the

frequency hopping diversity gain table, shown inFigure 3.


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Figure 3

The index into the diversity gain table is the number of carriers, n, and is calculated as:

gainanthopSn

Where

otherwise.

hoppingsupportscell-subandselectedisdiversityfrequency

1

hop

Shop

n

S

otherwise.

hoppingantennasupportscell-subandselectedishoppingantenna

1

2gainant

Bit Error Rate for the Average Non-Hopping Carrier

ho p

s

n

Sk

Skn

GE

shopno n

11diversityho pno n

CINRBER

BERBER

(6)

The summation is restricted to the non-hopping carriers on sub-cell S.

CINR for a Single Carrier

SJ

kJkJJJ

SkSk

NuP

P

thermalreceivedtrafffracDTX

received

....)CINR( (7)

with the adjacent and overlapping carrier factor, u ,given by

otherwise.0

oadjacent tisif

,if1adj

u


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Traffic Loading Factor

GPRSCSslot

traff

SS

SS

TT

T

. (8)

Fractional Loading Factor

0if1

0if

ho p

ho p

hop

ho pTRX

frac

S

S

S

S

S

n

nn

N

Averaged Control CINR

The averaged control CINR is calculated in a similar way to the traffic CINR. The difference is that

total hopping and non-hopping BER values are calculated by summing values over control layer

carriers only.


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3 SNAPSHOT OVERVIEW

The key purpose of a snapshot is to provide us with measures of system load for a particular

distribution of terminals. To obtain these measures of system load, we must calculate time-slot

consumption for all the links in the system. A snapshot involves the following stages:

Creating a random terminal distribution.

Setting random terminal parameters (speeds, shadow fades).

Calculating traffic load usingiterations.

Gathering results.

3.1 RANDOM TERMINAL DISTRIBUTION

The first stage of a snapshot involves creating a random distribution of terminals representing the

offered traffic in the network. The spatial distribution of terminals must be random, but more

importantly it must be unbiased. In other words, it must be reasonable compared to the terminal

density array provided by the user. To see how this is achieved, we need only consider a single pixel

(bin) in the simulation.

Consider a pixel that has a terminal density ofDterminal/km2and an area ofAkm

2, so that the average

number of terminals in the pixel isDA. We note that:

Terminal occurrences within the pixel are independent of each other and are spatially uniform

within the pixel. In other words, a terminal is just as likely to be located at one point within

the pixel as any other point within the pixel.

The probability that two or more terminals are located at exactlythe same point within a pixel

is zero. This is simply because there is an infinite number of locations within the pixel.

These imply that terminal occurrence is a spatial Poisson process within the pixel. Therefore the total

number of terminals in the pixel satisfies the Poisson distribution:

!

)()terminals(

k

eDAkP

DAk

.

We choose the number of terminals to assign to the pixel by drawing a number from this Poisson

distribution. Doing this at each pixel ensures our terminal distribution is unbiased. Since the sum of

many Poisson distributions is also a Poisson distribution, the total number of terminals in the snapshotwill also be Poisson distributed.

One may note that if the average number of terminals at a pixel is small (DA


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3.2 TIME-SLOT ITERATIONS

The main task of a snapshot is to calculate the traffic loading of the network. At the beginning of the

snapshot, the system is placed in a state of an unloaded network. This is achieved by making all time-slots available on all sub-cells, i.e. with no terminals connected. Traffic loading is then calculated

iteratively by cycling repeatedly though the list of randomly spread terminals and attempting to make a

connection. The following logic is applied to each terminal:

- If the terminal is already connected then disconnect it by freeing the time-slots used at the

sub-cell by the terminal.- Recalculate the control and traffic CINR values to account for the new traffic load.

- Try and connect the terminal to the network in the most favourable way possible. The

way in which the terminal connects may be different from the way the terminal connected

previously. This difference arises because the system load may have changed since the

previous iteration.

- If a connection is possible then connect the terminal. Update the time-slots used at thesub-cell to reflect the terminals connection. Recalculate the control and traffic CINR

values to account for the altered traffic load.

Several cycles through the terminal list are needed to achieve a stable system load. On the first cycle,the first few terminals will experience very little interference because the network is not fully loaded.The lack of interference means that these terminals can use higher data-rate bearers which have high

CINR requirements. As a consequence, these terminals use fewer time-slots on the sub-cell than if they

connected using lower data-rate bearers. As the system becomes loaded, interference increases. On

subsequent iterations, the terminals may achieve lower traffic CINR values and hence connect using

lower data-rate bearers. Lower data-rate bearers require more time-slots than higher rate bearers and

hence consume more time-slots on the sub-cells. After several cycles, the traffic loading no longerchanges significantly. The iterations have converged to produce a plausible picture of served and failed

terminals in the network.

3.3 CONVERGENCETEST

A good practical measure of convergence is to examine how the traffic load changes between cycles.

The user need only enter one parameter in the convergence criterion for iterations section of the

wizard for this convergence check. After each cycle through the terminal list, the percentage change in

traffic load is noted. If the change in traffic load falls within the specified limit for fifteen iterations

then the snapshot is considered to have converged.

3.4 GATHERING OF RESULTS

The final stage of a snapshot involves gathering results. The information gathered includes sub-cell

information (e.g. time-slot usage), information about the states of connected terminals, and the

failure reasons of terminals which failed to be served.


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4 CONNECTION EVALUATION IN A SNAPSHOT

4.1 CONNECTION SCENARIO PRIORITISATION

The connection scenario describes how a terminal connects to the network. It consists of the

following parameters:

The cell-layer used for the connection

The sub-cell load status (overloaded / under-loaded). A sub-cell is considered over-loaded if

the percentage of time-slots used is above the overflow load threshold.

The sub-cell for the connection (this is where the time-slots are consumed).

The traffic CINR of the sub-cell.

The downlink bearer used for the connection.

Typically, several connection scenarios are available to each terminal. Our snapshot attempts to

connect the randomly spread terminals to the network in the most favourable way possible. Logic is

required for ranking the different scenarios that each terminal may use.

The rules for ranking scenarios during connection evaluation are (in order of decreasing importance):

Prefer under-loaded sub-cells to overloaded sub-cells.

Prefer higher priority cell-layers to lower priority cell-layers.

Prefer higher traffic CINR to lower traffic CINR.

Prefer higher priority DL bearers to lower priority DL bearers.

The connection scenarios for each terminal are evaluated in turn (from most to least favoured) until one

that permits a network connection is found. The scenario employed by a terminal may change each

time it is evaluated in the loading iterations, and this flexibility provides us with link adaptation.

A downlink evaluation is carried out to examine the connection scenario and determine whether a

connection is possible.

4.2 GSMDOWNLINK EVALUATION

Received Signal Strength Check

The received signal strength must meet the receiver sensitivity requirement on the terminal for a

connection to be possible.

Traffic CINR and Control CINR Check

For the terminal to connect to a sub-cell, the control CINR must meet the terminals BCCH CINR

requirement. The traffic CINR is used to determine whether the bearer can be used for the connection.

A further check is made to ensure that the bearer is supported on the sub-cell. If the bearer is supported

and there are time-slots available on the sub-cell then the traffic CINR is used to establish how manytime-slots are required for the connection.


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4.3 FAILURE REASONS

A connection scenario can fail for one or more of the following reasons:

Low Signal.

The received signal does not meet the receiver sensitivity requirement specified on the

terminal type.

No Cell Time-Slots.

The sub-cell has too few time-slots to serve the bearer.

No Terminal Time-Slots

The terminal has too few time-slots available for the connection.

Low Control Channel CINR

The best server cannot meet the CINR requirement of the terminal.

Low Traffic Channel CINR

The best server cannot meet the CINR requirement of the bearer.

High Pathloss.There is no sub-cell on the pixel with a pathloss value sufficient to be considered as a serving

sub-cells.

If all of the connection scenarios available to a terminal fail to produce a connection, then the terminal

is classed as a failure. Each scenario in the list can fail for multiple reasons. Also, different scenariosin the list can fail for different sets of reasons. All of this makes failure reporting problematic. For

example, consider a terminal with the following scenario list containing only 2 scenarios:

Cell Name Cell Layer CINR Ctrl DL Bearer ProblemsCell_X CellLayer_A 4 dB 12kbps Low ctrl CINR & traffic CINR

Cell_Y CellLayer_B 20 dB 12kbps No Cell Time-Slots

In this example, CellLayer_A has a higher priority than CellLayer_B. This makes Cell_X the top

scenario even though it has a worse CINR than Cell_Y. What is the correct reason for failure for thisterminal? There is no correct way of assigning this. The tool records the failure reasons of the top

scenario only. In most cases the top scenario provides the most useful information as to why a terminal

fails. In the above example, the terminal is deemed to fail because of problems with Low Control

Channel CINRand Low Traffic CINRon Cell_X. The terminal contributes to the failure statistics for

Cell_X only, not Cell_Y. Hence the terminal does not affect the failure statistics for No Cell Time-

Slots.


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5 OUTPUT ARRAYS

5.1 ARRAY DEPENDENCIES

All arrays are produced on a per cell-layer basis. Many arrays depend on whether the terminal is taken

to be indoor or outdoor. Indoor arrays use the in-building parameters for the clutter type at each pixel(i.e. indoor loss and indoor shadow-fading standard deviation).

Coverage arrays can be drawn even if no snapshots have been run, but the user should note that the

arrays then refer to coverage in an unloaded system. To obtain coverage arrays for a loadedsystem the

user must run some snapshots; the key purpose of running snapshots is to provide measures of traffic

load. The arrays change little after a relatively small number of snapshots have been performed (10s ofsnapshots in most cases). This is because only a small number of snapshots are needed to get an idea

of the average loading on each sub-cell.

The following table lists the types of array that are available in the Simulator, and shows some of their

dependencies. Most terms (e.g. Indoor) are self-explanatory.

Fading means the array depends on the standard deviation of shadow fading for the clutter type.

Snapshots done means the accuracy of the array has a strong dependence on the number of snapshots

done, so the array will require 1000s of snapshots to give accurate results instead of 10s of snapshots.

Other Tech means that the presence of the array is dependent on the inclusion of other technology

types in the Simulation. Other technology types can be UMTS and Wi-Fi.

CE=Cell Layer T=Terminal S=Service O=Other TechI=Indoor F=Fading R=Reliability n=Snapshots done

CE T S I F R n O

Pathloss Arrays

DL Loss X X XNth DL Loss X X XCoverage and Data Rate Arrays

Best Server by RSS XNth Best Server by RSS XRSS X X XNth RSS XAll Servers X X XCoverage Probability X X X XCoverage Probability OK X X X X XCINR (Control) X X XCINR (Traffic + Control) X X XAchievable Bitrate X X X X

Composite Tech Arrays

Composite: Best Server X X X X X X

Composite: Tech Type X X X X X X

Terminal Info Arrays

Terminal Info: Failure Rate X X

Terminal Info: Failure Reason X X

Terminal Info: Tech Type (Failed) X X X

Terminal Info: Tech Type (Served) X X X

CE T S I F R n


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PATHLOSS ARRAYS

DL Loss & Nth DL Loss

Dependencies: Terminal, Cell layer, Indoor

These are the downlink losses of the Best Server by RSS and Nth Best Server by RSS. They represent

average values and are therefore calculated with fades of 0 dB.

5.2 COVERAGE AND DATA RATE ARRAYS

These arrays all provide information on coverage levels and coverage probabilities.

Best Server by RSS & Nth Best Server by RSS

Dependencies: Cell Layer

This is the sub-cell that provides the highest (and Nth highest) RSS for the terminal.

Best RSS & Nth Best RSS

Dependencies: Terminal, Cell Layer, Indoor

These are the highest (and Nth highest) RSS levels. They represent average values and are therefore

calculated with fades of 0 dB.

Coverage Probability

Dependencies: Terminal, Cell Layer, Indoor, Fading

This is the probability that the Best DL Cell (by RSS)satisfies the RSS requirement specified on the

terminal type. This probability depends on the standard deviation of shadow fading for the clutter type

at the pixel. If this standard deviation has been set to zero, then there are only three possible coverage

probabilities: 0% if the requirement is not satisfied, 50% if the requirement is satisfied exactly, and

100% if the requirement is exceeded.

Coverage Probability OK

Dependencies: Terminal, Cell Layer, Indoor, Fading, Reliability

This is a thresholded version of the Coverage Probability array and has just two values (Yes/No). Ithas the advantage of being quicker to calculate than the Coverage Probabilityarray. A value of Yes

means that the downlink coverage probability meets the coverage reliability level specified in Array

Settings Sim Display Thresholds.

CINR (Control)


These are the CINR(Control) values corresponding to the best serving sub-cells, i.e. notnecessarily the

highest CINR(Control) values.

CINR (Traffic + Control)


These are the CINR(Traffic + Control) values corresponding to the best serving sub-cells, i.e. not

necessarily the highest CINR(Traffic + Control) values.


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Achievable Bitrate

Dependencies: Terminal, Cell Layer, Service, Indoor

This is the highest bitrate that can be achieved by the terminal based on CINR regardless of system

loading.

5.3 COMPOSITE TECH ARRAYS

Composite Tech Arrays account for GSM, UMTS and Wi-Fi cells collectively.

Composite: Best Server

Dependencies: Terminal, Indoor, Service, Fading, Reliability, Other Tech

This is the serving cell identity. Wi-Fi is the top priority technology. UMTS and GSM relevant

priorities are as specified in the Service definition. Cells of a specific technology type are ranked by

Signal Strength (Wi-Fi: DL-RSS, UMTS: RSCP, GSM: RSS). The terminals requirements must bemet for the respective technology (Wi-Fi: Required Signal Strength, UMTS: Required RSCP, Ec/Io andPilot SIR, GSM: Receiver RSS Sensitivity). The display thresholds are set for each technology type

individually inArray Settings Sim Display Thresholds.

Composite: Tech Type

Dependencies: Terminal, Indoor, Service, Fading, Reliability, Other Tech

This is the technology type of the serving cell as determined in the previous array. The display

thresholds are set for each technology type individually inArray Settings Sim Display Thresholds.

5.4 TERMINAL INFO ARRAYS

Terminal Info: Failure Rate

Dependencies: Terminal, Snapshots

The failure rate is the proportion of attempted terminals at a pixel that failed to make a connection. It iscalculated as a percentage as follows:

Failure Rate (%) = 100 * ( Failed Terminals) / (Attempted Terminals)

The accuracy of the result at a pixel is clearly limited by the number of attempts made at the pixel. Forexample, if only one attempt has been made, the result will either be 0% or 100%. So the Failure Rate

array gives a rough visualisation of the problem areas of the network.

Terminal Info: Failure Reason

Dependencies: Terminal, Snapshots

This plot shows failures and successes in a single plot. The value shown at a pixel is determined by

last terminal that was attempted there, regardless of the snapshot in which it was attempted. So if the

last terminal that was attempted at a pixel succeeded, then the pixel will be labelled a success,

regardless of how many terminals may have failed there in other snapshots. Likewise, if the last

terminal at a pixel failed, then the pixel will be labelled as a failure, regardless of how many terminalssucceeded there in other snapshots. Therefore locations that are more likely to serve terminals in a

snapshot rather than fail them, are more likely to be labelled as successes than failures.


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A terminal can fail for multiple reasons. When this occurs, only a single reason is reported when

writing a value at the pixel. This is achieved by sensibly ranking the failure reasons for the terminal

and using the most dominant one. For example, there is no point in indicating a capacity failure for a

terminal if it does not have coverage. In other words, coverage failures rank more highly than capacity

failures.

The failure reason categories are ranked as follows (most dominant failure reasons first). For clarity,the categories in the legend are shown in the same order.

o Success

o No covering cells

o No valid scenarios

o Low Signal

o Low Ctrl SINR

o Low Traffic SINR

o

No Cell TS

o No Terminal TS

Terminal Info: Tech Type (Served)Dependencies: Terminal, Snapshots, Other Tech

This array shows the serving technology type (GSM, UMTS or Wi-Fi) where

the Terminal Info (GSM): Failure Reason array is reporting Success or

the Terminal Info (UMTS): Failure Reason array is reporting Success or

the Terminal Info (Wi-Fi): Failure Reason array is reporting Success.There is a separate category to show locations with No valid scenarios/No covering cells.

Terminal Info: Tech Type (Failed)

Dependencies: Terminal, Snapshots, Other Tech

This array shows the failed technology type (GSM, UMTS or Wi-Fi) where

the Terminal Info (GSM): Failure Reason array is not reporting Success or

the Terminal Info (UMTS): Failure Reason array not reporting Success or

the Terminal Info (Wi-Fi): Failure Reason array not reporting Success.

There is a separate category to show locations with No valid scenarios/No covering cells.


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6 COVERAGE ARRAY CALCULATIONS

The term coverageis used in the classical sense. It looks at the problem of a received signal being of

sufficient strength/quality given that it has been transmitted through a lossy channel with shadow

fading. Coverage probabilities are calculated analytically. This means that coverage plots can be

obtained after running a very small number of snapshots (typically 10s) and plots converge very

quickly. If no snapshots have been run, then coverage plots are still available but they give thecoverage probabilities in an unloaded system.

We will examine the different ways in which shadow fading affects our calculations. There are

essentially three cases to consider.

How fading is handled in the simulation snapshots.

How fading is handled when calculating mean values of quantities.

How fading is handled when calculating coverage probabilities.

6.1

NOTATION

We introduce the following notation to represent the probability density function for a normally

distributed random variable with mean and standard deviation .

2

2

2 2

)(exp

2

1),;(

xxN

6.2 FADES IN THE SIMULATION SNAPSHOTS

Shadow fading is modelled in a snapshot by randomising the pathlosses experienced by the randomlyscattered terminals. Shadow fades are log-normally distributed, and the user specifies the shadow

fading standard deviation for indoor and outdoor terminals in each clutter type. In reality, the fades

between a terminal and the cells that cover it will exhibit a degree of correlation. In particular, a

terminal is likely to have similar fades to cells that are located on the same site. To account for this, the

user specifies two parameters in the Monte Carlo Wizard:

The normalised inter-site correlation coefficient (terinc ). This is the correlation between

fades to cells on different sites.

The normalised intra-site correlation coefficient ( trainc ). This is the correlation between

fades to cells on the same site.


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These two parameters must satisfy the constraints 10 trainterin cc . For each randomly scatteredterminal in a snapshot, a set of correlated fades to the covering cells is generated using the following

procedure. All the random numbers mentioned below are independent and normally distributed with

zero mean and unit variance, and is the standard deviation of the shadow fading at the pixel in dB.

Generate a random number X .

For each siteI, generate a random numberIY .

For each sub-cellJ, generate a random number JZ .

The fade (in dB) to cellJon siteIis then set to

JI ZcYccXc

trainterintrainterin1 .

The above procedure is performed for each of the randomly scattered terminals at the beginning of a

snapshot. Fades for different terminals are uncorrelated even if they are located in the same pixel.

6.3 FADES IN ARRAYS FOR MEAN VALUES

Arrays showing the mean level of a quantity (e.g. DL linkloss, RSS, CINR, etc) are calculated with all

fades set to 0 dB.

6.4 FADES IN COVERAGE ARRAY CALCULATIONS

RSS Coverage Probability

In the absence of fading, let the RSS (in Watts) for sub-cellJbe represented by

JR .

If sub-cellJhas a fade ofJ

F dB, then the RSS is given by

)10(10/

JJFR

.

We can calculate a coverage probability for the RSS as follows:

Find the fade JF

that causes the RSS to satisfy exactlythe RSCP requirement specified on theterminal type. Call this fade *F . Note that *F may be positive or negative. Any fade bigger

than *F will give an inadequate RSS.

SinceJ

F is normally-distributed with a mean of 0 dB and standard deviation of dB, the

probability that*FFJ is given by

*

),0;()(*

F

JJJ dFFNFFP .

This is the probability that the RSS does not meet the requirement.

Documents

GSM Static Simulations