UMTS and HSPA Static Simulations

62
UMTS/HSPA STATIC SIMULATIONS V 7.0 ALGORITHMS AND OUTPUTS RELATING TO THE SIMULATOR

description

Description of Monte Carlo simulation principals and methods, with formulas

Transcript of UMTS and HSPA Static Simulations

Page 1: UMTS and HSPA Static Simulations

UMTS/HSPA STATIC SIMULATIONS

V 7.0

ALGORITHMS AND OUTPUTS RELATING TO THE

SIMULATOR

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© Copyright 2009 AIRCOM International Ltd. 2

© Copyright 2009 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 expressed

or 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

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VERSION HISTORY

Document Version Date Author Comments 1.0a 22/12/2009 A. Awad Adapted from V6.1 document

with subsequent changes

and description of HSPA-related

changes in V6.2.

1.0 01/02/2010 P. Nahi Approved

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CONTENTS

1 What Is A Snapshot?................................................................................................................... 5 1.1 Randomness in a Cellular Network .................................................................................. 5 1.2 Time-averaging in Coverage Evaluations......................................................................... 8 1.3 Time-averaging in Capacity Evaluations .......................................................................... 8 1.4 Why Produce Snapshots? .................................................................................................... 8 1.5 Activity Factors..................................................................................................................... 9 1.6 Bitrates and Processing Gain ............................................................................................ 10 1.7 Resource Types ................................................................................................................... 10

2 Formulae ..................................................................................................................................... 11 2.1 Notation ............................................................................................................................... 11 2.2 List of Principal Symbols .................................................................................................. 11 2.3 Downlink Power and Noise Formulae ............................................................................ 14 2.4 Uplink Power and Noise Formulae ................................................................................. 16 2.5 Link Budget Formulae ....................................................................................................... 17 2.6 Extended HSDPA Analysis Formulae ............................................................................. 21

3 Snapshot Overview................................................................................................................... 24 3.1 Random Terminal Distribution ........................................................................................ 24 3.2 Random Speed Distribution ............................................................................................ 25 3.3 Power Control Modelling ................................................................................................. 25 3.4 Power Iterations ................................................................................................................. 26 3.5 Convergence Test ............................................................................................................... 27 3.6 Gathering Of Results ......................................................................................................... 27

4 Connection Evaluation in a Snapshot ................................................................................... 28 4.1 Connection Scenario Prioritisation .................................................................................. 28 4.2 Production of a Candidate Active Set ............................................................................. 29 4.3 UMTS Uplink Evaluation .................................................................................................. 29 4.4 HSUPA Uplink Evaluation ............................................................................................... 31 4.5 UMTS Downlink Evaluation ............................................................................................ 31 4.6 HSDPA Downlink Evaluation .......................................................................................... 32 4.7 Failure Reasons ................................................................................................................... 34

5 Output Arrays ............................................................................................................................ 34 5.1 Array dependencies ........................................................................................................... 35 5.2 Pathloss Arrays ................................................................................................................... 37 5.3 Pilot Coverage Arrays ....................................................................................................... 37 5.4 Handover Arrays ............................................................................................................... 39 5.5 Uplink Noise Arrays .......................................................................................................... 40 5.6 Downlink Noise Arrays .................................................................................................... 40 5.7 Uplink Coverage Arrays ................................................................................................... 41 5.8 Downlink Coverage Arrays .............................................................................................. 42 5.9 Coverage Balance ............................................................................................................... 43 5.10 Soft Blocking Arrays .......................................................................................................... 43 5.11 Hard Blocking Arrays ........................................................................................................ 43 5.12 HSDPA Arrays ................................................................................................................... 44 5.13 HSUPA Arrays ................................................................................................................... 46

6 Coverage Array Calculations .................................................................................................. 48 6.1 Notation ............................................................................................................................... 48 6.2 Fades in the Simulation Snapshots .................................................................................. 49 6.3 Fades in Arrays for Mean Values ..................................................................................... 49 6.4 Fades in Arrays for Soft/Hard Blocking ......................................................................... 49 6.5 Fades in Coverage Array Calculations ............................................................................ 50 6.6 Conditional Expectation for Correlated Fades ............................................................... 54

7 Blocking Array Calculations ................................................................................................... 55 7.1 Uplink Soft Blocking Probability Array .......................................................................... 56 7.2 Downlink Soft Blocking Probability Array ..................................................................... 58

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7.3 Hard Blocking Probability Arrays (Resource Blocking) ............................................... 60 8 Blocking Probability and Failure Rate .................................................................................. 61

8.1 Calculation of Blocking Probability in the Blocking Report ......................................... 61 8.2 Failure Rate ......................................................................................................................... 61

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1 WHAT IS A SNAPSHOT?

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 associated

probability 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 patterns X1

and X2 are 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 X X

X

X

X

X

X

1 1

0

0

0

1 1 0

1

0

1

0

1

1 0

1

0

0

1 0 1

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 occurrence P(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 in

time. 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 ideal static simulation would calculate an average quantity (e.g. the average noise rise 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 be given by

ji TX

jiji TXPTXFF

,

),(),( . (a)

We can split this into separate spatial and temporal sums:

i jX

ij

T

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

The summations in (a) and in (b) 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 spatial randomness explicitly by sampling.

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

Instead of considering all spatial patterns, we consider a set of N sample spatial patterns drawn from

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

simple average over the set of N sample spatial patterns:

i jX

ij

T

ji XTPTXFN

F )|(),(1

.

Spatial randomness is therefore handled explicitly by 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 explicitly by sampling. (Simplification 2).

Model temporal randomness implicitly with time-averages. (Simplification 3).

Simplification 2: Model temporal randomness explicitly by sampling.

This simplification is fairly common but has some drawbacks as explained below. Firstly, as in the

previous 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 (a) 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 works

because 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 the

user 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 set of 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 not use Simplification 2 and use the following simplification instead.

Simplification 3: Model temporal randomness implicitly with 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 implicitly by 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 distribution of terminals”. The

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

DL interference, resource 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 of activity,

P = TX power in a period of activity,

L = linkloss,

N = time-average RX 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 interference N in the link-budget.

1.3 TIME-AVERAGING IN CAPACITY EVALUATIONS

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

In the UL, the capacity constraint is that the time-average noise rise at the cell must not exceed the

noise rise limit.

In the DL, the capacity constraint is that the time-average power of the cell must not exceed the

maximum cell power.

For resources, the capacity constraint is that the time-average number of resources consumed must not

exceed the user-specified limits.

For HSDPA, the capacity constraint is that the time-average HSDPA power of the cell must not exceed

the HSDPA link power. This is equivalent to saying that the sum of the activity factors of served

HSDPA users must not exceed 100%.

Time-averages are calculated by scaling quantities (i.e. powers transmitted and resources consumed) by

activity factors. (Note that the activity factor for a CS resource is always 100%, regardless of the

service activity factor.)

One should remember that our snapshot contains no information about the instants of time at which

links are active. Only two things are known about each link:

The power and resources required to service the link in a period of activity.

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

in the system.

1.4 WHY PRODUCE SNAPSHOTS?

The coverage in a CDMA system depends on system load. This effect is often called cell-breathing.

One cannot perform a coverage analysis for a CDMA system without knowing the extent to which the

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

particular, each snapshot tells us:

The total DL transmission power of each cell.

The total UL interference power (in-cell noise & out-cell noise) on each cell.

The total UL and DL throughput on each cell.

The resources consumed on each cell.

By running many snapshots, we obtain values for these quantities for different spatial distributions of

terminals, and can then proceed to analyse UL and 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. There are two areas where time-averaging is important and these

have separate activity factors. We call these the power-activity factor and the resource-activity factor.

The power-activity factor is used to calculate the time-average power and time-average

throughput for a link.

Time-average Power = Power Activity x Power when Active.

Time-average Throughput = Power Activity x User Bitrate.

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

link.

Time-average Resources = Resource Activity x Resources when Active.

The power-activity factor and resource-activity factor for a bearer are not necessarily the same.

For circuit-switched (CS) services, resources are consumed even during periods of inactivity.

Therefore CS services always have a resource-activity factor of 100%, regardless of the power-activity

factor.

For packet switched (PS) services, resources are only consumed during periods of activity. So one

could expect the power-activity factor and resource-activity factor for a bearer to be equal, and this is

the default behaviour in the tool. However, there are cases when the user may wish to consider the

resource-activity factor to be larger than the power-activity factor. For example, once a PS link has

ceased being active, resources may not be released immediately due to a release time-out. The user is

therefore given the option of editing the power and resource activities for PS services directly.

PS Activity Factor Calculation

For a PS service, the tool can automatically calculate the power-activity factor from the PS parameters

in the service definition:

airR Air interface 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: aircallspacketsbytesactive /)1(8 RrNNNT

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

Session time: inactiveactivesession TTT

Activity factor: session

active

T

T

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1.6 BITRATES AND PROCESSING GAIN

Air Interface Bitrate and Processing Gain

The Air Interface Bitrate is used to calculate the processing gain ( kk GG , ) in the bearer link-budget

equations (29-32). The quantities ( kk GG , ) are always calculated by dividing the system chiprate (W )

by the air interface bitrate.

For HSDPA bearers, the air-interface bitrate is automatically calculated to give the correct processing

gain after demodulation as follows:

Chip rate / Symbol rate = 16.

Bits per symbol = M = 2 or 4 (for QPSK & 16QAM respectively).

For a HSDPA bearer using N codes, the net gain after demodulation = )(/16 NM .

Therefore the air interface bitrate is set to 16

NMW, as this gives

NMGk

16.

User Bitrates

The User Bitrate is used to calculate data throughput on a cell, and it also affects certain outputs in the

Extended HSDPA Analysis.

1.7 RESOURCE TYPES

The user can define up to 6 different resource types in the tool and these can be pooled at various

locations in the network (i.e. site, site-carrier, or cell). A resource pooled at the site level is shared

between all the cells on that site. Similarly a resource pooled at the site-carrier level, is shared between

all the cells on a site that use that carrier.

“Air Interface” Resources

Any resource type that is flagged as being of type “air-interface” can only be pooled at the cell level.

In other words, these resources cannot be shared between cells. Also, “air-inteface” resources are not

consumed in the uplink on handover cells.

HSDPA Resource

The user can choose precisely one of the 6 resource types in the tool to represent a HSDPA resource

(i.e. HSDPA codes). A cell must be allocated some HSDPA resources in order to support HSDPA

users. HSDPA resources are downlink resources. (Please notice that HSUPA can be supported without

the need to specify any recources although any of the non-HSUPA resource types can be optionally

used to model HSUPA resources).

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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 cell.

J

indicates a sum over all cells.

A lowercase Roman subscript always indexes a terminal.

k

indicates a sum over all terminals.

Jk

indicates a sum over all terminals in cell J.

A superscript arrow ),( indicates if a quantity is uplink or downlink.

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

As an example, the quantity JkE represents the uplink Eb/No for the link between terminal k and cell

J using carrier .

2.2 LIST OF PRINCIPAL SYMBOLS

AA , UL (DL) adjacent carrier inteference ratio. This is the power leakage from

carrier to carrier . By definition 1AA .

k Interference cancellation efficiency of terminal k.

k Chip equalisation efficiency of terminal k.

JkE UL traffic channel Eb/No when UL is active.

JkE DL traffic channel Eb/No when DL is active.

pilotJkE Pilot channel Ec/Io.

SIRJkE Pilot channel SIR.

HSDPA

kJE HSDPA Eb/No.

HSUPA

kJE HSUPA Eb/No.

SCCH-HS

kJE HS-SCCH Ec/Nt

SINR HS

JkE HSDPA SINR.

kk GG , UL,DL processing gain.

antennaJG Cell attenna gain.

antennakG Terminal antenna gain.

mhaJG Mast head amplifier UL gain.

k Boltzmann constant. mhaJL Mast head amplifier (MHA) DL insertion loss.

JkJk LL , UL,DL linkloss between cell and terminal.

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pathlossJkL Pathloss between cell and terminal.

antennaJkL Antenna masking loss.

feederJL Feeder loss, including feeder connector loss.

bodykL Terminal body loss.

splitterJL Cell DL splitter loss.

thermalkN Thermal noise at terminal.

thermalJN Thermal noise at cell.

Max MSkP Power allocated to terminal k.

kP UL traffic channel TX power when UL is active.

Max BSJP Power allocated to cell J.

pilotJP Pilot channel TX power.

CCPCH-PJP P-CCPCH TX power.

CCPCH-SJP S-CCPCH TX power.

SCH-PJP P-SCH TX power.

SCH-SJP S-SCH TX power.

AICHJP AICH TX power.

PICHJP PICH TX power.

AGCH-E

JP E-AGCH TX power.

HICH-E

JP E-HICH TX power.

RGCH-E

JP E-RGCH TX power.

commonJP Time-average common channel TX power.

HSDPAJP Time-average total HSDPA TX power.

SCCH-HS

JP Time-average total HS-SCCH TX power.

PDSCH-HS

JP Time-average total HS-PDSCH TX power.

HSUPA

JP Time-average total HSUPA Downlink TX power.

HSUPA

JP Time-average total HSUPA Uplink TX power.

syncJP Time-average synchronisation channel TX power.

JkP DL traffic channel TX power when DL is active.

maxJP Maximum DL power for an active (non-HSDPA) link.

minJP Minimum DL power for an active (non-HSDPA) link.

linkHSDPA

JkP HSDPA link power (i.e. the HSDPA TX power for an active link).

maxHSDPA JP Maximum HSDPA link power (specified in the cell parameters).

HSUPA

kP Time-average HSUPA UL TX Power.

link SCCH-HS

JkP HS-SCCH link power (i.e. the HSDPA control TX power for an active link).

link SPDSCH-HS

JkP HS-PDSCH link power (i.e. the HSDPA data TX power for an active link).

k SCCH-HS

JP Time-average total HS-SCCH power for the other HSDPA links other than k.

totalJP Time-average total DL TX power.

UMTSJP Time-average total UMTS DL TX power.

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UMTS

JP Time-average total UMTS UL TX power.

k

JPUMTS Time-average interfering UMTS DL TX power for link to terminal k.

cell-inJR Time-average total UL “in-cell” noise.

cell-outJR Time-average total UL “out-cell” noise.

totalkR Time-average total DL noise at terminal.

totalJR Time-average total UL noise at cell.

T Temperature in Kelvin (for thermal noise calculation).

W Chip rate (bps). CCPCH-P

J P-CCPCH activity factor.

CCPCH-SJ S-CCPCH activity factor.

SCH-PJ P-SCH activity factor.

SCH-SJ S-SCH activity factor.

AICHJ AICH activity factor.

PICHJ PICH activity factor.

AGCH-E

J E-AGCH activity factor.

HICH-E

J E-HICH activity factor.

RGCH-E

J E-RGCH activity factor.

kk , UL,DL traffic channel activity factor.

kk , UL,DL traffic channel control-overhead factor

J Cell orthogonality factor.

k Terminal noise figure.

J Base station noise figure.

mhaJ Mast head amplifier noise figure.

feederJ Feeder noise figure ( =

feederJL ).

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2.3 DOWNLINK POWER AND NOISE FORMULAE

DL Loss

splittermha

antennaantenna

feederbodyantennapathloss

JJ

Jk

JkJkJkJk LL

GG

LLLLL . (1)

The first part of the above expression ( ) is read from the prediction file.

Time-average Common Channel TX Power

AGCHEAGCHEPICHPICHAICHAICHCCPCH-SCCPCH-SCCPCH-PCCPCH-Pcommon

JaJaJJJJJJJJJ PaPPPPP .

(2)

This is calculated by scaling the TX powers of the P-CCPCH, S-CCPCH, AICH and PICH by their

activity factors.

Time-average Synchronisation Channel TX Power

SCH-SSCH-SSCH-PSCH-Psync

JJJJJ PPP . (3)

This is calculated by scaling the TX powers of the P-SCH and S-SCH by their activity factors.

Time-average UMTS TX Power

UMTSk

Jkk

UMTSk

JkkJ PPPUMTS . (4)

The sums are over the UMTS terminals that are served by the cell. The first sum is the time-average

TX power for the traffic channels. The second sum is the total control overhead TX power for those

channels.

Time-average Interfering UMTS TX Power

JqqqJq

J PPP )(UMTSUMTS. (5)

The quantity q

JPUMTS is only relevant to UMTS terminals. It is similar to

UMTSJP except it excludes

the time-average TX power for the terminal q. The only purpose for defining this quantity is to

simplify the UMTS DL link budget equation.

Total HSDPA Links TX Power (for all simultaneously code-multiplexed active links)

DPA using if),(min

DPA usingnot if

UMTSHSUPA commonsyncpilotMax BSmaxHSDPA

maxHSDPA linkHSDPA

JJJJJJJ

JJ

PPPPPPP

PP

(6)

This refers to the total links power for an active link (i.e. HS-DSCH + HS-SCCH). When using

Dynamic Power Allocation (DPA), the total links power is the smaller of the available (non-HSDPA)

power on the cell and the HSDPA Link Power specified on the cell. When not using DPA, the total

antennapathlossJkJk LL

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links power is the HSDPA Link Power specified on the cell. This power can be shared by a number of

simultaneous users in the case of code multiplexing.

HSDPA Single Link TX Power

There are 2 components to the link power (link SCCH-HS

kJP and link PDSCH-HS

kJP ).

The instantaneous HS-SCCH power for the link (link SCCH-HS

kJP ) is calculated first. (Fixed or Dynamic)

The instantaneous HS-PDSCH power for the link (link PDSCH-HS

kJP ) is then given by:

ngmultiplexi codewith )(15

ngmultiplexi code nowith

kSCCH-HSlink SCCH-HSlinkHSDPA

link SCCH-HSlinkHSDPA

link PDSCH-HS

JkkJJkk

kJJk

kJPPP

N

PP

P

(7)

where kN is the number of codes used by the link.

The quantitykSCCHHS

JkP is the time-average total HS-SCCH power for the other HSDPA links, and is

given by:

link SCCH-HSSCCHHSkSCCHHS

JkkJJk PPP (8)

Time-average Total HS-SCCH TX Power

HSDPAk

kJkJ PP link -SCCHHSSCCHHS . (9)

Time-average Total HS-PDSCH TX Power

HSDPAk

kJkJ PP link PDSCH-HSPDSCH-HS . (10)

Time-average HSDPA TX Power

PDSCHHSSCCHHSHSDPA

JJJ PPP . (11)

This is the time-average HSDPA power transmitted by the cell. The sum is over the HSDPA terminals

that are served by the cell.

HSUPA Dedicated DL Channel TX Power

RGCH-ERGCH-EHICH-EHICH-EHSUPA

JJJJJ PPP . (12)

Time-average DL TX Power

SCCH-HSPDSCH-HSUMTSHSUPA commonsyncpilottotal

JJJJJJJJ PPPPPPPP . (13)

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DL Thermal Noise

kk WTkN thermal. (14)

Time-average Total DL Noise Power

J Jk

Jkk

L

PANR

totalthermaltotal . (15)

Time-average DL “out-cell” Interference

kJ

J

C kC

C

kJL

P

L

PAI

totaltotal

out . (16)

2.4 UPLINK POWER AND NOISE FORMULAE

UL Loss

mhaantennaantenna

feederbodyantennapathloss 1

JJk

JkJkJkJk

GGG

LLLLL . (17)

The first part of the above expression (antennapathlossJkJk LL ) is read from the prediction file.

UL Thermal Noise at Cell

feedermhamha

feedermha

feeder

mhathermal

/

11

JJ

J

J

JJ

J

JJ

LGGL

GWTkN . (18)

The first pair of brackets contains the net UL gain between the receiving antenna and the BS. The

second pair of brackets contains the net UL noise figure between the receiving antenna and the BS.

Time-average Total UL “in-cell” Noise

Jk kJ

kkk

Jk kJ

kkk

JL

P

L

PR

HSUPAUMTS

cell-in)1()(

. (19)

This is the total RX power from “in-cell” terminals. The sum is over terminals that have cell J as their

primary cell.

Time-average Total UL “out-cell” Noise

Jk Jk kJ

kkk

kJ

kkk

JL

P

L

PAR

HSUPAUMTS

cell-out)1()(

. (20)

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© Copyright 2009 AIRCOM International Ltd. 17

This is the total RX power from “out-cell” terminals. The sum is over terminals that do not have cell J

as their primary cell.

Time-average Total UL Noise Power

cell-outcell-inthermaltotal

JJJJ RRNR . (21)

This is the UL thermal noise plus the total RX power from all terminals.

UL Noise Rise

thermal

total

Rise) (NoiseJ

JJ

N

R. (22)

The UL noise rise is expressed in dB in the simulation report.

UL Load

JJ

Rise) (Noise

11Load) (UL . (23)

The UL Load is expressed as a percentage in the simulation reports.

UL Frequency Re-use Efficiency

cell-outcell-in

cell-in

FREJJ

JJ

RR

R. (24)

UL FRE is the total RX power from “in-cell” terminals divided by the total RX power from all

terminals. It is expressed as a percentage in the simulation reports.

2.5 LINK BUDGET FORMULAE

The following formulae are all expressions for signal to noise ratios, and are used to determine the

power required to successfully service a link. The basic relations below ignore handover gains, power

control headroom, power rise gain, and maximal ratio combining. The influence of these effects is

described in the section describing Connection Evaluation. Note that all denominators in our link

budgets contain time-averaged quantities.

Pilot Ec/Io

Jkk

JJk

LR

PE

total

pilotpilot

. (25)

HS-SCCH Ec/Nt

outinthermal

link SCCH-HS

SCCH-HS

)1(

/

kJkkJk

kJkJ

kJIIN

LPE . (26)

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where in

kJI is the time-average in-cell interference. There are 2 cases for this:

No code-multiplexing: In this case there is no interference between HSDPA users on a cell.

kJ

JJJJJJkJ

L

PPPPPI

))(1( UMTSHSUPA commonpilotsync

in

Code-multiplexing:

kJ

JJJJJJJJkJ

L

PPPPPPPI

))(1( kSCCHHSkPDSCH-HSUMTSHSUPA commonpilotsync

in

Pilot SIR

outinthermal

pilot

SIR

)1(

/

kJkkJk

kJJkJ

IIN

LPE . (27)

where k is the interference cancellation efficiency of the terminal, and in

kJI is the time-average in-

cell interference:

kJ

JJJJJJJkJ

L

PPPPPPI

))(1( SCCH-HSPDSCH-HSUMTSHSUPA commonsync

in .

Own pilot is not considered as interference. Own-cell interference from common channels, UMTS,

and HSDPA channels is reduced because of orthogonality.

HS-PDSCH SINR

outinthermal

link PDSCH-HS

SINR HS

)1(

/16

kJkkJk

kJkJ

kJIIN

LPE . (28)

where in

kJI is the time-average in-cell interference. There are 2 cases for this:

No code-multiplexing: In this case there is no interference between HSDPA users on a cell

kJ

JJJJJJkJ

L

PPPPPI

))(1( UMTSHSUPA commonpilotsync

in

Code-multiplexing:

In this case we calculate a worst case SINR by assuming we have interference from the other ( kN15 )

HSDPA codes that are not used by the user. So if the user’s data power is link PDSCH-HS

kJP , the

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interfering HS-PDSCH power is link PDSCH-HS)

15( kJ

k

k PN

N. This is reduced by the chip equalisation

efficiency k of the terminal.

kJ

kJk

kkJJJJJJJ

kJL

PN

NPPPPPP

I

))15

)(1()(1( link PDSCH-HSkSCCHHSUMTSHSUPA commonpilotsync

in

Own-cell HSDPA power is not considered as interference. Own-cell interference from pilot, common,

and UMTS traffic channels is reduced because of orthogonality.

HS-PDSCH Eb/No

SINR HSPDSCH-HS

16kJ

k

kJ EG

E (29)

The above formula gives the Eb/No for the HS-PDSCH. See section 1.6 for the calculation of kG for

a HSDPA bearer.

HSUPA Eb/No

HSUPAtotal

HSUPAHSUPA

HSUPA

)1( kkkkJJ

kk

JkPLR

PGE (30)

UMTS UL Eb/No

kkkJkJ

kkJk

PLR

PGE

)(total. (31)

Own link power is not considered as interference. See section 1.6 for the calculation of kG for a

bearer.

UMTS DL Eb/No

outinthermal )1(

/

kJkkJk

kJkJk

kJIIN

LPGE . (32)

where in

kJI is the time-average in-cell interference.

kJ

JJJJJJJJ

kJL

PPPPPPPI

))(1( SCCHHSPDSCH-HSkUMTSHSUPA commonpilotsync

in

The quantitykUMTS

JP is the time-average total UMTS power for the other links, and is given by:

kJkkJJ PPP )(UMTSkUMTS

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Own link power is not considered as interference. Own-cell interference from other UMTS and

HSDPA channels is reduced because of orthogonality. See section 1.6 for the calculation of kG for a

bearer.

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2.6 EXTENDED HSDPA ANALYSIS FORMULAE

The calculations that make up the Extended HSDPA Analysis are performed after the snapshots have

been run. All outputs are related to the Achievable HSDPA Bearer plot. The achievable HSDPA

bearer at each pixel provides us with:

An achievable user-bitrate for the service in the pixel.

An activity factor for the service in the pixel. This is just the power-activity factor of the

Achievable HSDPA Bearer.

A cell that “owns” the pixel. The cell that supports the Achievable HSDPA Bearer and

provides the strongest pilot “owns” the pixel.

Offered HSDPA Pixel Load

This is the mean number of service M terminals in pixel k, weighted by activity factor.

powerkMkMkM N . (33)

kM = Offered load from service M terminals in pixel k.

kMN = Mean number of offered service M terminals in pixel k (read from the traffic density array).

powerkM = Power-activity factor of service M terminals in pixel k. This is the activity factor of the

Achievable HSDPA Bearer for the service M terminal in pixel k.

Offered HSDPA Cell Load

Offered HSDPA cell loads are calculated by summing individual pixel loads. Each pixel load is

assigned to one of the cells that cover the pixel. The cell that “owns” the pixel receives the load. In the

following formula, the first summation indicates that the HSDPA load for cell J is found by summing

individual pixel loads. The second summation is over the services that support HSDPA.

Jk M

kMJ

HSDPAsupports

. (34)

J = Offered load on Cell J.

kM = Load from service M terminals on pixel k.

Effective Service Rate (Unloaded)

The effective service rate at a pixel is found by calculating the Achievable HSDPA Bearer at the pixel.

The effective service bitrate is the user-bitrate of the bearer, multiplied by the activity factor of the

bearer.

kMkM

kM

M

kM CT

X powerunloaded . (35)

powerkM = Power activity factor of service M in pixel k.

kMC = Achievable DL HSDPA user-rate for service M in pixel k.

MX = Total data (in bits) for service M (calculated from the PS parameters of the service).

kMT = Unloaded session time in seconds, i.e. the session time when there is no queuing delay.

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Effective Service Rate (Loaded)

A high cell load ( J ) increases the session time and so decreases the effective service rate at a pixel.

unloaded

power

loaded

)1(1

1kM

kMJ

JkM . (36)

If 1J then 0loadedkM .

Effective Cell Service Rate (Unloaded)

This is the effective bitrate for a service M user on cell J when there is no queuing delay.

JMJM TX /unloaded . (37)

MX = Total data (in bits) for service M (calculated from the PS parameters of the service).

JT = Mean service time for a user in cell J (defined later).

If the cell load ( J ) is zero, then both JT and unloadedJM are undefined, and this is indicated by

assigning an effective cell service rate of -1.

Effectice Cell Service Rate (Loaded)

This is the effective bitrate for a service M user on cell J when there is queuing delay. A high cell load

( J ) decreases the effective cell service rate.

)1(unloadedloadedJJMJM . (38)

If 1J then 0loadedJM .

If the cell load ( J ) is zero, then both unloadedJM and

loadedJM are undefined, and this is indicated by

assigning an effective cell service rate of -1.

Mean Service Time in Pixel

The mean service time ( kMS ) for a user of service M in pixel k is the time spent transmitting data, and

is related to the unloaded session time ( kMT ) as follows

kMMkMkMkM CXTS /power

. (39)

powerkM = Power activity factor of service M in pixel k.

MX = Total data (in bits) for service M (calculated from the PS parameters of the service).

kMC = Achievable DL HSDPA user-rate for service M in pixel k.

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Mean Service Time in Cell

The mean service time for a user in cell J is given by

Jk M kM

kM

Jk M

kM

J

S

T . (40)

In other words, it is a weighted harmonic mean of the mean service times at pixels, weighted by offered

pixel loads. If the offered load on a cell is zero, then both the numerator and denominator in the above

expression are zero, and so JT is undefined. This means that the Effective Cell Service Rate

(Unloaded) and the Effective Cell Service Rate (Loaded) will both be undefined.

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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 uplink and

downlink transmission powers 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, power control errors).

Calculating link powers using power iterations.

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 can be achieved, we need only consider a single

pixel (bin) in the simulation.

Consider a pixel that has a terminal density of D terminal/km2 and an area of A km

2, so that the average

number of terminals in the pixel is DA. 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 exactly the same point within a pixel

is zero. This is simply because there are 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 snapshot

will also be Poisson distributed.

One may note that if the average number of terminals at a pixel is small (DA << 1), then working to

first order in DA,

.) terminal1 (

,)1() terminal0 (

DAP

DAP

So one is effectively making a binary decision about whether a terminal should be placed at the pixel.

After creating the random terminal distribution, the terminals are randomly sequenced. This

determines the order in which they will be considered during the power iterations.

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3.2 RANDOM SPEED DISTRIBUTION

Each randomly scattered terminal in a simulation is given a random speed according to its terminal type

and the clutter type in which it resides. For each combination of terminal type and clutter type, the

user specifies 4 parameters that determine the speed distribution. These are:

speed Mean speed.

speed Standard deviation of the speed distribution.

mins Minimum speed.

maxs Maximum speed.

A random speed is then given by

)),max(,min( speedspeedminmax Xsss .

where X is a random number drawn from a normal distribution of zero mean and unit variance.

Terminals are randomly assigned as being indoor or outdoor, according to their terminal type and the

clutter type in which they reside. Indoor terminals are all given a speed of zero.

When defining a bearer, the user specifies how speed affects the Eb/No requirement and handover

gains for that bearer. The user enters values at speeds of (in SI units) 3 km/h, 50 km/h, 120 km/h.

Values at other speeds are obtained by linear interpolation. Values are not extrapolated to speeds

higher than 120 km/h or lower than 3 km/h, which explains the labels (0-3 km/h & >= 120km/h).

Therefore stationary terminals will always use the values corresponding to 0-3km/h, and there is no

difference between a stationary terminal and one travelling at 3 km/h. The output arrays for the

simulation are available at 3 different speeds (0-3 km/h, 50 km/h, 120 km/h) so the user can more

clearly see how coverage changes with speed.

3.3 POWER CONTROL MODELLING

Power control in a real network

In a real network, link powers are modified by stepping up or down by a power step size, so

the set of possible link TX powers is discrete. A step size of 0 dB is meaningless since powers

could never change.

Power control is dynamic and imperfect. Hence served terminals will sometimes

underachieve Eb/No requirements and sometimes overachieve them.

Power control in a snapshot

Link powers in a snapshot are modified but not by stepping up or down. It is computationally

more efficient to calculate a required link power and set it directly, rather than trying to

achieve the power via several steps up or down. Therefore there is no reason to restrict link

TX powers to a discrete set, although the user can still do this by entering a non-zero Power

Step Size in the terminal definition. A Power Step Size of 0 dB simply implies that a

continuum of link powers is available.

A snapshot is not dynamic, in the sense that there is no concept of the network changing with

respect to time. It is possible to produce a snapshot where all links exactly satisfy their Eb/No

requirements, which is something that would never be observed in reality. In reality, the

errors between achieved and required Eb/No values follow a log-normal distribution. The

user can randomise the “perfect” set of link powers produced by a snapshot using the Power

Control Std Dev parameter in the simulation wizard. This takes the “perfect” link powers of

served terminals and adds random (log-normal) errors to them so that the served terminals

underachieve and overachieve their Eb/No requirements.

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It is recommended that users set the Power Step Size parameter to 0 dB and the Power Control Std Dev

parameter to 0 dB for the following reasons:

Their effects are insignificant compared to the input sources of error to the simulation (i.e. the

pathloss predictions and terminal density array supplied by the user).

Given that the snapshot spends a great deal of time trying to accurately calculate link powers,

it is wasteful to then throw away this work by quantising or randomising the results.

3.4 POWER ITERATIONS

The main task in a snapshot is to assign a set of link powers satisfying the Eb/No requirements of the

randomly spread terminals. Before commencing the power iterations, the system is placed in the state

of an unloaded network by setting all link powers to zero, and making all resources available at the

cells. The link powers in the system are then calculated iteratively by repeatedly cycling through the

list of randomly spread terminals and applying the following logic to each terminal.

If the terminal is already “connected”, then “disconnect” it as follows:

o Zero the UL & DL powers for the terminal.

o Zero the cell resources used by the terminal.

o Recalculate the UL interference on all cells (because the UL power for the terminal

has been zeroed).

o Recalculate the total DL power on all cells (because the DL powers for the terminal

have been zeroed).

o Recalculate resources available on all cells (because the terminal has released

resources).

Try and “connect” the terminal to the network in the most favourable way possible. Note that

this may be different to the way it was previously “connected”. For example, it may be

preferable to use a different carrier if interference has increased since the last time the terminal

was evaluated. The procedure for finding the most favourable method of connection is

described in the section on Connection Evaluation.

If a connection is possible, then “connect” the terminal as follows:

o Set the UL and DL powers for the terminal.

o Set the cell resources used by the terminal.

o Recalculate the UL interference on all cells (because the UL power for the terminal

has been set).

o Recalculate the total DL power on all cells (because the DL powers for the terminal

have been set).

o Recalculate resources available on all cells (because the terminal has consumed

resources).

Several cycles through the list of terminals must be performed before a stable set of link powers

emerge. The following diagram illustrates how a snapshot converges with successive cycles through

the terminal list. The histograms show how “connected” terminals underachieve their Eb/No

requirements.

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After the first cycle through the terminal list, the majority of “connected” terminals underachieve their

Eb/No requirements. This is because terminals connected at the beginning of the first cycle see little or

no interference and so have their link powers set to low values. By the end of the first cycle, the

interference in the system is higher. Therefore terminals evaluated at the beginning of the cycle no

longer achieve their Eb/No requirements by the end of the cycle. Successive cycles through the

terminal list produce increasingly accurate pictures of network interference. After a few cycles,

practically all the “connected” terminals have link powers that achieve the Eb/No requirements, and the

system interference no longer changes significantly. The power iterations have converged to produce a

plausible picture of served and failed terminals in the network.

3.5 CONVERGENCE TEST

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

This is considerably faster than measuring the distribution of achieved Eb/No values described above.

Asset3g now uses a much stronger convergence criterion for simulation snapshots than previous

versions of the tool (Version 5.0 and earlier), since both the UL and DL are checked. The user only

needs to enter a single parameter, namely a percentage power change. After each cycle through the

terminal list, the percentage changes in total UL RX power and total DL TX power are noted. If these

both fall within the user specified limit for 15 consecutive iterations, then the snapshot is considered to

be converged. So the percentage changes in UL and DL noise must not only become small but must

remain small also. Note that the user no longer enters a maximum number of iterations parameter (i.e.

maximum number of cycles) as in older versions of the tool, and power iterations will now run until the

snapshot has converged, so there is no possibility of producing non-converged snapshots.

3.6 GATHERING OF RESULTS

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

information (e.g. resource and power usage), information about the states of “connected” terminals, and

the reasons for failure of terminals which failed to be served.

End of 3

cycles

-8 -6 -4 -2 0 2

Error (dB)

End of 1

cycle

-8 -6 -4 -2 0 2

Error (dB)

End of 7

cycles

-8 -6 -4 -2 0 2

Error (dB)

End of 5

cycles

-8 -6 -4 -2 0 2

Error (dB)

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4 CONNECTION EVALUATION IN A SNAPSHOT

4.1 CONNECTION SCENARIO PRIORITISATION

A connection scenario describes how a terminal “connects” to the network and consists of the

following set of parameters:

The carrier used for connection.

Carrier load status (overloaded/underloaded). If any covering cell with the carrier exceeds its

“load balance threshold”, then the carrier load status is “overloaded”, otherwise it is

“underloaded”.

The primary cell for the connection (this is where the primary resources are consumed)

The Ec/Io of the primary cell.

The DL bearer used.

The UL bearer used.

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, so some

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 underloaded carriers to overloaded carriers.

Prefer higher priority carriers to lower priority carriers.

Prefer cells with higher Ec/Io levels to cells with lower Ec/Io levels.

Prefer higher priority DL bearers to lower priority DL bearers.

Prefer higher priority UL bearers to lower priority UL bearers

As an example, the scenarios available to a terminal may be (from most to least favoured):

Cell_X Carrier_1 Ec/Io = -10 DL=24 kbps UL = 12 kbps

Cell_X Carrier_1 Ec/Io = -10 DL=12 kbps UL = 12 kbps

Cell_Y Carrier_1 Ec/Io = -12 DL=24 kbps UL = 12 kbps

Cell_Y Carrier_1 Ec/Io = -12 DL=12 kbps UL = 12 kbps

Cell_Z Carrier_1 Ec/Io = -14 DL=24 kbps UL = 12 kbps

Cell_Z Carrier_1 Ec/Io = -14 DL=12 kbps UL = 12 kbps

Cell_A Carrier_2 Ec/Io = -8 DL=24 kbps UL = 12 kbps

Cell_A Carrier_2 Ec/Io = -8 DL=12 kbps UL = 12 kbps

Cell_B Carrier_2 Ec/Io = -9 DL=24 kbps UL = 12 kbps

Cell_B Carrier_2 Ec/Io = -9 DL=12 kbps UL = 12 kbps

In this example, the user has specified Carrier_1 to be of higher priority than Carrier_2, so cells with

Carrier_1 are preferred even though there are better Ec/Io levels on Carrier_2. Cell_X is the most

preferred cell since it has the highest Ec/Io of the Carrier_1 cells. The 24 kbps DL bearer has been

given a higher priority than the 12 kbps bearer, so it is the preferred DL bearer on every cell.

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 power iterations, and this flexibility provides us with link adaptation.

There are 3 stages to evaluating a connection scenario to see if a connection is possible:

Production of a candidate active set for the terminal.

Uplink evaluation.

Downlink evaluation.

We now describe each stage in turn.

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4.2 PRODUCTION OF A CANDIDATE ACTIVE SET

In order for a cell to be in the candidate active set of a terminal, it must have an adequate number of

resources available, and the pilot levels (SIR, Ec/Io, RSCP) for the cell must also be acceptable. It is

necessary to produce a candidate active set before the uplink and downlink can be evaluated. A

candidate active set is produced by the following procedure.

Check primary resource availability & pilot levels (SIR, Ec/Io, RSCP) of primary cell.

Check handover resource availability & pilot Ec/Io levels of other cells.

The connection scenario being examined sets the candidate primary cell. This cell is checked to see if

it has a sufficient number of primary resources available, and to see if it provides an adequate pilot for

the terminal. If these conditions are met, the cell is flagged as the primary cell of the candidate active

set.

The remaining covering cells are evaluated to see if they can be handover cells. Cells with the best

pilot levels are checked before cells with weaker pilots. A handover cell must have a sufficient number

of handover resources available, and provide a pilot Ec/Io level of adequate strength (i.e. within the

handover margin of the Ec/Io level of the primary cell). Each cell that satisfies these requirements is

flagged as a handover cell unless the active set size limit specified on the primary cell has been

reached.

4.3 UMTS UPLINK EVALUATION

This is the process of determining the terminal transmit power required to meet the uplink Eb/No

requirement. It is necessary to consider several effects here, such as handover gains, power control

headroom, and noise rise limits on cells. Before describing the uplink evaluation procedure, we

describe each of these effects in turn.

Terminal Power Reduction (TXP Gain)

The Terminal Power Reduction (reductionpower

kG ) is a gain that reduces the required transmit power of a

terminal in soft handover. It is equivalent to a reduction in the uplink Eb/No requirement.

Average Power Rise

The Average Power Rise (risepower

kP ) effect is due to fast power control. Fast power control can

compensate for fading in a channel and keep the uplink received power from a terminal fairly constant

in the cell providing the power control. However this compensation for fades causes peaks in the

terminal transmission power. This results in a rise in the average interference experienced in other

cells. This is modelled in the simulator by adding an average transmit power rise to the terminal

transmit power when calculating the uplink interference caused to other cells. When calculating the

interference a terminal causes to its own cell, the average power rise is not added.

Power Control Headroom

The Power Control Headroom (PCHkH ) is an overhead on the transmit power a terminal requires to

make the uplink. It is a function of terminal speed, and the overhead is largest for slow moving

terminals. The overhead ensures that the uplink power control is able to compensate for deep fades at a

cell edge.

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Soft Handover Gain against Average Power Rise (PR Gain)

The Soft Handover Gain against Average Power Rise ( risepower kG ) reduces the average power rise for

soft handover cells. For non-handover cells, 1risepower

kG .

Soft Handover Gain against Power Control Headroom (PCH Gain)

The Soft Handover Gain against Power Control Headroom (PCHkG ) reduces the power control

headroom when a terminal is in soft handover.

UPLINK TX POWER CALCULATION

For each cell in the active set, use the link budget equation (31) to calculate the uplink traffic

channel TX power needed to meet the uplink Eb/No requirement. Call the smallest of these

powers best

kP .

Assuming the terminal transmits at full power, calculate the difference in dB between the two

best uplink Eb/No’s. Call this difference Eb/Nok .

Get the values of reductionpower

kG ,risepower

kP ,PCHkH ,

risepower kG ,

PCHkG based on

Eb/Nok and the

speed of the terminal. If the service does not support soft handover then

1PCHrisepower PCHrisepower reductionpower kkkkk GGHPG .

The uplink traffic channel TX power in an active period is given by reductionpower best / kkk GPP .

The uplink control overhead TX power in both active and inactive periods is kk P , where

k is the control overhead factor of the uplink bearer.

Therefore, the total uplink TX power in an active period is kk P)1( .

UPLINK COVERAGE CHECK

The uplink is covered if

PCH

PCHMax MS)1(

k

kkkk

H

GPP ,

where Max MS

kP is the maximum power of the mobile.

UPLINK SOFT CAPACITY CHECK

The time-average uplink interference that the terminal would produce on its own cell (J) is

Jk

kkk

L

P)(,

where k is the bearer activity factor and JkL is the UL loss.

The time-average uplink interference that the terminal would produce on another cell (Q) is

risepower

risepower )(

k

k

Qk

kkk

G

P

L

P.

The terminal will not be connected to the network if doing so would cause the total uplink

interference on any cell to increase to a level that breaks the cell’s noise rise limit.

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4.4 HSUPA UPLINK EVALUATION

The HSUPA link evaluation is the same as the UMTS Uplink one with the exception that when a

terminal tries to connect to a cell, the simulator should check if both the terminal and cell support

HSUPA as well as if the TTI duration, Min SF and Max Number of Codes used by the bearer are

supported by both the terminal and cell.

4.5 UMTS DOWNLINK EVALUATION

This is the process of determining the cell transmit powers required to meet the downlink Eb/No

requirement at the terminal.

Downlink Eb/No Target Reduction

The Downlink Eb/No Target Reduction (reductionpower

kG ) is a gain that reduces the downlink Eb/No

requirement of a terminal in soft handover.

DOWNLINK COVERAGE CHECK

For each cell J in the active set, set the downlink traffic channel TX power to

k

JJ

PP

1

max

,

where max

JP is the maximum allowed power for a downlink, and k is the control overhead

factor of the downlink bearer. The downlink control overhead power is kJP and so the

total link power in an active period is max

)1( JJk PP .

For each link in the active set, use the downlink link budget equation (32) to calculate the

achieved Eb/No for the traffic channel in an active period. The total downlink Eb/No after

maximal ratio combining (totalkE ) is the sum of the Eb/No values for the individual links (in

normal units, not dB).

Calculate the difference in dB between the two best pilot Ec/Io levels in the active set. Call

this difference Ec/Iok .

Get the value of reductionpower

kG based on Ec/Iok and the speed of the terminal. If the service

does not support soft handover then 1reductionpower

kG .

The downlink is covered if reductionpower requiredtotal / kkk GEE ,

where requiredkE is the downlink Eb/No requirement of the traffic channel in a period of

activity.

DOWNLINK TX POWER CALCULATION & DOWNLINK SOFT CAPACITY CHECK

For the link with the primary cell, use the downlink link budget equation (32) to calculate the

downlink traffic channel TX power ( T ) needed to meet the DL Eb/No requirement in an active

period.

We find the downlink traffic channel powers for cells in the active set by iterating over the

value T as follows:

o For each cell J in the active set, set the DL traffic channel TX power to

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kk

J

k

J

k

J TPPP

1,

1max,

1,

1min

minmaxavailable

,

where min

JP is the minimum allowed power for a downlink and the time-average

power available on the cell is given by totalMax BSavailableJJJ PPP .

In other words, try to set all link powers to T but make sure links do not transmit

more power than is available.

o For each link in the active set, use the downlink link budget equation (32) to calculate

the achieved Eb/No for the traffic channel in an active period. The total downlink

Eb/No after maximal ratio combining (totalkE ) is the sum of the Eb/No values for the

individual links (in normal units, not dB).

o Modify T as follows

total

reductionpower required/

k

kk

E

GETT .

This reduces to TT if the Eb/No requirement is satisfied exactly.

o Repeat the previous 3 steps until totalkE has converged to some value

finalkE .

If reductionpower requiredfinal / kkk GEE then we have enough power on the cells to serve the user,

and the traffic channel TX power for cell J in an active period is

kk

J

k

J

k

JJ

TPPPP

1,

1max,

1,

1min

minmaxavailable

.

Since the control overhead power is Jk P , the total link power in an active period is given

by Jk P)1( and satisfies

)),max(,,min()1(minmaxavailable TPPPP JJJJk .

If reductionpower requiredfinal / kkk GEE then we do not have enough power on the cells to serve

the user, so the terminal will not be connected to the network.

4.6 HSDPA DOWNLINK EVALUATION

HSDPA DOWNLINK TX POWER CALCULATION

Each HSDPA link is transmitted in two parts: Control Channel link SCCH-HS

kJP

and data channel

link PDSCH-HS

kJP . The calculation of the control channel depends on the HS-SCCH dynamic power setting

of the cell, while the calculation of the data channel depends on the code-multiplexing setting of the

cell as given by equation (7).

HSDPA DOWNLINK COVERAGE CHECK

Use the HSDPA link budget equations (26) and (29) to calculate the HS-SCCH Ec/Nt (SCCH-HS

JkE ) and the HS-PDSCH Eb/No at the terminal (

PDSCH-HS

JkE ).

The DL is covered if

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requiredSCCHt -HSSCCH-HS

JkJk EE AND

required PDSCHPDSCH-HS

JkJk EE

where required SCCH-HS

JkE and

required PDSCH-HS

JkE is the HS-SCCH Ec/Nt requirement of the

terminal and the DL Eb/No requirement of the HSDPA bearer, respectively.

HSDPA DOWNLINK SOFT CAPACITY CHECK

We must ensure that connecting the terminal will not cause the time-average HSDPA power on

the cell (HSDPAJP ) to exceed

linkHSDPA JP . This condition is equivalent to saying that the sum of

the activity factors of served HSDPA users must not exceed 100%.

We must ensure that connecting the terminal will not cause the time-average cell power (totalJP

) to exceed Max BS

JP . The same rule applies to non-HSDPA links.

ON THE USE OF CQI TABLES

When evaluating a connection to a terminal demanding a service set up to use HSDPA CQI tables the

evaluation follows the same procedure described earlier with the exception that the simulation will first

need to decide which list of bearers (i.e. which CQI table) to consider for the set of produced scenarios.

This is achieved by checking the HSDPA terminal category (selected by the user) and the serving cell’s

HSDPA capability. Based on both ends’ capabilities the simulation will choose one or more CQI table

bearers to evaluate using the following table.

Table 1 Applicability of CQI mapping tables

Category

Used CQI mapping table

64QAM/MIMO not configured

64QAM configured MIMO configured

1-6 A N/A

7 and 8 B N/A

9 C N/A

10 D N/A

11 and 12 E N/A

13 C F N/A

14 D G N/A

15 C N/A H

16 D N/A I

17 C F H

18 D G I

As can be seen from the table, some terminal categories may support multiple tables depending on

whether 64QAM and/or MIMO are supported by the cell. The simulation will still create scenarios for

all the terminal-supported tables as the simulation may need to evaluate multiple covering cells –with

different capabilities- before finding a suitable connection scenario.

A final note on the usage of CQI tables is regarding the order in which CQI table entries are evaluated.

When the user sets up a service to use HSDPA CQI tables they may notice that all entries of all CQI

tables (A to I) are listed in an ascending order as supported bearers. To clear any confusion over this

display it should be stated that the ascending order is being used only for display clarity. When creating

the connection scenarios CQI table entries are sorted in a descending order starting with the highest

index (e.g. A30 to A1). Also, the reason why all tables are displayed is because the service will not

know which CQI tables are to be used until both the terminal category and the cell are identified.

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4.7 FAILURE REASONS

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

Low Pilot.

This means that one or more of the pilot requirements specified on the terminal type (i.e.

Ec/Io, SIR, RSCP) are not satisfied.

No UL/DL Resources.

This means that the primary cell has too few resources to serve the UL/DL bearer.

No UL/DL Primary Resources.

This means that the primary cell had too few primary resources to serve the UL/DL bearer.

UL Eb/No (Range).

This means the terminal cannot meet the Eb/No requirement of the UL bearer, even if the

terminal transmits at maximum power. More precisely, the scenario fails the UPLINK

COVERAGE CHECK described in section 4.3.

UL Noise Rise.

This means that the connection would break the noise rise limit on the cell. More precisely,

the scenario fails the UPLINK SOFT CAPACITY CHECK described in section 4.3.

DL Eb/No (Range).

This means the cells in the active set cannot meet the Eb/No requirement of the DL bearer,

even if all links are transmitted at maximum power. More precisely, the scenario fails the

DOWNLINK COVERAGE CHECK described in section 4.4 (and section 4.5 for HSDPA

bearers).

DL Eb/No (Capacity).

This means the cells in the active set have insufficient available power to meet the Eb/No

requirement of the DL bearer. More precisely, the scenario fails the DOWNLINK SOFT

CAPACITY CHECK described in section 4.4 (and section 4.5 for HSDPA bearers).

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

is classed as a failure. Note that each scenario in the list can fail for multiple reasons. Also, different

scenarios in 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 Carrier Ec/Io (dB) DL Bearer UL Bearer Problems

Cell_X 1 -18 24 kbps 12 kbps Noise rise, Low Pilot.

Cell_Y 2 -16 24 kbps 12 kbps DL Eb/No Range.

In this example, Carrier 1 has a higher priority than Carrier 2, and so Cell_X is the top scenario even

though it has a worse Ec/Io than Cell_Y. What is the correct reason for failure to assign to the

terminal? There is no correct way of doing this. The tool only records the failure reasons of the top

scenario, as in most cases this provides the most useful information as to why a terminal fails. So in

the above example, the terminal would be deemed to have failed because of problems with Noise Rise

and Low Pilot on Cell_X. The terminal would only contribute to the failure statistics for Cell_X, not

Cell_Y, and it would not affect the failure statistics for DL Eb/No (Range).

5 OUTPUT ARRAYS

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5.1 ARRAY DEPENDENCIES

All arrays are produced on a per carrier basis.

Most arrays have a dependency on terminal-type because body loss and terminal antenna gain are

always included in the linkloss.

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). Indoor terminals are always taken to be slow moving.

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 loaded system the

user must run some snapshots. Remember that the key purpose of running snapshots is to provide

measures of system load.

Arrays for coverage tend to have a weak dependence on the number of snapshots run, and the arrays

change little after a relatively small number of snapshots have been performed (10s of snapshots in

most cases). This is because only a small number of snapshots are needed to get an idea of the average

noise rise and average DL traffic power on each cell.

Arrays for hard or soft blocking probabilities have a strong dependence on the number of snapshots

run. This is because blocking is evaluated by reporting the proportion of snapshots that would block

further connections. For example, if the user has run 1 snapshot then all blocking probabilities will be

either 0% or 100%. If 5 snapshots have been run then all blocking probabilities will belong to the set

{0%, 20%, 40%, 60%, 80%, 100%}.

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) should be self explanatory.

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

“Reliability level” means the array depends on the coverage reliability threshold in the array settings

dialog. The user can change this parameter and then redraw the array without running any more

snapshots.

“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.

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C=Carrier T=Terminal, S=Service U=UL Bearer, D=DL Bearer

V=Velocity I=Indoor F=Fading R=Reliability level n=Snapshots done

C T S U D V I F R n

DL Loss X X X

Nth DL Loss X X X

Best DL Cell by RSCP X

Best RSCP X X X

Nth Best RSCP X X X

RSCP Coverage Probability X X X X

RSCP Coverage OK X X X X X

Number of RSCP OK X X X X X

Pilot Ec/Io X X X

Nth Best Pilot Ec/Io X X X

Pilot Ec/Io Coverage Probability X X X X

Pilot Ec/Io Coverage OK X X X X X

Number of Pilot Ec/Io OK X X X X X

Pilot SIR X X X

Pilot SIR Coverage Probability X X X X

Pilot SIR Coverage OK X X X X X

Number of Pilot SIR OK X X X X X

Available Soft/Softer Cells X X X

Available Soft Cells X X X

Available Softer Cells X X X

Active Set Size X X X

Pilot Polluters X X X

UL Load X

UL FRE X

DL Io X X

DL Iother / Iown X

DL FRE X

Best UL Cell X

UL Eb/No Margin X X X X X X

UL Req TX Power X X X X X X

UL Coverage Probability X X X X X X X

UL Coverage Probability OK X X X X X X X X

Achievable UL Bearer X X X X X X X

Best DL Cell X

DL Eb/No Margin X X X X X X

DL Coverage Probability X X X X X X X

DL Coverage Probability OK X X X X X X X X

Achievable DL Bearer X X X X X X X

Coverage Balance X X X X X X X

UL Soft Blocking Probability X X X X X X X

DL Soft Blocking Probability X X X X X X X

Hard Blocking Probability X X X X X X X X

Hard Blocking Probability – Primary X X X X X X X X

HSDPA - Best DL Cell by SINR X

HSDPA -SINR X X X

HSDPA - DL Eb/No Margin X X X X X X

HSDPA - DL Coverage Probability X X X X X X X

HSDPA - DL Coverage Probability OK X X X X X X X X

HSDPA - Achievable DL Bearer X X X X X X X

HSDPA - Cell for Achievable DL Bearer X X X X X X X

HSDPA - Achievable Data Rate (kbps) X X X X X X X

HSDPA - Offered Load X X X

HSDPA - Effective Service Rate (Unloaded) X X X X X X X

HSDPA - Effective Service Rate (Loaded) X X X X X X X

HSDPA - Effective Cell Service Rate (Unloaded) X X X X

HSDPA - Effective Cell Service Rate (Loaded) X X X X

HSUPA - Best UL Cell X

HSUPA - UL Eb/No Margin X X X X X X

HSUPA - UL TX Power X X X X X X

HSUPA - UL Coverage Probability X X X X X X X

HSUPA - UL Coverage Probability OK X X X X X X X X

HSUPA - Achievable UL Bearer X X X X X X X

HSUPA - Cell for Achievable UL Bearer X X X X X X X

HSUPA - Achievable Data Rate (kbps) X X X X X X X

C T S U D V I F R n

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5.2 PATHLOSS ARRAYS

DL Loss & Nth DL Loss

Dependencies: Terminal, Carrier, Indoor

These are the lowest (and Nth lowest) downlink losses. They represent average values and are

therefore calculated with fades of 0 dB.

5.3 PILOT COVERAGE ARRAYS

These arrays all provide information on pilot levels and coverage probabilities. There are 3 types of

quantity relating to the pilot (RSCP, Ec/Io, SIR) and there are arrays for all of these.

Best DL Cell by RSCP

Dependencies: Carrier

This is the cell that provides the highest RSCP for the terminal.

Best RSCP & Nth Best RSCP

Dependencies: Terminal, Carrier, Indoor

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

calculated with fades of 0 dB.

RSCP Coverage Probability

Dependencies: Terminal, Carrier, Indoor

This is the probability that the Best DL Cell (by RSCP) satisfies the RSCP 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.

RSCP Coverage OK

Dependencies: Terminal, Carrier, Indoor

This is a thresholded version of the RSCP Coverage Probability array and has just two values

(Yes/No). It has the advantage of being quicker to calculate than the RSCP Coverage Probability

array. A value of “Yes” means that the RSCP coverage probability meets the coverage reliability level

specified in Array Settings Sim Display Settings.

Number of RSCP OK Dependencies: Terminal, Carrier, Indoor

This is the number of covering cells with a satisfactory RSCP. A cell is counted as having a

satisfactory RSCP if its RSCP coverage probability meets the coverage reliability level specified in

Array Settings Sim Display Settings.

Pilot Ec/Io & Nth Best Pilot Ec/Io

Dependencies: Terminal, Carrier, Indoor

These are the highest (and Nth highest) Ec/Io values. They represent average values and are therefore

calculated with fades of 0 dB.

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Pilot Ec/Io Coverage Probability

Dependencies: Terminal, Carrier, Indoor

This is the probability that the Best DL Cell (by RSCP) satisfies the Ec/Io 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.

Pilot Ec/Io Coverage OK

Dependencies: Terminal, Carrier, Indoor

This is a thresholded version of the Pilot Ec/Io Coverage Probability array and has just two values

(Yes/No). It has the advantage of being quicker to calculate than the Pilot Ec/Io Coverage Probability

array. A value of “Yes” means that the pilot Ec/Io coverage probability meets the coverage reliability

level specified in Array Settings Sim Display Settings.

Number of Pilot Ec/Io OK

Dependencies: Terminal, Carrier, Indoor

This is the number of covering cells with a satisfactory pilot Ec/Io. A cell is counted as having a

satisfactory pilot Ec/Io if its pilot Ec/Io coverage probability meets the coverage reliability level

specified in Array Settings Sim Display Settings.

Pilot SIR

Dependencies: Terminal, Carrier, Indoor

This is the best Pilot SIR value. It represents an average value and is therefore calculated with fades of

0 dB.

Pilot SIR Coverage Probability Dependencies: Terminal, Carrier, Indoor

This is the probability that the Best DL Cell (by RSCP) satisfies the pilot SIR 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.

Pilot SIR Coverage OK

Dependencies: Terminal, Carrier, Indoor

This is a thresholded version of the Pilot SIR Coverage Probability array and has just two values

(Yes/No). It has the advantage of being quicker to calculate than the Pilot SIR Coverage Probability

array. A value of “Yes” means that the pilot SIR coverage probability meets the coverage reliability

level specified in Array Settings Sim Display Settings.

Number of Pilot SIR OK

Dependencies: Terminal, Carrier, Indoor

This is the number of covering cells with a satisfactory pilot SIR. A cell is counted as having a

satisfactory pilot SIR if its pilot SIR coverage probability meets the coverage reliability level specified

in Array Settings Sim Display Settings.

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5.4 HANDOVER ARRAYS

The aim of the following arrays is to provide the planner with an idea of potential handover areas, and

to indicate areas of pilot pollution. All arrays are based on mean Pilot Ec/Io levels calculated with

fades of 0 dB.

Available Soft/Softer Cells

Dependencies: Terminal, Carrier, Indoor

This is the number of suitable handover candidates for the Best DL Cell (by RSCP). If the Ec/Io level

of the best DL cell is below the Ec/Io requirement on the terminal type then no result is given.

Otherwise all the other cells are checked to see if their pilot Ec/Io levels make them suitable handover

candidates. Note that the primary cell is not counted as a handover cell, so an area where 3-way

handoff is possible will report Available Soft/Softer Cells=2.

Available Soft Cells

Dependencies: Terminal, Carrier, Indoor

This is the number of suitable soft handover candidates for the Best DL Cell (by RSCP). If the Ec/Io

level of the best DL cell is below the Ec/Io requirement on the terminal type then no result is given.

Otherwise all the other cells (on different sites to the best cell) are checked to see if their pilot Ec/Io

levels make them suitable handover candidates.

Available Softer Cells

Dependencies: Terminal, Carrier, Indoor

This is the number of suitable softer handover candidates for the Best DL Cell (by RSCP). If the Ec/Io

level of the best DL cell is below the Ec/Io requirement on the terminal type then no result is given.

Otherwise all the other cells (on the same site as the best cell) are checked to see if their pilot Ec/Io

levels make them suitable handover candidates.

Active Set Size

Dependencies: Terminal, Carrier, Indoor

This is the potential size of the active set. It is related the Available Soft/Softer Cells array (see above)

by

Active Set Size = min (1 + Available Soft/Softer Cells , Max Active Set Size).

Pilot Polluters

Dependencies: Terminal, Carrier, Indoor

If the Pilot Pollution Threshold specified by the user in the Simulation Wizard is X dB then:

For UMTS: The number of pilot polluters at a location is the number of cells that are not in the active

set, but provide an Ec/Io level within X dB of the best Ec/Io in the active set. Therefore the pilot

pollution threshold in UMTS is a relative quantity. A typical value is 5 dB.

For CDMA2000: The number of pilot polluters at a location is the number of cells that are not in the

active set, but provide an Ec/Io level higher than X dB. Therefore the pilot pollution threshold in

CDMA2000 is an absolute quantity. A typical value is -16 dB.

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5.5 UPLINK NOISE ARRAYS

UL Load

Dependencies: Carrier

This is the uplink cell load of the Best DL Cell (by RSCP). Note that for OTSR cells, there can be a

different uplink load on each antenna used by the cell (just as in the uplink simulation reports for OTSR

cells).

UL FRE

Dependencies: Carrier

This is the uplink frequency re-use efficiency of the Best DL Cell (by RSCP). Note that for OTSR

cells, there can be a different uplink FRE on each antenna used by the cell (just as in the uplink

simulation reports for OTSR cells).

5.6 DOWNLINK NOISE ARRAYS

DL Io

Dependencies: Terminal, Carrier, Indoor

This is the total downlink power spectral density. It represents an average value and is therefore

calculated with fades of 0 dB.

DL Iother/Iown

Dependencies: Carrier

This is the ratio of downlink power received from other cells to downlink power received from own

cell, where “own cell” is the Best DL Cell (by RSCP).

DL FRE

Dependencies: Carrier

This is the downlink frequency re-use efficiency at a pixel and it is related to DL Iother/Iown as

follows.

DL FRE = 1 / ( 1 + Iother / Iown ).

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5.7 UPLINK COVERAGE ARRAYS

Uplink coverage arrays are available for each bearer at different speeds.

Best UL Cell

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is the cell requiring the minimum uplink transmit power. For UMTS bearers, the only real

dependence is on the carrier used. However for CDMA2000 bearers, the Best UL Cell must have an

RC type that is supported by the terminal type.

UL Eb/No Margin

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is how much we exceed the uplink Eb/No requirement by on the Best UL Cell, assuming the

terminal transmits at full power.

UL Req TX Power

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is the required UL TX power of the terminal. It is equal to the maximum output power of the

terminal type (dBm) minus the UL Eb/No margin (dB).

UL Coverage Probability

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is the probability of satisfying the uplink bearer Eb/No requirement on the Best UL Cell, assuming

the terminal transmits at full power. 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.

UL Coverage Probability OK

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is a thresholded version of the UL Coverage Probability array and has just two values (Yes/No).

It has the advantage of being quicker to calculate than the UL Coverage Probability array. A value of

“Yes” means that the uplink coverage probability meets the coverage reliability level specified in Array

Settings Sim Display Settings.

Achievable UL Bearer

Dependencies: Terminal, Carrier, Indoor, Service, Speed

The purpose of this array is to provide a combined coverage plot for the uplink bearers of a service.

The array shows the highest priority uplink bearer with acceptable uplink coverage, i.e. with UL

Coverage Probability meeting the coverage reliability level specified in Array Settings Sim Display

Settings.

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5.8 DOWNLINK COVERAGE ARRAYS

Downlink coverage arrays are available for each bearer at different speeds.

Best DL Cell

Dependencies: Terminal, Carrier, Indoor, Service, DL Bearer, Speed

This is the cell requiring the minimum downlink transmit power. For UMTS bearers, the only real

dependence is on the carrier used, and so this array is exactly the same as the Best DL cell by RSCP.

However for CDMA2000 bearers, the Best DL Cell must have an RC type that is supported by the

terminal type.

DL Eb/No Margin

Dependencies: Terminal, Carrier, Indoor, Service, DL Bearer, Speed

This is how much we exceed the downlink Eb/No requirement by, assuming that the link powers of

cells in the active set are at maximum allowed levels.

DL Coverage Probability

Dependencies: Terminal, Carrier, Indoor, Service, DL Bearer, Speed

This is the probability of satisfying the downlink bearer Eb/No requirement, assuming that the link

powers of cells in the active set are at maximum allowed levels. 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.

DL Coverage Probability OK

Dependencies: Terminal, Carrier, Indoor, Service, DL Bearer, Speed

This is a thresholded version of the DL Coverage Probability array and has just two values (Yes/No).

It has the advantage of being quicker to calculate than the DL Coverage Probability array. A value of

“Yes” means that the downlink coverage probability meets the coverage reliability level specified in

Array Settings Sim Display Settings.

Achievable DL Bearer

Dependencies: Terminal, Carrier, Indoor, Service, Speed

The purpose of this array is to provide a combined coverage plot for the downlink bearers of a service.

The array shows the highest priority downlink bearer with acceptable downlink coverage, i.e. with DL

Coverage Probability meeting the coverage reliability level specified in Array Settings Sim Display

Settings.

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5.9 COVERAGE BALANCE

Coverage Balance

Dependencies: Terminal, Carrier, Indoor, Service, Speed

The purpose of this array is to provide a composite uplink/downlink coverage plot for a service. The

uplink is deemed to have coverage if any of the uplink bearers on the service have UL Coverage

Probability meeting the coverage reliability level specified in Array Settings Sim Display Settings.

Similarly, the downlink is deemed to have coverage if any of the downlink bearers on the service have

DL Coverage Probability meeting the coverage reliability level specified in Array Settings Sim

Display Settings.

5.10 SOFT BLOCKING ARRAYS

UL Soft Blocking Probability

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is the probability of uplink soft blocking on the Best UL Cell. Uplink soft blocking occurs if an

additional connection with the uplink bearer would cause the noise rise limit to be exceeded. The

uplink soft blocking probability is determined by examining the proportion of snapshots that would

block a connection with the uplink bearer in this way. Note that for OTSR cells, the noise rise is

measured on a per antenna basis (as in the simulation reports), so the soft blocking probability depends

on the antenna that covers the pixel.

DL Soft Blocking Probability

Dependencies: Terminal, Carrier, Indoor, Service, DL Bearer, Speed

This is the probability of downlink soft blocking on the Best DL Cell. Downlink soft blocking occurs if

an additional connection with the downlink bearer requires more power than is available on the cell.

The downlink soft blocking probability is determined by examining the proportion of snapshots that

would block a connection with the downlink bearer in this way.

5.11 HARD BLOCKING ARRAYS

There a two types of hard blocking arrays for each uplink and downlink resource type. The exception

is the HSDPA resource type used to represent HSDPA codes. This does not have a “primary” blocking

array because there are no “primary” limits for HSDPA codes.

Hard Blocking Probability

Dependencies: Terminal, Carrier, Indoor, Service, Bearer, Speed

This is the probability of hard blocking on the Best DL Cell because of lack of resources. This sort of

blocking occurs if an additional connection with the bearer requires more resources than are available.

The blocking probability is determined by examining the proportion of snapshots that would block a

connection with the bearer in this way.

Hard Blocking Probability – Primary

Dependencies: Terminal, Carrier, Indoor, Service, Bearer, Speed

This is the probability of hard blocking on the Best DL Cell because of lack of primary resources. This

sort of blocking occurs if an additional connection with the bearer requires more primary resources

than are available. The blocking probability is determined by examining the proportion of snapshots

that would block a connection with the bearer in this way.

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5.12 HSDPA ARRAYS

HSDPA - Best DL Cell by SINR

Dependencies: Carrier

This is the cell that provides the highest SINR level for the terminal.

HSDPA -SINR

Dependencies: Terminal, Carrier, Indoor

This is the highest SINR level. It represents an average value and is therefore calculated with fades of

0 dB.

HSDPA - DL Eb/No Margin

Dependencies: Terminal, Carrier, Indoor, Service, HSDPA Bearer, Speed

This is the extent to which the Eb/No requirement of the HSDPA bearer is exceeded. The cell of

interest is chosen by examining the SINR levels of cells that support the HSDPA bearer, and choosing

the cell with the largest level.

HSDPA - DL Coverage Probability

Dependencies: Terminal, Carrier, Indoor, Service, HSDPA Bearer, Speed

This is the probability of satisfying the Eb/No requirement of the HSDPA bearer. The cell of interest is

chosen by examining the SINR levels of cells that support the HSDPA bearer, and choosing the cell

with the largest level. The 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.

HSDPA - DL Coverage Probability OK

Dependencies: Terminal, Carrier, Indoor, Service, HSDPA Bearer, Speed

This is a thresholded version of the HSDPA - DL Coverage Probability array and has just two values

(Yes/No). It has the advantage of being quicker to calculate than the HSDPA - DL Coverage

Probability array. A value of “Yes” means that the coverage probability meets the coverage reliability

level specified in Array Settings Sim Display Settings.

HSDPA -Achievable DL Bearer

Dependencies: Terminal, Carrier, Indoor, Service, Speed

The purpose of this array is to provide a combined coverage plot for the HSDPA bearers of a service.

The array shows the highest priority HSDPA bearer with acceptable coverage. i.e. with HSDPA - DL

Coverage Probability meeting the coverage reliability level specified in Array Settings Sim Display

Settings.

HSDPA –Cell for Achievable DL Bearer

Dependencies: Terminal, Carrier, Indoor, Service, Speed

This is the cell that provides the best achievable HSDPA DL bearer for a terminal (The achievable

HSDPA DL bearer is given by the previous array).

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HSDPA –Achievable Data Rate (kbps)

Dependencies: Terminal, Carrier, Indoor, Service, Speed

This is the user rate of the best achievable HSDPA DL bearer for a terminal. The HSDPA bearer’s user

rate is modified to reflect any Spatial Multiplexing rate gains if MIMO is supported by both the cell

and the terminal.

HSDPA - Offered Load

Dependencies: Carrier,

This is the offered HSDPA load on the Best DL Cell by RSCP. Note that the offered load is calculated

for each HSDPA resource pool in the network. Therefore, if the HSDPA resources have been pooled

on a site, all HSDPA cells on that site will show the same offered load. The offered load is expressed

as a percentage value between 0% and 100%. See section 2.6 of this document for a more detailed

description of the offered load calculation.

HSDPA - Effective Service Rate (Unloaded)

Dependencies: Terminal, Carrier, Indoor, Service, Speed

This is the bitrate that the user experiences at a location when there is no queuing delay on the cell. It

is calculated by multiplying the bitrate of the HSDPA – Achievable DL Bearer by its activity factor.

See section 2.6 of this document for a more detailed description of the effective service rate

calculations.

HSDPA - Effective Service Rate (Loaded)

Dependencies: Terminal, Carrier, Indoor, Service, Speed

This is the bitrate that the user experiences at a location when there is queuing delay on the cell. The

rate drops to zero as the HSDPA load on the cell approaches 100%. See section 2.6 of this document

for a more detailed description of the effective service rate calculations.

HSDPA - Effective Cell Service Rate (Unloaded)

Dependencies: Carrier, Service

This is the total amount of data in a service session (bits) divided by the mean service time per user on

the cell (seconds) assuming there is no queuing delay. If the offered HSDPA load is zero, then the

Effective Cell Service Rate is undefined, and this is indicated by assigning the rate a value of -1 in the

view. See section 2.6 of this document for a more detailed description of the effective cell service rate

calculations.

HSDPA - Effective Cell Service Rate (Loaded)

Dependencies: Carrier, Service

This is like the previous array except that the mean service time per user on the cell is increased

because of queuing delay. As the offered HSDPA load on the cell approaches 100%, the queuing delay

approach infinity and the Effective Cell Service Rate (Loaded) drops to zero. If the offered HSDPA

load is zero, then the Effective Cell Service Rate is undefined, and this is indicated by assigning the rate

a value of -1 in the view. See section 2.6 of this document for a more detailed description of the

effective cell service rate calculations.

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5.13 HSUPA ARRAYS

HSUPA - Best UL Cell

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is the HSUPA-supporting cell requiring the minimum uplink transmit power. For HSUPA

bearers, the bearer (in terms of spreading factor, modulation and number of codes) has to be supported

by the cell before that cell is considered as a server.

HSUPA - UL Eb/No Margin

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is how much we exceed the HSUPA Eb/No requirement by on the Best HSUPA Cell, assuming the

terminal transmits at full power.

HSUPA - UL TX Power

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is the required UL HSUPA TX power of the terminal. It is equal to the maximum output power of

the terminal type (dBm) minus the HSUPA Eb/No margin (dB).

HSUPA - UL Coverage Probability

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is the probability of satisfying the HSUPA uplink bearer Eb/No requirement on the Best HSUPA

Cell, assuming the terminal transmits at full power. 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.

HSUPA - UL Coverage Probability OK

Dependencies: Terminal, Carrier, Indoor, Service, UL Bearer, Speed

This is a thresholded version of the HSUPA - UL Coverage Probability array and has just two values

(Yes/No). It has the advantage of being quicker to calculate than the UL Coverage Probability array.

A value of “Yes” means that the uplink coverage probability meets the coverage reliability level

specified in Array Settings Sim Display Settings.

HSUPA - Achievable UL Bearer

Dependencies: Terminal, Carrier, Indoor, Service, Speed

The purpose of this array is to provide a combined coverage plot for the HSUPA uplink bearers of a

service. The array shows the highest priority HSUPA bearer with acceptable uplink coverage, i.e. with

HSUPA UL Coverage Probability meeting the coverage reliability level specified in Array Settings

Sim Display Settings.

HSUPA –Cell for Achievable UL Bearer

Dependencies: Terminal, Carrier, Indoor, Service, Speed

This is the cell that provides the best achievable HSUPA UL bearer for a terminal (The achievable

HSUPA UL bearer is given by the previous array).

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HSUPA –Achievable Data Rate (kbps)

Dependencies: Terminal, Carrier, Indoor, Service, Speed

This is the user rate of the best achievable HSUPA UL bearer for a terminal.

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6 COVERAGE ARRAY CALCULATIONS

Coverage arrays are calculated in a different way to Version 5.0 simulations. The key differences are

The term coverage is 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.

In Version 5.0, the Coverage Probability array represents an overall connection probability. It

examines both coverage and capacity constraints, which makes it hard to perform a pure

coverage analysis.

Separate coverage arrays are available for the pilot channel, uplink bearers, and downlink

bearers. Each probability is well defined in that it refers to a particular cell, namely the Best

UL Cell or Best DL Cell.

In Version 5.0, separate coverage arrays are not available. The probability reported at a pixel

is a mixture of results involving different cells, bearers, and terminals.

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 the coverage probabilities in an unloaded system.

In Version 5.0, the probabilities are not calculated analytically but by sampling. The accuracy

of the probability reported at a pixel depends strongly on the number of samples (i.e.

connection attempts) at the pixel. This typically means that a large number of snapshots are

required to produce an accurate result. The sampling process also makes the simulation

memory-hungry. If no snapshots have been run, then there are no samples, and so no coverage

plot is available.

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

essentially 4 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 soft/hard blocking probabilities.

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

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6.2 FADES IN THE SIMULATION SNAPSHOTS

Shadow fading is modelled in a snapshot by randomising the pathlosses experienced by the randomly

scattered 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.

These two parameters must satisfy the constraints 10 trainterin cc . For each randomly scattered

terminal 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 site I, generate a random number IY .

For each cell J, generate a random number JZ .

The fade (in dB) to cell J on site I is then set to

JI ZcYccXc trainterintrainterin 1 .

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, RSCP, Ec/Io, etc) are calculated with all

fades set to 0 dB.

6.4 FADES IN ARRAYS FOR SOFT/HARD BLOCKING

The main factor affecting blocking probability is the free capacity at the cell rather than the fading in

the channel, so arrays for soft & hard blocking are calculated with all fades set to 0 dB.

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6.5 FADES IN COVERAGE ARRAY CALCULATIONS

Pilot RSCP Coverage Probability

In the absence of fading, let the pilot RSCP (in Watts) for cell J be represented by

pilotJR .

If cell J has a fade of JF dB, then the pilot RSCP is given by

)10(10/pilot

JJF

R .

We can calculate a coverage probability for the pilot RSCP as follows:

Find the fade JF that causes the pilot RSCP to exactly satisfy the RSCP requirement specified

on the terminal type. Call this fade *F . Note that

*F may be positive or negative. Any fade

bigger than *F will give an inadequate RSCP.

Since JF 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 pilot RSCP meets the requirement.

Pilot Ec/Io Coverage Probability

Although slow-fading has a log-normal distribution, one cannot always assume that signal-to-

interference ratios (such as pilot Ec/Io) also have log-normal distributions. For example, consider a

single isolated cell where the DL Io is dominated by own-cell interference and the thermal component

of DL Io is negligible. If the terminal experiences a fade, the signal and interference both decrease by

the same factor, so Ec/Io is effectively unchanged. Because of this, care must be taken in calculating

coverage probabilities for quantities such as Ec/Io.

Consider the situation when there are several cells. In the absence of fading, we can write the pilot

Ec/Io for cell J in terms of mean received cell powers as follows:

JK

KJ

JJoc

RRN

RIE

totaltotalthermal

pilot

.

When we have fades to the cells, the Ec/Io is given by:

JK

FK

FJ

FJ

JocKJ

J

RRN

RIE

)10()10(

)10(10/total10/totalthermal

10/pilot

.

There are two ways of dealing with the random fades in the above expression to arrive at a coverage

probability.

The first way is to use an experimental approach that involves sampling the fading distribution. In

other words, we examine the value of Ec/Io for many different sets of random fades. This is the way

output arrays are calculated in the Version 5.0 simulator. The advantage of this method is that it can

handle complex sets of correlated fades, but it has the drawback of requiring a large amount of time to

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evaluate an adequate number of samples. This makes it an impractical approach for calculating

coverage probabilities.

The second way is to use an approximation that makes an analytic calculation of coverage probability

possible. This is what is done to create the coverage arrays in the current simulator. The idea is to use

an approximation for Ec/Io that involves a single random variable, namely the fade for the cell of

interest ( JF ), and to replace the other fades ( KF ) by their expected values conditioned on JF . In

other words, we make the substitution:

)|( JKK FFEF .

As shown in section 6.6, correlated fades in the simulation are produced by a method that leads to the

result:

JJKJK FcFFE )|(

where JKc is the correlation coefficient between fades to cells J and K. So if the fade to cell K is

perfectly correlated with the fade to cell J, we give cell K a fade of JF dB. If the fade to cell K is

completely uncorrelated with the fade to cell J, we give cell K a fade of 0 dB, since that is the expected

value of the fade given no other information. So we obtain the following approximation for Ec/Io:

JK

FcK

FJ

FJ

JocJJKJ

J

RRN

RIE

)10()10(

)10(10/total10/totalthermal

10/pilot

.

Although the resulting expression for Ec/Io is not log-normal, it depends on a single normally-

distributed random variable ( JF ). We can calculate a coverage probability for the pilot Ec/Io as

follows:

Find the fade JF that causes the pilot Ec/Io to exactly satisfy the pilot Ec/Io requirement

specified on the terminal type. Call this fade *F . Note that

*F may be positive or negative.

Any fade bigger than *F will give an inadequate pilot Ec/Io.

Since JF 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 pilot Ec/Io meets the requirement.

Notice that the two-step procedure for obtaining a coverage probability for Ec/Io is identical to the

procedure used to obtain a coverage probability for pilot strength. The only difference is that the fade

JF influences the Ec/Io formula in a more complex way than the pilot strength formula. In the case of

the pilot strength formula, finding *F is trivial. Finding

*F for the pilot Ec/Io formula cannot be

done analytically in general, and so a numerical method (repeated bisection) is used to determine *F

in this case.

Pilot SIR Coverage Probability

This uses the same method of approximation used in the pilot Ec/Io calculation. Namely the fade to

cell K is replaced by its expected value conditioned on the fade to cell J. The only difference is that the

formula for pilot SIR is used instead of the formula for Ec/Io.

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Uplink Bearer Coverage Probability

We calculate the uplink coverage probability for the Best UL Cell of a terminal. The analysis examines

if a terminal is in a soft handover region, and modifies the link budget accordingly. See section 4.3 for

descriptions of the various handover gains in the uplink.

Assuming all shadow fades are 0 dB, use the link budget equation (29) to calculate the uplink

traffic channel TX power needed to meet the uplink Eb/No requirement on each covering cell.

The cell that requires the lowest power is the Best UL Cell.

Determine which cells are handover cells for the Best UL Cell. The cells with the best Ec/Io

levels enter the active set, providing they have an Ec/Io of sufficient quality (relative to the

Best UL Cell) and that the active set size limit has not been reached.

Assuming the terminal transmits at full power, calculate the difference in dB between the two

best uplink Eb/No’s in the active set. Call this difference Eb/Nok .

Get the values of , , based on Eb/Nok and the speed of the

terminal. If the service does not support soft handover then

1PCHPCHreductionpower kkk GHG .

Set the uplink traffic channel TX power in an active period to its maximum possible value,

remembering to account for control overhead and any handover gains:

PCH

PCHMax MS

)1( k

k

k

kk

H

GPP .

Use the link budget equation (31) to calculate JkE on the Best UL Cell. This is the uplink

Eb/No in the absence of fading.

If cell J has a fade of JF dB, then the uplink Eb/No is given by )10(10/JF

JkE . Find the fade

that causes )10(10/JF

JkE to exactly satisfy the Eb/No requirement of the uplink bearer (

requiredkE ). This fade

*F is given by

reductionpower required10/ /)10(*

kkF

Jk GEE .

Note that *F may be positive or negative. Any fade bigger than

*F will give an inadequate

uplink Eb/No.

Since JF 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 uplink service-bearer meets the Eb/No requirement.

reductionpower kG

PCHkH PCH

kG

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Downlink Bearer Coverage Probability (non-HSDPA)

This uses the same method of approximation used to calculate the pilot Ec/Io coverage probability. We

take the main random variable in the link budget to be the fade ( JF ) to the Best DL Cell and replace all

other fades by their expected values conditioned on JF .

Assuming there is no shadow fading, find the cell that provides the highest Ec/Io and supports

the bearer. This is the Best DL Cell.

Determine which cells are handover cells for the Best DL Cell. The cells with the best Ec/Io

levels enter the active set, providing they have an Ec/Io of sufficient quality (relative to the

Best DL Cell) and that the active set size limit has not been reached.

Calculate the difference in dB between the two best pilot Ec/Io levels in the active set. Call

this difference Ec/Iok .

Get the value of reductionpower

kG based on Ec/Iok and the speed of the terminal. If the service

does not support soft handover then 1reductionpower

kG .

For each cell J in the active set, set the downlink traffic channel TX power to

k

JJ

PP

1

max

where max

JP is the maximum allowed power for a downlink on cell J, and k is the control

overhead factor of the downlink bearer.

Find the fade JF that causes the DL Eb/No to be satisfied exactly. In practice we need to find this

value numerically by repeated bisection. To test a particular value of JF , we do the following:

Set the fade for the Best DL Cell to JF dB. For each other cell K, set the fade to JJK Fc dB

where JKc is the correlation coefficient between fades to cells J and K.

For each cell in the active set, use the link budget equation (32) to calculate the achieved Eb/No

for the traffic channel in an active period. The total downlink Eb/No after maximal ratio

combining (totalkE ) is the sum of the Eb/No values for the individual links (in normal units, not

dB).

The downlink Eb/No requirement is satisfied exactly if requiredreductionpower totalkkk EGE ,

where requiredkE is the downlink Eb/No requirement.

HSDPA Bearer Coverage Probability

This is identical to the above procedure for downlink non-HSDPA bearers but with the following

simplifications:

The Best DL Cell is determined by examining the cells that support the HSDPA bearer, and

choosing the one that provides the best Ec/Io.

There is no handover for HSDPA, and so there is no handover gain ( 1reductionpower

kG ).

The downlink power for a HSDPA link is linkHSDPA

JP (not max

JP ).

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6.6 CONDITIONAL EXPECTATION FOR CORRELATED FADES

We now derive the expected value of the fade to cell K ( KF ), given that we know the fade to cell J (

JF ) and the correlation coefficient between the two fades ( JKc ). The correlated fades in a snapshot

are produced by weighted sums of independent zero-mean normally-distributed (ZMND) random

variables (RVs) of unit variance, so that the fade to cell J on site I is given by

JI ZcYccXc trainterintrainterin 1 .

The number of RVs involved is large since we generate a RV for every terminal ( X ), every site ( IY ),

and every cell ( JZ ). However, for the analysis that follows here, we only ever need to consider a

single pair of correlated fades, and the above procedure can be reduced to a simpler construction using

only 3 independent ZMND RVs of unit variance RQP ,, as follows:

QcPcF JKJKJ 1 ,

RcPcF JKJKK 1 .

We can further reduce the number of independent RVs to 2, by using the ZMND RVs U and V

defined by

QcPcU JKJK 1

Rc

Qc

cP

c

ccV

JKJK

JK

JK

JKJK

1

1

11

22

It is easy to show that 1)()( 22 VEUE and 0)(UVE , so U and V have unit variance and are

uncorrelated. Expressed in terms of U and V , the fades become

UFJ ,

VcUcF JKJKK2

1 .

This gives the result

JJKJKJKJKKJK FcUcUVEcUUEcUFEFFE )0()|(1)|()|()|(2 .

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7 BLOCKING ARRAY CALCULATIONS

Blocking arrays are calculated in a different way to Version 5.0 simulations. The key differences are:

The blocking arrays have different names to those in Version 5.0. For example a Noise Rise

Failure in Version 5.0 is now described as Uplink Soft Blocking. A DL Eb/No Capacity

Failure in Version 5.0 now corresponds to a situation of Downlink Soft Blocking.

Separate blocking arrays are now available for the different uplink and downlink bearers. The

blocking probabilities are well defined in the sense that they refer to either the Best UL Cell or

Best DL Cell.

In Version 5.0, separate blocking arrays were not available. The probability reported at a pixel

is a mixture of results involving different cells, bearers, and terminals.

The coverage probability arrays are calculated analytically. An analytic calculation is possible because

the dominant random variables affecting coverage are the shadow fades to cells, and these have a

known probability distribution specified by the user. The same cannot be said for blocking

probabilities. The main random variables affecting blocking on a cell relate to availability of particular

“resources”. For downlink soft blocking, the “resource” of interest is the downlink power of the cell.

For uplink soft blocking, the “resource” of interest is the noise rise on the cell. Unlike shadow fading,

we do not know the probability distribution for noise rise on a cell, or downlink power on a cell, so an

analytic calculation of blocking probabilities is not possible. We must therefore calculate blocking

probabilities by sampling. In other words, we must find the proportion of snapshots that block further

connections. The accuracy of the result obtained will depend strongly on the number of samples taken

(i.e. snapshots performed).

In all blocking calculations, it is assumed that the dominant factor is not the shadow fading (which is

taken to be 0 dB) but rather the probability distribution of the quantity that limits capacity. For

example, for uplink soft blocking on a cell, we must consider the probability distribution of uplink

noise rise. In particular, we will want to know the probability that the noise rise on the cell is so large

that it cannot accommodate an extra user.

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7.1 UPLINK SOFT BLOCKING PROBABILITY ARRAY

All arrays dealing with uplink capacity analysis (UL Load, UL FRE, UL Soft Blocking Probability)

refer to the Best UL Cell. This is the cell that gives the lowest mobile UL power requirement.

The uplink soft blocking analysis does not use exactly the same logic as the randomly scattered

terminals in the simulator. The simulator prevents a terminal from connecting if it will cause any cell

to break its UL noise rise limit. This is necessary to ensure that no noise rise limits are exceeded when

producing a snapshot of the network. The UL Soft Blocking Probability array considers only the Best

UL Cell.

The soft blocking probability array is calculated independently of any coverage analysis. Therefore it

is assumed that there are no coverage problems, and even pixels with poor coverage can have a result.

Remember the aim of the soft blocking probability array is to highlight cells where uplink capacity is a

problem, rather than locations where uplink capacity is a problem.

The uplink soft blocking probability calculation:

Estimates the probability that an additional connection will be blocked by examining the noise

rises attained in the snapshots, and seeing how often an overloaded situation occurs. The

probability is therefore not calculated analytically but by sampling.

The blocking probability is not an Erlang-B or Erlang-C blocking probability, and in fact most

closely resembles an LCH blocking probability (Erlang-A).

Assumes no soft handover (therefore no soft HO gains, and no power rise effects).

Uses a modified Eb/No requirement depending on terminal speed and cell TX/RX diversity.

Considers the sectorised uplink for an OTSR cell. In other words, two antennas (sectors) on

the cell may have differing noise rises and hence differing soft blocking probabilities.

The uplink noise power (in Watts) on the Best UL Cell is a random variable ( totalN ) that depends on

the number of terminals in the network, their locations, and levels of activity. If we perform M

snapshots, then we will have a set of M sample values for totalN .

Consider the uplink budget that must be satisfied when connecting an additional terminal to a cell:

G

NLEP

total

,

where

P is the required traffic channel TX power in a period of activity.

E is the traffic channel Eb/No requirement in a period of activity,

L is the UL loss,

G is the processing gain,

We know all the quantities on the right-hand-side of the above link budget, and so can calculate P .

The time-average interference power ( linkN ) that the link will produce at the cell is given by

GNELPN /)(/)( totallink,

where

is the activity factor,

is the control overhead factor for the bearer.

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The total UL noise power on the cell has a maximum allowed level ( limitN ) determined by the user-

specified noise rise limit for the cell. The additional connection will be blocked if

limitlinktotal NNN .

This inequality can be rewritten as

GE

NN

/)(1

limittotal

.

All the quantities on the RHS of this expression are known, so we can obtain a measure of the soft

blocking probability by finding the proportion of snapshots where totalN satisfies the above inequality.

The accuracy of the result depends on the number of snapshots performed. For example, if only 2

snapshots have been performed then blocking probabilities are reported as either 0% or 100%.

Typically, planners will be interested in seeing low blocking probabilities (of the order of a few of

percent) and so many hundreds of snapshots are required to obtain sufficient accuracy in the reported

blocking probabilities. Consequently, it is advised that planners perform their uplink capacity analysis

by looking at quantities that converge more quickly. For example the uplink noise rise and uplink load

on a cell.

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7.2 DOWNLINK SOFT BLOCKING PROBABILITY ARRAY

The quantity that limits (soft) capacity in the uplink is the noise rise limit of the cell. In the downlink,

the quantity that limits (soft) capacity is the total cell power. However, soft capacity in the downlink is

not well defined in general, because downlink MRC permits a terminal to be served even when cells in

the active set have insufficient power to serve the terminal on their own. So capacity in the downlink

generally depends on the available power on a set of cells rather than the available power on an

individual cell.

Since we aim to highlight capacity problems on individual cells, we perform a simplified analysis of

soft blocking in the tool. Our array for DL Soft Blocking Probability refers to blocking on the Best DL

Cell. This is the cell with the best RSCP (and for a CDMA2000 system the cell must also have an RC

that supports the terminal type). We perform the analysis by seeing if the cell can serve an additional

terminal that is not in handover.

For an additional link on cell J, the time-average DL TX power is given by

GLENP J /)(totalJ

linkJ ,

where

totalJN is the total DL interference power at the pixel when for a link to cell J,

E is the Eb/No requirement for the traffic channel in a period of activity,

is the activity factor,

is the control overhead factor for the bearer,

G is the processing gain,

JL is the DL loss for cell J.

The total DL interference can be split into thermal, in-cell, and out-cell parts

cell-outcell-inthermaltotal

JJJ NNNN .

The in-cell interference is given by

J

JJJ

L

PPN

synctotalcell-in )1(

,

where is the DL orthogonality factor, and the total cell power is given by

HSDPAUMTSsynccommonpilottotal

JJJJJJ PPPPPP .

We have DL soft blocking if the total power after connection exceeds the cell power (max

JP ), i.e. if

maxlinktotal

JJJ PPP .

After some substitution, we find we can write this condition as

G

E

L

PNN

G

LEP

PJ

JJ

JJ

J )()1(1

)(sync

cell-outthermalmax

total.

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We assume that the dominant factor influencing blocking is the total DL power on the cell (total

JP ) and

we treat this as the only random variable in our expression, and replace the other random variables ( JL

, cell-outN ) on the RHS by their mean values

JJ LL ,

JK K

KJJ

L

PNN

totalcell-outcell-out

,

where

JL is the linkloss to cell J with no shadow fading,

total

KP is the mean total downlink power of cell K.

So the inequality for DL soft blocking becomes

G

E

L

P

L

PN

G

LEP

PJ

J

JK K

KJJ

J )()1(1

)(synctotal

thermalmax

total.

Note that there is a minimum allowed DL traffic power on each cell, and we must have at least this

power available to serve another user, so we also get DL soft blocking when

powerlink min maxtotal

JJJ PPP .

So the overall expression is

G

E

L

P

L

PN

G

LEP

PPPJ

J

JK K

KJJ

JJJ )()1(1

)(

,min

synctotalthermalmax

powerlink min maxtotal .

The quantity on the RHS is known at every pixel, and we obtain the blocking probability for that pixel

by examining the proportion of snapshots where total

JP exceeded the quantity on the RHS.

As in the case of UL soft blocking probability, the accuracy of the result depends on the number of

snapshots performed, and since planners will be interested in seeing low blocking probabilities (of the

order of a few percent), many hundreds of snapshots need to be performed to get confidence in the

reported blocking probabilities. Consequently, it is advised that planners perform their downlink

capacity analysis by looking at quantities that converge more quickly. For example, the total downlink

traffic power in the simulation reports.

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7.3 HARD BLOCKING PROBABILITY ARRAYS (RESOURCE BLOCKING)

The hard blocking probability refers to the Best DL Cell. This is the cell that supports the bearer and

provides the highest pilot Ec/Io. The hard blocking probability for a bearer is calculated by finding the

proportion of snapshots where the Best DL Cell had sufficient resources available to serve an additional

terminal with that bearer. For example, if the time-average number of resources required by a bearer is

M, then the blocking probability is the proportion of snapshots where the time-average number of

available resources on the Best DL Cell is greater than or equal to M. Since the blocking probability is

being estimated by sampling, the accuracy of the result depends on the number of snapshots performed.

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8 BLOCKING PROBABILITY AND FAILURE RATE

8.1 CALCULATION OF BLOCKING PROBABILITY IN THE BLOCKING REPORT

The blocking probabilities for cells (shown in the blocking report) cannot be found by simply

averaging the blocking probabilities at pixels in the 2d-view for the following reasons:

Pixels with high traffic should have more influence on cell blocking probability than pixels

with low traffic.

Pixels in coverage holes should not influence cell blocking probability, even if they contain

high traffic.

A service may use some bearers more frequently than others. Frequently used bearers should

have more influence on the blocking probability than infrequently used bearers.

Several cells may serve the traffic at a pixel.

We need a measure of blocking probability that is sensibly weighted with respect to all the above

factors. We can find such a measure by selective passive-scanning at the end of a snapshot. This is

different to the usual (global) passive-scanning used to produce coverage arrays. Global passive-

scanning tests all pixels, whereas selective passive-scanning only tests a subset of pixels and scenarios

at the end of each snapshot. To determine which pixels and scenarios to check, we take the

successfully served terminals from the previous snapshot and use them to check for blocking at the end

of the current snapshot. Each terminal is placed at the location it had in the previous snapshot, and

checked to see if it can connect to the cell that previously served it, using the previous uplink and

downlink bearer. By doing this, we automatically make sure that the cell blocking probability is

correctly weighted, since the most likely terminal locations and connection scenarios are checked.

8.2 FAILURE RATE

The blocking probability measured in the tool is more similar to a Lost Call Held blocking probability

than a Lost Call Cleared (Erlang-B) blocking probability. This is a consequence of the way the

simulator works. The simulator simply tries to serve as much of the offered traffic as possible. The

following formulae show how these probabilities are related in a simple situation. Note that these

formulae are not used to explicitly calculate blocking probabilities in the tool, since the probabilities in

the tool are all found by sampling snapshots.

Take a system with fixed capacity C , and Poisson traffic with arrival rate users per second and

mean holding time seconds. The mean offered traffic is uA .

The probability that exactly C users are offered is given by:

!CAeS CA

The probability that more than C users are offered is given by:

1

!Ck

kA kAeS

The probability that less than C users are offered is given by:

1

0

!C

k

kA kAeS

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Lost Call Cleared: In an LCC system, blocked users do not try again.

C

k

k

C

LCC

kA

CA

SS

SCAP

0

!/

!/),(

Lost Call Held: In an LCH system, blocked users immediately retry.

Ck

kA

LCH kAeSSCAP !),(

It is easy to show that ),(),( CAPCAP LCCLCH . The two probabilities are most similar to each

other for low blocking probabilities.

Note that the “Failure Rate” ( F ) in the failure report is the proportion of offered terminals that fail.

A

kAeCk

F Ck

kA

1

!)(

)E(attempts

)E(failures

This is not a blocking probability and it should never be treated as one. The failure rate can be an order

of magnitude lower than both the LCC and LCH blocking probabilities.