Optimization of Random Access in 3G Long Term Evolution

Institutionen för systemteknikDepartment of Electrical Engineering

Examensarbete

Optimization of Random Access in 3G Long TermEvolution

Examensarbete utfört i Reglerteknikvid Tekniska högskolan i Linköping

av

Filip Andrén

LiTH-ISY-EX--09/4318--SE

Linköping 2009

Department of Electrical Engineering Linköpings tekniska högskolaLinköpings universitet Linköpings universitetSE-581 83 Linköping, Sweden 581 83 Linköping

Optimization of Random Access in 3G Long TermEvolution

Examensarbete utfört i Reglerteknikvid Tekniska högskolan i Linköping

av

Filip Andrén

LiTH-ISY-EX--09/4318--SE

Handledare: Patrik Axelssonisy, Linköpings universitet

Mehdi AmirijooEricsson Research, Ericsson AB

Examinator: Fredrik Gunnarssonisy, Linköpings universitet

Linköping, 28 September, 2009

Avdelning, InstitutionDivision, Department

Division of Automatic ControlDepartment of Electrical EngineeringLinköpings universitetSE-581 83 Linköping, Sweden

DatumDate

2009-09-28

SpråkLanguage

� Svenska/Swedish� Engelska/English

�

�

RapporttypReport category

� Licentiatavhandling� Examensarbete� C-uppsats� D-uppsats� Övrig rapport�

�

URL för elektronisk versionhttp://www.control.isy.liu.se

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-20957

ISBN—

ISRNLiTH-ISY-EX--09/4318--SE

Serietitel och serienummerTitle of series, numbering

ISSN—

TitelTitle

Optimering av Random Access i 3G Long Term EvolutionOptimization of Random Access in 3G Long Term Evolution

FörfattareAuthor

Filip Andrén

SammanfattningAbstract

Before a mobile can commence services it needs to have access to a base station.The access method is often referred to as random access (RA). One way to mea-sure the performance of the RA procedure is the access delay (AD) of the mobiles,where AD is the time from which a mobile wants to start a RA attempt until ithas received access.

There are different approaches to optimize the RA procedure. Manual optimiza-tion is possible but costly. Automated optimization is preferable because of thelower costs and the possibility to change configuration fast in the base stationwhen the operational conditions change. This thesis focuses on automated opti-mization of the RA procedure with regard to AD.

A controllability and observability study of AD is first presented in this thesis.The controllability study shows that AD can be controlled by a number of RAparameters, whereas the observability study show that AD cannot always be cor-rectly observed. The next part of this thesis presents a controller synthesis, wherethree different controllers are presented to control a specified percentile of AD. It isshown, through experiments, that the controllers derived can be used to optimizethe RA procedure with regard to AD.

NyckelordKeywords Random Access, LTE, Optimization, Access Delay, Backoff, Control

AbstractBefore a mobile can commence services it needs to have access to a base station.The access method is often referred to as random access (RA). One way to mea-sure the performance of the RA procedure is the access delay (AD) of the mobiles,where AD is the time from which a mobile wants to start a RA attempt until ithas received access.

There are different approaches to optimize the RA procedure. Manual optimiza-tion is possible but costly. Automated optimization is preferable because of thelower costs and the possibility to change configuration fast in the base station whenthe operational conditions change. This thesis focuses on automated optimizationof the RA procedure with regard to AD.

A controllability and observability study of AD is first presented in this thesis.The controllability study shows that AD can be controlled by a number of RAparameters, whereas the observability study show that AD cannot always be cor-rectly observed. The next part of this thesis presents a controller synthesis, wherethree different controllers are presented to control a specified percentile of AD. It isshown, through experiments, that the controllers derived can be used to optimizethe RA procedure with regard to AD.

SammanfattningInnan en mobil vill använda sig av möjliga tjänster måste den få access till enbasstation. Accessmetoden brukar kallas för random access (RA). Ett sätt att mä-ta prestandan av RA proceduren är den access delay (AD) som mobilerna får, därAD är tiden från att en mobil vill börja RA proceduren tills den fått access.

Det finns flera ansatser till att optimera RA proceduren. Manuell optimering ärmöjlig men kostsam. Automatiserad optimering är att föredra på grund av de lägrekostnaderna och möjligheten att snabbt ändra inställningarna i basstationen vidändrade förutsättningar under körning. Den här uppsatsen fokuserar på automa-tiserad optimering av RA proceduren med avseende på AD.

Först presenteras en studie i huruvida AD är styr- och observerbart. Styrbar-hetsstudien visar att AD kan styras med ett antal RA-parametrar, medan obser-verbarhetsstudien visar att AD inte alltid kan observeras korrekt. Nästa del avrapporten presenterar en regulatorsyntes, där tre olika regulatorer presenteras för

v

vi

att reglera en specificerad percentil av AD. Genom experiment visas att de fram-tagna regulatorerna kan användas för att optimera RA proceduren med avseendepå AD.

Acknowledgments

I would like to thank my supervisor Mehdi Amirijoo at Ericsson for all his help andgood answers to every question I had. I would also like to thank my supervisorPatrik Axelsson at the Department of Electrical Engineering (ISY) for his helpand support throughout the thesis. Thanks also goes to Fredrik Gunnarsson atEricsson for support and guidance and to Ove Linnell, also at Ericsson, for theopportunity to write this thesis.

A final thanks goes to my girlfriend Susanne who supported me all the way, fromthe beginning until the end of this thesis.

vii

Contents

Abbreviations xiii

List of Symbols xv

1 Introduction 11.1 3G Long Term Evolution . . . . . . . . . . . . . . . . . . . . . . . 11.2 Description of the Random Access Procedure . . . . . . . . . . . . 3

1.2.1 Random Access Procedure . . . . . . . . . . . . . . . . . . . 31.2.2 Broadcasted Information . . . . . . . . . . . . . . . . . . . . 51.2.3 Correlation of Received Signals . . . . . . . . . . . . . . . . 71.2.4 Backoff Parameter . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Optimization of the Random Access Procedure . . . . . . . . . . . 81.4 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Problem Formulation 112.1 Access Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Backoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Controller Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 Sampling Period . . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Control Structures . . . . . . . . . . . . . . . . . . . . . . . 13

3 Simulator 153.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Simulator Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.1 Changing of Parameters . . . . . . . . . . . . . . . . . . . . 163.2.2 Manage UEs . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.3 Modelling of PUSCH . . . . . . . . . . . . . . . . . . . . . . 163.2.4 Modelling of the Random Access Procedure . . . . . . . . . 173.2.5 The End of the Loop . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Definition of Parameters . . . . . . . . . . . . . . . . . . . . . . . . 183.3.1 Timing Factors . . . . . . . . . . . . . . . . . . . . . . . . . 183.3.2 Configuration Period . . . . . . . . . . . . . . . . . . . . . . 193.3.3 Backoff Indicator . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 Random Access Attempt Example . . . . . . . . . . . . . . . . . . 20

ix

x Contents

4 Access Delay 234.1 Introduction to Access Delay . . . . . . . . . . . . . . . . . . . . . 234.2 Controllability of Access Delay . . . . . . . . . . . . . . . . . . . . 23

4.2.1 Experiment: Effects of Varying PRACH Configuration andRACH Load . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2.2 Experiment: Effects of Varying Power Control Parameters . 284.2.3 Experiment: Effects of Varying PUSCH Load . . . . . . . . 314.2.4 Controllability Summary . . . . . . . . . . . . . . . . . . . 34

4.3 Observability of Access Delay . . . . . . . . . . . . . . . . . . . . . 344.3.1 Observer Algorithm . . . . . . . . . . . . . . . . . . . . . . 344.3.2 Penalty Estimator 1 . . . . . . . . . . . . . . . . . . . . . . 374.3.3 Penalty Estimator 2 . . . . . . . . . . . . . . . . . . . . . . 384.3.4 Penalty Estimator 3 . . . . . . . . . . . . . . . . . . . . . . 394.3.5 Access Delay Observer Experiments . . . . . . . . . . . . . 414.3.6 Experiment: Accuracy at Varying PRACH Configuration

and RACH Load . . . . . . . . . . . . . . . . . . . . . . . . 414.3.7 Experiment: Accuracy at Varying Power Control Parameters 454.3.8 Experiment: Accuracy at Varying PUSCH Load . . . . . . 494.3.9 Experiment: Accuracy at Varying RACH Load and P0_RACH 534.3.10 Observability Summary . . . . . . . . . . . . . . . . . . . . 55

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5 Backoff 575.1 Introduction to Backoff . . . . . . . . . . . . . . . . . . . . . . . . 575.2 Effects of Backoff on Access Delay . . . . . . . . . . . . . . . . . . 57

5.2.1 Inclusion of Backoff in Observers . . . . . . . . . . . . . . . 575.2.2 Experiment: Accuracy at Varying RACH Load . . . . . . . 58

5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6 Sampling Period 636.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.2 Experiment: Accuracy of Sampled Access

Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

7 Control Structures 677.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677.2 Definition of Control Parameters . . . . . . . . . . . . . . . . . . . 677.3 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

7.3.1 Modelling with regard to P0_RACH . . . . . . . . . . . . . . 697.3.2 Modelling with regard to ∆RACH . . . . . . . . . . . . . . . 717.3.3 Modelling with regard to PRACH Configuration . . . . . . 727.3.4 Modelling Summary . . . . . . . . . . . . . . . . . . . . . . 73

7.4 Description of Controllers . . . . . . . . . . . . . . . . . . . . . . . 747.4.1 I-Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 747.4.2 Double-Percentile Controller . . . . . . . . . . . . . . . . . 77

Contents xi

7.4.3 Mid-Range Controller 1 . . . . . . . . . . . . . . . . . . . . 787.4.4 Mid-Range Controller 2 . . . . . . . . . . . . . . . . . . . . 797.4.5 PUSCH Controller . . . . . . . . . . . . . . . . . . . . . . . 79

7.5 Controller Experiments . . . . . . . . . . . . . . . . . . . . . . . . 807.5.1 Simulation Scenario . . . . . . . . . . . . . . . . . . . . . . 817.5.2 Experiment: Double-Percentile Controller . . . . . . . . . . 817.5.3 Experiment: Mid-Range Controller 1 . . . . . . . . . . . . . 867.5.4 Experiment: Mid-Range Controller 2 . . . . . . . . . . . . . 90

7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

8 Summary and Future Work 958.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Bibliography 99

Abbreviations

3GPP 3rd Generation Partnership Program

AD Access Delay

AP Access Probability

CDF Cumulative Distribution Function

CI Confidence Interval

CP Contention Probability

CyP Cyclic Prefix

DMP Detection Miss Probability

DP Detection Probability

eNB Base Station

eNodeB Base Station

ISD Inter-Site Distance

KPM Key Performance Metric

LTE Long Term Evolution

PRACH Physical Random Access Channel

PUSCH Physical Uplink Shared Channel

RA Random Access

RACH Random Access Channel

RB Resource Block

RMSE Root Mean Squared Error

SIR Signal-to-Interference Ratio

SON Self-Organizing Networks

UE User Equipment/Mobile

xiii

List of Symbols

Symbol Description Page

M Maximum number of allowed attempts . . . . . . . . . . . . . . . . . . . . . . . . . . 4Pmax Maximum allowed UE transmission power [dBW] . . . . . . . . . . . . . . . . 6PL Path loss [dB] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6P0_RACH Wanted received power level at first attempt [dBW] . . . . . . . . . . . . . 6∆RACH Power ramping step [dB] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6N Number of sent preambles/number of attempts . . . . . . . . . . . . . . . . . . 6∆Preamble Power offset in RACH power control [dB] . . . . . . . . . . . . . . . . . . . . . . . . 6B Backoff parameter [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7AD Access delay [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8AP Access probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8LoadRACH Mean preamble arrival intesity [preambles/s/cell] . . . . . . . . . . . . . . . 17LoadPUSCH Ratio of number of scheduled RBs and total number of RBs . . . . 17TconfP Configuration period [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19DMP Detection miss probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34CP Contention probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34nSent Number of sent preambles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35nDetect Number of detected preambles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35nAccess Number of accessed UEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35α0 First attempt delay [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36α1 Detection delay [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36α2 Detection miss delay [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36α3 Random access finished delay [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36α4 Contention resolution failed delay [ms] . . . . . . . . . . . . . . . . . . . . . . . . . 36TrespW RA response window size (ra-ResponseWindowSize) [ms] . . . . . . . 38TcontW

Contention resolution timer (mac-ContentionResolution-Timer) [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Tnext Time after a waiting window until next RA opportunity [ms] . . . 38traResp RA response time vector [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39tra Time of RA opportunity in eNB [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . 39traResp Time of RA response in eNB [ms] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39traCont Time of RA contention resolution response in eNB [ms] . . . . . . . . .39CI Confidence Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66q Time shift operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

xv

xvi List of Symbols

ε Prediction error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68VN Model validity parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68s Complex number in the Laplace domain . . . . . . . . . . . . . . . . . . . . . . . . 75KI Integral gain, tuning parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Kff Feed-forward gain, tuning parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . 78rAD Reference for access delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Tr Rise time in step response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85AM Overshoot in step response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Chapter 1

Introduction

Random access is the method used by mobiles to access a base station in a mobilesystem. This thesis will focus on how this access procedure in the 3G Long TermEvolution (LTE) can be optimized. The standardization of LTE is organized bythe 3rd Generation Partnership Program (3GPP) and some of the design targetsfor LTE are for example [11]:

• Higher bit rates

• Lower latency

• Lower complexity

One way to increase the performance and lower the complexity is to introduce moreSelf-Organizing Network (SON) functionality. This is also the case in 3GPP’s workon LTE [6]. The definition of SON is however quite wide, but three of its centralparts are self-configuration, self-optimization and self-healing, where this thesiswill concentrate mainly on the second one, namely self-optimzation.

A self-optimizing system continuously adapts its parameters to meet a given per-formance specification. This is illustrated in Figure 1.1. The disturbance couldfor example be interference caused by the surrounding base stations. If the in-terference is increased the base station can inform its mobiles to use a highertransmission power to compensate for the higher interference and thus keepingthe same bit rate. One part of LTE that could benefit from self-optimization isthe random access procedure.

1.1 3G Long Term EvolutionTo get some overview of which parts of LTE that are addressed in this thesis, thissection contains some information about LTE. For more information refer to thestandardization documents produced by 3GPP [7].

Communication over LTE is divided into different channels. These channels can

1

2 Introduction

ControllerBaseStation-

Disturbance

Bit rate

Measuered/estimated bit rate

Figure 1.1. A simple system with a controller that compensates for the disturbance.

also be divided into uplink and downlink channels. A transmission is sent uplinkif it travels from the mobile or user equipment (UE) to the base station (eNB) anddownlink if it is sent from the base station to the mobile. In this thesis we aremostly interested in the physical channels and the transport channels used in theuplink. The signal processing is done in the physical channels and the transportchannels are used to transport blocks of information to the control channels alsocalled the logical channels. This can be seen in Figure 1.2, where the channels ofinterest are filled with grey. The random access channel (RACH) is a transportchannel even if it is dedicated to control the random access procedure. Its coun-terpart among the physical channels is called the physical random access channel(PRACH). The physical uplink shared channel (PUSCH) is the physical channelto handle the uplink data traffic between the eNB and the UEs. In Figure 1.2five other channels are inlcuded for completeness. They are not important forthe accomplishment of this thesis and are therefore not explained here. For moredetailed information refer to [3].

Logicalchannels

Transportchannels

Physicalchannels

PRACH PUSCH PUCCH

RACH UL-SCH

CCCH DTCH DCCH

Figure 1.2. Uplink channel mapping.

The physical uplink structure in LTE is divided into a time-frequency structure.This is visualized in Figure 1.3. As can be seen, there are so-called random access(RA) opportunities at the edge of the frequency band and they are always sixresource blocks (RBs) wide. One RB is 180 kHz and the total channel bandwith

1.2 Description of the Random Access Procedure 3

can vary between 6 RBs to 110 RBs, i.e., from roughly 1MHz to around 20Mhz.Another thing to notice in Figure 1.3 is the minimum time scale of 1ms, which isalso called a subframe. The next level in time is called a radio frame and consistsof 10 subframes. More information about the time-frequency structure of LTE canbe found in [3] and [1].

frequency

time

1 ms

1 R

B

PRACH

PUSCH

Figure 1.3. Time-frequency structure of the uplink in LTE.

1.2 Description of the Random Access ProcedureWhen a UE wants to execute a service, for example make a voice call, it firstrequires to have access to the network. To get access, the UE has to do a randomaccess procedure. Before starting with the random access procedure the UE scansthe surrounding cells to locate its best cell. The eNB associated with the cell isbroadcasting information needed by the UE to connect. For example the eNBtells the UE when it can try to connect and what power it should use. It is alsothe parameters in the broadcasted information that can be used to optimize therandom access procedure. Therefore, to get a better understanding of when andwhere the broadcasted information is used and what effects it may have if it ischanged, this section contains a short description of the random access procedureand its different parts.

The procedure described here is the random access procedure in LTE as it has beenspecified by 3GPP. More information and details on the random access procedurecan be found in [11], [3], [1], [4] and [2].

1.2.1 Random Access ProcedureThe random access procedure can be divided into four steps, as shown in Figure 1.4and explained below.

1. Random Access PreambleThe UE transmits a random access preamble, which is a simple ID, to thebase station at a random access opportunity. The preamble is randomlyselected from 64 available. The preambles are explained in more detail inSection 1.2.2.

4 Introduction

UE eNB

Random Access Preamble

Random Access Response

Scheduled Transmission

Contention Resolution

1.

2.

3.

4.

Figure 1.4. The steps of the random access procedure in LTE.

2. Random Access ResponseIn this step the eNB answers each one of the UEs, who’s preamble was de-tected in step 1. The answer contains among other things the same preamblethat the detected UE sent. The detection of the preambles and more infor-mation about what the answer contains can be found in Section 1.2.3.

3. Scheduled TransmissionIf a UE receives a RA response in step 2 containing a preamble that matchesits own preamble sent in step 1, the UE transmits its unique identity to theeNB. This unique identity makes it possible for the eNB to separete UEswho have sent the same preamble. If a UE does not receive its own preamblein this step it has to declare this random access attempt unsuccessful andstart over from step 1.

4. Contention ResolutionThe eNB once again responds, but this time with the unique identity of theUE, received in step 3. This means that UEs who have chosen the samepreamble may all have come this far, but only one of them will receive itsown unique identity in the contention resolution response. The other UEswho do not receive their identity have to declare this random access attemptunsuccessful and start over from step 1.

If a UE exceeds the maximum number of allowed RA attempts, denoted M , thewhole random access procedure is declared as failed. After this the UE can forexample try to access another cell.

Contention Free Random Access

In some situations it is necessary that the delay during the random access proce-dure is as small as possible. This can for example be during a handover, i.e., a


UE moves from one cell to another. In these situations a so-called contention freerandom access procedure is used. In this procedure the cell reserves a preamblefor the UE. A reserved preamble can only be used by the UE it was assigned toand hence steps 3 and 4 in the non-contention free random access are not needed.

1.2.2 Broadcasted InformationThe eNB broadcasts information that is needed by the UE to perform a randomaccess attempt. In this thesis, only the parameters in the broadcasted informa-tion that are important for the random access procedure will be discussed. Theimportant parameters that are broadcasted can be found in [5] and are listed asfollows:

• Set of preambles that can be used for non-contention free random access

• Random access opportunity slots

• Preamble transmission power

In the following sections these parameters will be presented in a bit more detail.

Random Access Preambles

Each cell must provide 64 preambles that can be used by the UEs as a temporaryID [1]. The preambles are derived from so called root sequences and the one usedin LTE is the Zadoff-Chu sequence [1]. A Zadoff-Chu sequence has low correlationwith other Zadoff-Chu sequences which suppresses the interference with other UEs.The preambles are then derived from the Zadoff-Chu sequence by cyclically shiftingthe sequence. This has the effect that all preambles derived from the same Zadoff-Chu sequence are orthogonal to each other. In smaller cells it is possible to deriveall of the 64 preambles from one root sequence, but larger cells need more thanone root sequence.

Some of the preambles are dedicated for so called contention free random access.In normal random access the UEs choose one of the provided preambles randomly.During a contention free random access on the other hand, a UE is given a uniquepreamble that it can use. This means that there is no risk of another UE choosingthe same preamble and thus there is no contention.

PRACH Configuration

The PRACH configuration tells the UE which format the preamble has and inwhich subframes there are random access opportunities [1]. There are four differentpreamble formats, see Figure 1.5. The Cyclic Prefix (CyP) is needed to compensatefor any transmitting delays and is simply the last part of the preamble copied andprefixed the preamble. For the longer formats (Format 2 and Format 3) the RAsequence is repeated. This enables a higher received energy without increasing thetransmission power.

6 Introduction

RA sequenceCyPtime

TX

≈ 103 μs 800 μs

a) Format 0

RA sequenceCyPtime

TX

≈ 684 μs 800 μs

b) Format 1

RA sequenceRA sequenceCyPtime

TX

≈ 203 μs 1600 μs

c) Format 2

RA sequenceCyP

TX

≈ 684 μs

d) Format 3

RA sequencetime

1600 μs

Figure 1.5. Preamble format in LTE.

Recall from Section 1.1 that the random access opportunities in LTE are reservedin resource blocks. The PRACH configuration tells the UE where these RBs arelocated in every radio frame, see Figure 1.3. The different configurations offer anaccess period between 1ms and 20ms. For more detail on what configurations areavailable see [1].

Transmission Power

The RACH transmission power for the UE is set according to [4] and is expressedas

PRACH = min{Pmax, P0_RACH + PL+ (N − 1)∆RACH + ∆Preamble} (1.1)

where Pmax is the maximum power allowed for the UE and PL is the estimatedpath loss. The parameter P0_RACH is broadcasted by the eNB and representsthe wanted received power level at first attempt. The parameter ∆RACH is alsobroadcasted by the eNB and represents the power ramping step. The parame-ter P0_RACH can vary between -150 dBW and -120 dBW in steps of 2 dBW and∆RACH can vary between 0 dB and 6 dB in steps of 2 dB. The number of preambletransmission attempts is given by N . This means that the UE will increase itstransmission power with ∆RACH for every attempt. The last parameter ∆Preamble

is an offset based on the preamble format. This offset is zero for the formats 0 and1 and is -3 dB for formats 2 and 3, see Section 1.2.2 and [4].


1.2.3 Correlation of Received Signals

After the UEs have sent their preambles to the base station in step 1 of the ran-dom access procedure, see Section 1.2.1, the eNB correlates the received signal ineach random access opportunity slot with all possible preambles. If a preamble isdetected the eNB will signal the same preamble back together with timing adjust-ment information, a temporary mobile identity and an uplink resource allocation.The timing adjustment allows the UE to start its transmissions in time for thesignal to arrive at the eNB exactly at the beginning of the designated time-slot.The timing adjustment is therefore necessary and is derived from the estimatedround trip time wich can be seen in Figure 1.6. All the UEs that sent a preamblein step 1 of the random access procedure will listen for a response containing theirpreamble and read the information that it contains.

Correlation

Detection thresholdPreamble

Noise and interference

Time

Round trip timeestimation

Figure 1.6. Correlation of a random access preamble with round trip time estimation.

1.2.4 Backoff Parameter

If the random access attempt of a UE fails, either because the preamble sent bythe UE was not detected by the eNB or the UE lost the contention resolution,the UE has to start the process over again. To avoid contention and overload, theeNB can signal the UEs that they have to wait a certain time before they try toconnect again. The parameter that controls this is called the backoff parameter(B) and is signaled by the eNB in the random access response. The actual timethe UE should backoff is chosen uniformly by the UE in the interval [0, B]. Asmentioned, the backoff parameter is sent in the RA response, but all RA responsescan however be read by all UEs who sent a preamble in step 1 of the random accessprocedure. This means that also a UE that did not get a random access responsewith its own preamble, i.e., was not detected, can receive the backoff parameterand use it.

8 Introduction

1.3 Optimization of the Random AccessProcedure

As explained in Section 1.2 there are many parameters that affect the RACH per-formance. In a normal case, all of these parameters have to be set by an operator.In order to get the best performance possible these parameters have to be chosenaccording to the individual conditions of each cell. There are different approachesto set the RACH parameters. One of them is to use one set of parameters for allthe base stations in a network. This may however lead to settings that are notoptimal for cells where the conditions differ a lot from the average case. Anotherway to find the RACH parameters is to do extensive simulations for each cell. Thesimulations are however time consuming and costly. Therefore self-optimizationof the random access procedure has great potential. For the RACH process thereare many parameters that can be used, see Section 1.2.2. Different approachesare to tune the transmission power of the UE and thus increasing the probabilityof a UE getting access, or to change the RA opportunity period to decrease theprobability of contention.

1.4 Previous WorkThere is previous work done on SON as described in the following text. A study onhow the RACH interferes with the uplink traffic channel in WCDMA systems andhow to optimize the RACH parameters in order to maximize the uplink capacityis done by S. Kim et al. in [12]. By analyzing the retransmission probabilitiesof a preamble, they could estimate the interference level caused by RACH on theuplink traffic channel. From this they could find a wanted signal-to-interferenceratio (SIR) to maximize the uplink capacity. This thesis is however focused onthe performance of the RACH process and not so much on the performance of theuplink channel. In [16], the RACH performance with regard to access delay (AD),i.e., how long it takes for a UE to get access, and random access success ratio isstudied for a WCDMA system. They show that if the target SIR is set correctlythe AD and the RA success ratio can be optimized. No theory on how to controlthe RACH process is however presented. Another difference from this thesis isthat in both [12] and [16] a WCDMA system is studied, whereas in this thesis westudy LTE.

A beginning study of self-optimization of the random access procedure in LTE hasbeen done recently by M. Amirijoo et al. and is presented in [9]. They presentresults and suggestions on how to alter the RACH performance using a number ofthe broadcasted parameters, for example P0_RACH and ∆RACH . The performancespecification model used in the investigations was the access probability (AP),i.e., the probability that a UE requires access. The target AP was specified asthe wanted AP for a certain attempt N . An example specified of a performancespecification could be

AP1 = 0.80, AP3 = 0.99

1.4 Previous Work 9

which means that the operator is satisfied with 80% of the UEs getting accessin their first attempt and 99% of the UEs having access after their third at-tempt. Their investigations show that it is possible to change the AP by alteringP0_RACH , ∆RACH and the PRACH configuration. This thesis is in some cases acontinuation of the report by M. Amirijoo et al., but with a focus on access delayinstead of access probability.

Access delay is regarded as an important characteristic parameter, when one wantsto evaluate the performance of the random access procedure. There are differentways to estimate the AD. Some of them are presented in [17] and [13] wherethey derive the total average AD from the detection probability (DP ), i.e., theprobability that the preamble sent by a UE is detected by the eNB. Their calcu-lations however, depend on how the delay of the UE is distributed in time. Theprobability that the AD is lower than a certain number of time slots is derived in[10] by estimating the collision probability. A collision occurs when two or moreUEs send their preamble in the same time-frequency slot. The problem with [17],[13] and [10] is that their results are based on another system structure than theLTE structure. One of the main assumptions in this thesis is that the number ofattempts needed by the UE to get access is known. It would therefore be moreconvenient to base an estimation of AD on the number of attempts.

Chapter 2

Problem Formulation

As explained in Chapter 1 there are many ways to increase the performance ofthe random access procedure, for example by changing the wanted received powerlevel P0_RACH or power ramping step ∆RACH , see Section 1.2.2. The systemitself is highly nonlinear with many cross connections between parameters. Forexample, access delay can the be changed by altering the PRACH configurationbut this would also mean that the number of RBs assigned to PUSCH wouldchange at the same time. The work that has been done before, see Section 1.4,mostly investigates how different RACH parameters affect the access probability.The goal of this thesis is to see how well the random access procedure can beoptimized with regard to access delay. This will be done by continuing the workthat has been done before and extend it to include more parameters of the randomaccess procedure. The work can be divided into the following steps

1. Access Delay:A controllability and observability study of AD.

2. Backoff Parameter:How does different values on the backoff parameter affect the observabilityof AD.

3. Controller Synthesis:The goal here is to collect the previous results and combine them into oneor more controllers. This step can itself be divided into two steps:

• Sampling period: A study on how different sampling periods affect thereliability of the AD measurements.• Controller Structure: Look at different controller structures and studytheir advantages and disadvantages.

2.1 Access DelayIn previous work, AP has been used in a performance specification and from thissome of the RACH parameters have been set accordingly. See section 1.4 for more

11

12 Problem Formulation

details. When these parameters are combined in different ways, the total AD willvary. For example, it has been shown in [9] that a higher P0_RACH decreases thenumber of attempts needed by a UE to get access. This would require a shorterAD than for more attempts. Due to the importance of fast access times it wouldbe desirable to be able to specify the desired performance of the RA procedure bymeans of using AD in a performance specification for the system. To be able touse AD in a performance specification model for the system it has to be evaluatedhow AD is affected by the different parameters of the random access procedure.This evaluation process can be divided into several steps including

1. Study the controllability of AD by studying how AD is affected by the dif-ferent parameters. This can for example be power control and PRACHconfiguration.

2. Study the observability of AD. This can be done by finding and studyingdifferent ways to measure or observe the AD, either by using measurementsfrom the UE or by using estimates in the eNB.

If AD can not be controlled by changing parameters it is not possible to use ADin a performance specification. If there are no good ways of observing the ADonly using known parameters in the eNB it has to be assumed that the UEs canprovide measurements of their AD to the base station.

2.2 BackoffAs described in Section 1.2.4 the eNB can force the UE to wait a certain timebefore it tries to connect again. An example of a backoff time chosen by the UEcan be seen in Figure 2.1. The maximum length of the backoff time is signaled tothe UE by the eNB with the backoff parameter B. One possible scenario is thatthe backoff only is activated when there is an overload in the system. Therefore itwould be interesting to study how the observations of AD are affected by differentvalues on B, during different conditions of the system. If the AD observers cannotbe upgraded to accurately estimate an eventual backoff it would mean that theeNB is depending on AD reports from the UEs.

RA RA RA

Backoff timeAttempt 1 ends Attempt 2 starts

RA

Figure 2.1. Backoff example. When attempt 1 ends the UE have to wait the backofftime before it can start attempt 2.

2.3 Controller SynthesisThe synthesis can be split up in different parts. When having the possibility touse different parameters to control a system it is important to combine them in a

2.3 Controller Synthesis 13

most efficient way, for example if they have different working areas or if they shouldbe changed with different intervals. A study on how the reliability of measuredpercentiles and the average of AD are affected by different sampling periods willthen be carried out. After this, different controller structures will be studied andtheir performance evaluated.

2.3.1 Sampling PeriodThe choice of sampling period can have a great effect on how reliable the measuredpercentiles and the average of AD are. The longer the sampling period is themore data, to base the measurement on, has been collected since the last sample.This suggests that the measurement of AD will be better the longer the samplingperiod is, assuming a stationary condition. The question however is how muchbetter the measurements get and how to handle the trade-off between reliabilityof measurements and the speed of the control. It would therefore be interestingto study different sampling periods and see how accuracy at different percentilesof AD is varied with different sampling periods.

2.3.2 Control StructuresWhen designing controllers for different systems it is often necessary to use morethan one controller. For example if a system consists of many parts it can bedifficult and sometimes impossible to design one controller for the whole system.One way to combine the controllers for a system, that is widely used, is to designcontrollers for different parts of the system separately, i.e., the different controllersdoes not know of each others existence. An example of this is an industrial robot.Here every joint of the robot is controlled separately from the others, and themotions from the other joints are seen as disturbances.

Controller1 System1Controller2 System2-

Figure 2.2. A cascade controller.

Sometimes it can however be advantageous to combine the controllers at hand to amore complex structure. It can for example be that the controllers work at differentspeeds or that they have different working points. A so called cascade controller hasnested control loops working at different speeds. This kind of controller can be seenin Figure 2.2. Instead of letting the controllers disturb each other, one can let themtake part of each others information and thus creating a better controller. This isfor example done in so called feed-forward control, see Figure 2.3. Because of themany parameters that affect the random access procedure it may be advantageousto use a control structure where the controllers for the different parameters are

14 Problem Formulation

combined. When evaluating controllers it is important to have key performancemetrics (KPMs) defined that can measure the performance of the system. Onecommon way to do this is by performing a step response. From this the speed andthe accuracy of the controller under extreme conditions can easily be measured.

Controller System

Controller

Measureddisturbance

-

Figure 2.3. A feed-forward control system.

Chapter 3

Simulator

3.1 OverviewThe simulator has been developed in Matlab and is based on the Astrid simulator,developed at Ericsson. It simulates a network with a number of cells and UEsinteracting with each other. The simulator is dynamic in time and it assumesa synchronized network, which means that each subframe starts exactly at thesame point in time for all cells. During the time of this thesis the simulator hasbeen increased in detail and new features have been added. Below is however thedescription of the simulator as it was at the end of the thesis.

3.2 Simulator LoopThe main loop of the simulator consists of a number of steps. An overview of thesesteps can be seen in Figure 3.1.

Change Parameters

Manage UEs Process PUSCH

Perform RA Process RACH Collect Results

Controller

Start

Figure 3.1. The main simulator loop.

15

16 Simulator

When all the steps in the loop have been executed one subframe has ended. Thatis, the simulator has a granularity of 1ms. Each of the steps are explained in moredetail below.

3.2.1 Changing of ParametersIn the first step of the loop, Change Parameters seen in Figure 3.1, eventualparameters are changed. For example the PUSCH load or the RACH load can bechanged during a simulation, in order to simulate an increase in incoming UEs.

3.2.2 Manage UEsIn the step Manage UEs in Figure 3.1, the creation, deletion and the managing ofUEs take place. The UEs are created following a Poisson process, where the meanarrival intensity, denoted LoadRACH , is set with the unit preambles/s/cell. Aftera UE has been created it follows a state machine that is seen in Figure 3.2.

unDetectedwaitingRA-Response

waitingRA-ContRes

hasAccess

waiting-Backoff

Start

Figure 3.2. The state machine of a UE in the simulator.

When a UE is created it is in state unDetected. The transition from state un-Detected to state waitingRAResponse occurs when the UE sends its preamble tothe eNB. When the UE gets a RA response from the eNB the UE is transfered tostate waitingRAContRes. If no RA response is received when the UE is in statewaitingRAResponse, or if no contention resolution response is received when theUE is in state waitingRAContRes it is transfered to state waitingBackoff. Whenthe backoff time is over the UE is transfered back to state unDetected. Note that abackoff of zero can be used and in this case the state waitingBackoff is skipped. Ifa UE gains access, it is transfered from state waitingRAContRes to state hasAccessand is after that deleted.

3.2.3 Modelling of PUSCHSince the focus of this thesis is to analyse the random access procedure in LTE,PUSCH is modelled as simply as possible. This means that only the parts of

3.2 Simulator Loop 17

PUSCH that are important enough are included in the simulator. The interferencefrom PUSCH on the PRACH impacts the preamble detection probability. Anotherimportant aspect is the number of needed resource blocks for PUSCH. This affectswhat PRACH configuration is possible to use, since a short opportunity periodwill have the affect that more RBs are used for RA and can thus not be used forPUSCH. These two parts of the PUSCH are included in the simulator and thecalculations are done in step Process PUSCH in Figure 3.1.

Both the interference from PUSCH and the number of RBs needed by PUSCH aredepending on the PUSCH load. The PUSCH load is defined as below.

Definition 3.1 PUSCH LoadThe PUSCH load, denoted LoadPUSCH is defined as the ratio between the numberof scheduled RBs for PUSCH, denoted nScheduled, and the number of availableRBs, denoted nTotal, i.e.,

LoadPUSCH = nScheduled

nTotal.

The PUSCH load is randomized according to a normal distribution with a meanthat can be changed in the simulator and a standard deviation set to 0.05.

3.2.4 Modelling of the Random Access ProcedureThe steps Perform RA and Process RACH in Figure 3.1 can be described togetheras the modelling of the random access procedure in the simulator. To be able torun simulations with regard to AD, the detail level of the random access procedureneeds to be high. Therefore the best way to model the random access procedureis to include each step of the random access procedure in the simulator. Howeverdue to the high complexity this would lead to, only three steps are included intothe simulator, see Figure 3.3.

UE eNB

Random Access Preamble

Random Access Response

Contention Resolution

1.

2.

3.

Figure 3.3. Description of how the random access procedure is modelled in the simula-tor.

18 Simulator

A UE transmits a preamble in step 1. In step 2 the eNB answers the UEs who’spreambles were detected. If there is no contention the detected UEs from step 2will get access in step 3. If there is contention the UEs that will be given accessare chosen randomly in step 3. This means that step 3 of the real random accessprocedure, described in Section 1.2, is not modelled in the simulator. This stepis a complex process, since a more detailed model of how the uplink user data isscheduled and where there are free RBs to use for RA needs to be included in thesimulator. The relative gain from modelling it in the simulator is also low andit is therefore not included. The time between step 2 and step 3 in the real RAprocedure is also a timing factor that cannot be affected by any of the broadcastedparameters from the eNB. This means that leaving this step out of the simulatoris reasonable.

In case of a failed access attempt the UE has to wait a certain time before it canconnect again. This waiting time is usually called the backoff time. To be able torun experiments when the system is tested with regard to this backoff time this isalso modelled in the simulator.

3.2.5 The End of the LoopIn the step Collect Results in Figure 3.1 the needed data is sampled and stored indata structures. Thus the analyses can be done after the simulation is finished.

The last step of the simulation loop is the step Controller. Here the control of thesystem takes place. Since the synthesis of a control system for the random accessprocedure is part of this thesis, this step will be explained more in detail later onin the thesis.

3.3 Definition of ParametersThere are a number of parameters that affect the access delay. Some of them areof a greater interest because with their help it is possible to control the AD. Whateffects these parameters have on AD will be discussed in the Chapter 4, but some ofthe definitions will be addressed here. There are also some other parameters thatwill not be used for controlling AD in this thesis, but their definition however, willbe discussed in this section. All of these parameters are included in the simulatorand can be set to wanted values before the simulation starts.

3.3.1 Timing FactorsThere are three major timing factors that affect the access delay of one attempt.To get a good modelling of the AD these timing factors are also included in thesimulator. The first timing factor is the time a UE waits for a RA responseafter it has sent its preamble. This timing factor is controlled by the parameterra-responseWindowsSize, [4] which is broadcasted to the UE by the eNB. Thiswindow starts 2ms, see [2], after preamble is sent and during this window the

3.3 Definition of Parameters 19

UE waits for a RA response. The second timing factor is the time a UE haveto wait after the received RA response until it can send its unique identity. Thistiming factor is controlled by the scheduler in the eNB and tells the UE in theRA response in which subframe it can send its unique identity. Depending on theload and other factors this timing factor is hard to predict, but according to [2]the unique identity can be sent no sooner than 6 ms after the RA response. Thusthis timing factor is set to 5ms in the simulator. The third factor is the time aUE waits for a contention resolution response after it has sent its unique identityand is controlled by the parameter mac-ContentionResolutionTimer, [4] which isbroadcasted to the UE by the eNB. The values of ra-ResponseWindowsSize andmac-ContentionResolutionTimer are seen in Table 3.1 and [5].

Table 3.1. Values of ra-responseWindowsSize and mac-ContentionResolutionTimer.

Parameter Time (subframes)ra-ResponseWindowsSize 2, 3, 4, 5, 6, 7, 8 and 10mac-ContentionResolutionTimer 8, 16, 24, 32, 40, 48, 56 and 64

These two parameters, ra-ResponseWindowsSize and mac-ContentionResolution-Timer, can be set in the simulator to affect how long the random access proceduretakes for a UE.

3.3.2 Configuration PeriodThe PRACH configuration is described in Section 1.2.2. Each PRACH configu-ration is associated with a period of time between the RA opportunities and thistime is important for the simulator. The period of time is called configurationperiod, denoted with TconfP and is measured in subframes. The PRACH configu-rations with corresponding configuration period are seen in Table 3.2, where theyhave been grouped by configuration period.

Table 3.2. PRACH configurations with corresponding configuration period.

PRACH Configuration System Frame number TconfP (subframes){0, 1, 2} Even 20{3, 4, 5} Any 10{6, 7, 8} Any 5{9, 10, 11} Any 3.333{12, 13} Any 2{14} Any 1

As can be seen the period for configurations {9, 10, 11} is not an integer. Becausethese configurations do not have a constant period, the configuration period calcu-lated is the mean configuration period. The RA opportunities for configurations

20 Simulator

{9, 10, 11} are limited to three subframes per radio frame. Therefore betweenthe last subframe in one radio frame to the first subframe in the next radio framethere are 4 ms. See [1] for more information about the PRACH configurations.

3.3.3 Backoff IndicatorWhen it comes to backoff there is only one parameter that affects how long the UEswait until they can try again. This is the backoff parameter, which is indicated byan index sent from the eNB to the UE. These backoff indicators have been definedin [4] and can be seen in Table 3.3.

Table 3.3. Backoff parameter values as defined in [4].

Indicator/index Backoff parameter, B (ms)0 01 102 203 304 405 606 807 1208 1609 24010 32011 48012 960

The actual time the UE waits is called the backoff time and is defined as below.

Definition 3.2 Backoff TimeThe backoff time is defined as the time a UE waits after a random access attempthas been declared unsuccessful until the UE is free to try again. The backoff timeis chosen uniformly by the UE in the interval [0, B].

3.4 Random Access Attempt ExampleTo conclude some of the information in this chapter an example will be given.This shows the different states of the UE and where the timing factors come in tothe picture. In Figure 3.4 a time axes is shown with the important events marked.

The numbered events in the figure represent the steps a UE would go throughif it would get access in one attempt. The steps are the same as described

3.4 Random Access Attempt Example 21

0 9 9 9 9 9

1.

ra-ResponseWindowSize = 5 mac-ContentionResolutionTimer = 24

B = 102. 3.

Figure 3.4. Example of how the RA procedure can take place. 1. Send preamble. 2.RA response. 3. Contention resolution.

in Figure 3.3. In the figure the timing factors ra-ResponseWindowSize, mac-ContentionResolutionTimer and B can also be seen. They are placed wherethey affect the AD in the random access procedure. The second timing factorfrom Section 3.3.1, modelled as 5 subframes, is seen from step 2 until the mac-contentionResolutionTimer starts. The two subframes before ra-ResponseWindowSizestarts, is a standardized waiting time before the UE starts to listen for a RA re-sponse. More information can be found in [4]. It can also be noted that one ofPRACH configurations {6, 7, 8} have been used (actually PRACH configuration6, see [1]). Some of the subframes are marked with a number (0 or 9) whichrepresents their position in their radio frame.

Chapter 4

Access Delay

4.1 Introduction to Access DelayA key factor when a systems performance is measured is the speed of the system.This can for example be the bit rate of a mobile network, but in the case of therandom access procedure in LTE the speed can defined as the time it takes for aUE to get access. This measurement of speed is called access delay and can bedefined as follows.

Definition 4.1 Access DelayThe access delay, denoted ADi of a UE i is the time in ms from when the UEwants to start the random access procedure until the time the UE has access. Letts be the time when the UE wants to start the random access procedure and let tabe the time when the UE has been granted access by the eNB. The access delaycan then be calculated as

ADi = ta − ts.

To optimize the performance of the random access procedure one important pa-rameter to look at is therefore the access delay. One way to optimize the RAprocedure is to tune its parameters to follow a target AD. To be able to do thisAD needs to be controllable and observable. If this is the case it would be possibleto use AD in a performance specification model. This chapter will focus on thecontrollability and observability of access delay. First the controllability will bestudied and after that the observability of AD will be studied. In the end therewill be a conclusion of the chapter, summarizing the results and discussions of thechapter.

4.2 Controllability of Access DelayThe controllability of a system is an important analysis. It tells us which param-eters we can use to control the system and how well the system can be controlled.This can be done theoretically, but the complexity of the RACH system would

23

24 Access Delay

make a theoretical analysis unpractical. The controllability of AD has insteadbeen investigated by performing a number of experiments where different param-eters of the RACH process has been altered and the metrics of interest collected.

The parameters investigated below are the power control parameters P0_RACHand ∆RACH and the PRACH configuration. Furthermore, the load on the systemis investigated by studying the RACH load and the PUSCH load. The two windowparameters ra-ResponseWindowSize and mac-ContentionResolutionTimer are notstudied here since they are more seen as parameters to control the load of the eNB.This is outside the scope of this thesis. To evaluate the results different percentilesof AD are studied. In a list of measured ADs, the p-th percentile is the AD belowwhich p percent of the observations may be found. In a cumulative distributionfunction (CDF) of AD the p-th percentile is the value of AD when the CDF is ppercent.

It should be noted that the results below only apply to the conditions and assump-tions made in the simulator. This means that the same experiments run on a realsystem could generate different results.

4.2.1 Experiment: Effects of Varying PRACH Configura-tion and RACH Load

The goal of this experiment is to study how AD is affected by different PRACHconfigurations and different RACH loads and to see to what extent AD can becontrolled by PRACH configuration. The outline of this experiment is given inTable 4.1. It can be noted that P0_RACH is set to -120 dBW. The reason for this isto get as high detection probability of the preambles as possible, i.e., the majorityof the preambles sent from UEs will be detected at the first attempt. Thus weminimize the effects of detection miss on AD and can see how the RACH load andthe PRACH configuration affects the AD.

Table 4.1. Setup of PRACH configuration and RACH load experiment.

Parameter ValueLoadPUSCH (mean value) 0.5LoadRACH 100, 300, 500, 700, 900 preambles/s/cellRACH Format 0

PRACH Configuration {0, 1, 2}, {3, 4, 5}, {6, 7, 8}, {9, 10, 11},{12 ,13} ,{14}

P0_RACH -120 dBW∆RACH 2 dBM 8ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 100 sInter-site Distance 500 m

4.2 Controllability of Access Delay 25

0 50 100 1500

0.2

0.4

0.6

0.8

1

CDF(AD); LoadRACH

= 100 preambles/s/cell

Access Delay (ms)0 50 100 150

0

0.2

0.4

0.6

0.8

1

CDF(AD); LoadRACH


Access Delay (ms)

0 50 100 1500

0.2

0.4

0.6

0.8

1

CDF(AD); LoadRACH



0

0.2

0.4

0.6

0.8

1

CDF(AD); LoadRACH


Access Delay (ms)

0 50 100 1500

0.2

0.4

0.6

0.8

1

CDF(AD); LoadRACH


Access Delay (ms)

Config 0,1,2Config 3,4,5Config 6,7,8Config 14

Figure 4.1. CDF as a function of AD for different PRACH configurations and RACHloads.

For each RACH load and PRACH configuration one simulation of 100 s was run.At the end of each simulation the CDF of AD was derived. These CDFs are shownin Figure 4.1. We can see that the CDFs for configurations {6, 7, 8} until {14} arevery similar, also between different RACH loads. The reason for the somewhatstrange shape of the CDFs is that the number of needed attempts changes. In Fig-ure 4.2 the CDF as a function of sent preambles for LoadRACH = 900 and PRACHconfiguration {0, 1, 2} is given. It can be seen that the changes in number of sentpreambles coincides with the sharp changes in the corresponding CDF of the AD.This is for example seen at around 50ms in the CDF of AD where the derivativeof the CDF decreases. This decrease in derivative coincides with the change from1 sent preambles to 2 sent preambles in Figure 4.2.

26 Access Delay

1 2 3 4 5 6 7 80.85

0.9

0.95

1

CDF(Sent Preambles); LoadRACH


Sent Preambles

Config 0,1,2

Figure 4.2. CDF as a function of sent preambles for PRACH configurations {0, 1, 2}and LoadRACH = 900.

From the CDFs in Figure 4.1, the AD for each combination of RACH load andPRACH configuration at different percentiles is derived. This is given in Fig-ure 4.3. When the period time between the RA opportunities decreases, i.e., theconfiguration number increases, the AD is also decreased. The AD between dif-ferent RACH loads is increased as the load is increased. This is however morenoticeable for the higher percentiles. As we noted from the CDFs there is alsohere in general small difference between PRACH configurations {6, 7, 8} until{14} for all RACH loads, except for the 99th percentile. The small changes inAD between the configurations is connected with the small changes in period timebetween the configurations. The largest change in period time is 10 ms from con-figurations {0, 1, 2} to {3, 4, 5} and it is also there the largest change in AD is.

The conclusion from this experiment is that AD can be controlled by the PRACHconfiguration. Altering the configuration leads in general to small changes in AD,but this is also something that changes depending on which percentile one stud-ies. The use of PRACH configuration when controlling AD is therefore dependingon how the performance specification is set. For example if the RACH load is700 and the performance specification is stated as P (AD < 60) = 0.99. This isthe same as when the 99th percentile for LoadRACH = 700 in Figure 4.3 has avalue under 60 ms, which occurs for configurations {9, 10, 11}, {12, 13} and {14}.If the performance specification, for the same RACH load, on the other hand isstated as P (AD < 60) = 0.90, the 90th percentile should have a value under 60ms. With this specification all configurations except configuration {0, 1, 2} can be


0,1,2 3,4,5 6,7,8 9,10,11 12,13 1420

40

60

80

100

120

LoadRACH


Acc

ess

Del

ay (

ms)

PRACH−Configuration0,1,2 3,4,5 6,7,8 9,10,11 12,13 14

20

40

60

80

100

120

LoadRACH


Acc

ess

Del

ay (

ms)

PRACH−Configuration

0,1,2 3,4,5 6,7,8 9,10,11 12,13 1420

40

60

80

100

120

LoadRACH


Acc

ess

Del

ay (

ms)

PRACH−Configuration0,1,2 3,4,5 6,7,8 9,10,11 12,13 14

20

40

60

80

100

120

LoadRACH


Acc

ess

Del

ay (

ms)


0,1,2 3,4,5 6,7,8 9,10,11 12,13 1420

40

60

80

100

120

LoadRACH


Acc

ess

Del

ay (

ms)


50th percentile80th percentile90th percentile99th percentile

Figure 4.3. AD as a function of PRACH configuration and RACH load for differentpercentiles.

used. That is, the effects from changing the configuration highly depends on whichpercentile we are interested in. If the effects from changing the configuration arehigh, the PRACH configuration can to a higher extent be used to control the AD.One must however keep in mind that the PRACH configuration also effects theamount of resource blocks assigned to PUSCH. The amount of resources neededfor PUSCH must therefore also be kept in mind when using the configuration tocontrol the access delay.

28 Access Delay

4.2.2 Experiment: Effects of Varying Power Control Param-eters

The goal of this experiment is to study the effects of P0_RACH and ∆RACH on ADand to show between which limits it is possible to control AD using these powercontrol parameters. The outline of this experiment is shown in Table 4.2.

Table 4.2. Setup of power control experiment.

Parameter ValueLoadPUSCH (mean value) 0.5LoadRACH 100 preambles/s/cellRACH Format 0PRACH Configuration {9, 10, 11}P0_RACH -120, -125, -130, -135, -140, -145, -150 dBW∆RACH 0, 2, 4, 6 dBM 50ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 100 sInter-site Distance 500 m

For each P0_RACH and ∆RACH one simulation of 100 s was run. At the end of eachsimulation the CDF of AD was derived. These CDFs are shown in Figure 4.4. Ingeneral a smal ratio of UEs have a high AD, above 75ms, when P0_RACH increases.However the difference between the CDFs for different P0_RACH decreases when∆RACH increases. In the case of P0_RACH = −150 dBW and ∆RACH = 0dBthe ratio of UEs never getting access was too high, i.e., there were too many UEsneeding more then the maximum number of allowed attempts, which normally iseight. Thus the maximum number of allowed attempts, M , was increased to 50 inthis experiment.

From the CDFs in Figure 4.4, the AD for each combination of P0_RACH and∆RACH at different percentiles is derived. This is shown in Figure 4.5. In gen-eral AD decreases nonlinearly for increasing P0_RACH and ∆RACH . However forhigher P0_RACH , above -130 dBW, there is a small difference in AD for all ∆RACH .The reason for the small differences in AD when P0_RACH is high, is that the APis highly increased when P0_RACH is increased and thus leading to a lower prob-ability of a UE needing more than one attempt. The greatest reason for longaccess delays is many attempts. In the simulations where P0_RACH ≥ −130dBW,almost all of the UEs only need one attempt to get access and therefore we alsohave a very small change in AD between these simulations. This corresponds wellto the results in [9], where a very high DP for P0_RACH ≥ −130 dBW is obtained.The number of attempts needed for ∆RACH = 0 can be seen in Figure 4.6. Whencompared to the corresponding CDF of AD it is clear that the number of attempts


0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

CDF(AD); ∆RACH

= 0 dB

Access Delay (ms)0 50 100 150 200

0

0.2

0.4

0.6

0.8

1

CDF(AD); ∆RACH

= 2 dB

Access Delay (ms)

0 50 100 150 2000

0.2

0.4

0.6

0.8

1

CDF(AD); ∆RACH

= 4 dB

Access Delay (ms)0 50 100 150 200

0

0.2

0.4

0.6

0.8

1

CDF(AD); ∆RACH

= 6 dB

Access Delay (ms)

P0_RACH

= −150 dBW

P0_RACH

= −135 dBW

P0_RACH

= −120 dBW

Figure 4.4. CDF as a function of AD for different P0_RACH and ∆RACH .

has a great effect on the AD.

The conclusion of this experiment is that it is possible to control AD usingP0_RACH and ∆RACH . Both parameters P0_RACH and ∆RACH make it possibleto decrease AD by decreasing the number of attempts needed by the UEs to getaccess. When only one RA attempt is needed, neither P0_RACH nor ∆RACH canbe used to decrease AD. One way of using the parameters P0_RACH and ∆RACH

could be to control the AD on a higher level, that is use P0_RACH and ∆RACH todecrease the number of attempts needed for the UEs to get access.

30 Access Delay

−150 −145 −140 −135 −130 −125 −1200

100

200

300

400

500

∆RACH

= 0 dBA

cces

s D

elay

(m

s)

P0_RACH

(dBW)−150 −145 −140 −135 −130 −125 −12020

40

60

80

100

120

∆RACH

= 2 dB

Acc

ess

Del

ay (

ms)

P0_RACH

(dBW)

−150 −145 −140 −135 −130 −125 −12020

40

60

80

100

120

∆RACH

= 4 dB

Acc

ess

Del

ay (

ms)

P0_RACH

(dBW)−150 −145 −140 −135 −130 −125 −12020

40

60

80

100

120

∆RACH

= 6 dB

Acc

ess

Del

ay (

ms)

P0_RACH

(dBW)


Figure 4.5. AD as a function of P0_RACH and ∆RACH for different percentiles.

0 5 10 15 20 25 30 35 40 45 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CDF(Sent Preambles); ∆RACH

= 0 dB

Sent Preambles

P0_RACH

= −150 dBW

P0_RACH

= −140 dBW

P0_RACH

= −130 dBW

P0_RACH

= −120 dBW

Figure 4.6. CDF as a function of sent preambles for ∆RACH = 0 dB and differentP0_RACH .


4.2.3 Experiment: Effects of Varying PUSCH LoadThe goal of this experiment is to study the effects of P0_RACH and PUSCH loadon AD. The PUSCH load has a direct effect on the inter-cell interference on RACHand it is therefore interesting to study the impact of this. The outline of this ex-periment is given in Table 4.3.

Table 4.3. Setup of PUSCH load experiment.

Parameter ValueLoadPUSCH (mean value) 0.0, 0.2, 0.4, 0.6, 0.8, 1.0LoadRACH 100 preambles/s/cellRACH Format 0PRACH Configuration {9, 10, 11}P0_RACH -120, -130, -140, -150 dBW∆RACH 2 dBM 8ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 100 sInter-site Distance 500 m

In Figure 4.7 the CDFs from this experiment can be seen. In general the AD isnegatively affected when the PUSCH load is increased, however for P0_RACH ≥−130 dBW there are minor differences to the CDFs when the PUSCH load ischanged. This suggest that it is possible to reduce the negative effects a highPUSCH load has on the AD.

How AD is affected by P0_RACH and the PUSCH load can also be seen in Fig-ure 4.8. Access Delay is plotted for different percentiles, as a function of P0_RACHand PUSCH load. It can be seen that AD is nonlinearly decreased as P0_RACHis increased. The maximum value for AD is increased as the PUSCH load is in-creased. It is also here possible to see that using a P0_RACH higher than -130 dBWminimizes the effects that a high PUSCH interference has on AD.

The conclusion of this experiment is that AD is highly affected by the PUSCHload. The experiment show however also that it is possible to counteract theseeffects by choosing a high enough P0_RACH , i.e., -130 dBW and higher.

32 Access Delay

0 50 100 1500

0.2

0.4

0.6

0.8

1

CDF(AD); LoadPUSCH

= 0.0


0

0.2

0.4

0.6

0.8

1

CDF(AD); LoadPUSCH

= 0.2

Access Delay (ms)

0 50 100 1500

0.2

0.4

0.6

0.8

1

CDF(AD); LoadPUSCH

= 0.4


0

0.2

0.4

0.6

0.8

1

CDF(AD); LoadPUSCH

= 0.6

Access Delay (ms)

0 50 100 1500

0.2

0.4

0.6

0.8

1

CDF(AD); LoadPUSCH

= 0.8


0

0.2

0.4

0.6

0.8

1

CDF(AD); LoadPUSCH

= 1

Access Delay (ms)

P0_RACH

= −150 dBW

P0_RACH

= −140 dBW

P0_RACH

= −130 dBW

P0_RACH

= −120 dBW

Figure 4.7. CDF as a function of AD for different P0_RACH and PUSCH loads.


−150 −140 −130 −12020

40

60

80

100

120

LoadPUSCH

= 0.0

Acc

ess

Del

ay (

ms)

P0_RACH

(dBW)−150 −140 −130 −12020

40

60

80

100

120

LoadPUSCH

= 0.2

Acc

ess

Del

ay (

ms)

P0_RACH

(dBW)

−150 −140 −130 −12020

40

60

80

100

120

LoadPUSCH

= 0.4

Acc

ess

Del

ay (

ms)

P0_RACH

(dBW)−150 −140 −130 −12020

40

60

80

100

120

LoadPUSCH

= 0.6

Acc

ess

Del

ay (

ms)

P0_RACH

(dBW)

−150 −140 −130 −12020

40

60

80

100

120

LoadPUSCH

= 0.8

Acc

ess

Del

ay (

ms)

P0_RACH

(dBW)−150 −140 −130 −12020

40

60

80

100

120

LoadPUSCH

= 1

Acc

ess

Del

ay (

ms)

P0_RACH

(dBW)


Figure 4.8. AD as a function of P0_RACH and PUSCH load for different percentiles.

34 Access Delay

4.2.4 Controllability SummaryAs has been shown in the sections above the AD can be controlled by alteringeither the PRACH configuration or the power control parameters. The resultshave shown that it is especially the power control parameters that give the largestchange in AD. This can be explained by the decrease in DP when decreasing forexample P0_RACH . This leads to an increase in the number of attempts neededby the UE to get access and thus also an increase in AD. As such, the best wayto decrease the AD is to decrease the number of attempts needed by the UEs toget access.

4.3 Observability of Access DelayOne way of using AD when optimizing the random access procedure could be touse it in a performance specification model, i.e., the wanted performance of thesystem will be expressed in terms of AD. To be able to do so not only does ADneed to be controllable, but also observable. To be observable means that AD caneither be measured explicitly or it can be estimated using other known parameters.

In the sections below, the observer algorithm and the different estimators are firstdiscussed. After this follows the results from the experiments where the observerswere tested.

4.3.1 Observer AlgorithmThe total AD of a UE depends on how many attempts the UE needs. The numberof attempts depends on the AP. AP can be expressed as [9]

AP = (1−DMP )(1− CP )

where DMP and CP are detection miss probability and contention probabilityrespectively, as below.

Definition 4.2 Detection Miss ProbabilityThe detection miss probability, denoted DMP is defined as the probability thata preamble sent by a UE is not detected by the eNB.

Definition 4.3 Contention ProbabilityThe contention probability, denoted CP is defined as the probability that a UEdoes not get access because of contention.

Since DMP and CP can not be measured, they need to estimated using ratios. Assuch they can be estimated as [9]

DMP ={

1− nDetectnSent , nSent > 00, nSent = 0 (4.1)

4.3 Observability of Access Delay 35

CP ={

1− nAccessnDetect , nDetect > 00, nDetect = 0 (4.2)

where nDetect is the number of detected preambles, nSent is the number of sentpreambles and nAccess is the number of UEs getting access. Since DMP dependon the number of sent preambles, nSent, which is not measureable at the basestation, nSent needs to be estimated. If it is assumed that all UEs get accessbefore they have reached the maximum number of attempts the estimation ofnSent can be expressed as

nSent =M∑i=1

i · nAccessi

whereM is the maximum number of allowed attempts and nAccessi is the numberof UEs who got access at attempt i. This can be put into (4.1) to get an estimationof DMP, [8].

As we have seen in Section 4.2.1 and Section 4.2.3 the AD is also depending onthe current RACH and PUSCH load. If the estimators of DMP and CP in (4.1)and (4.2) are used, the effects caused by different loads are covered. The DMPdepends implicitly on the PUSCH load, i.e., the ratio nDetect/nSent is higher ifthe PUSCH load is low, and the CP depends implicitly on the RACH load, i.e., theratio nAccess/nDetect is higher if the RACH load is low. This has been shownin [9]. If we also assume that the number of RA attempts needed to get access isreported to the base station when the UE gets access, we can formulate an ADobserver algorithm based on the number of attempts N , DMP and CP .

α1

α0

α2

α4α3

DMP1-DMP

CP1-CP

Detection miss (A)

Access (C) Contention resolution

failure (B)

Figure 4.9. Probability diagram for one random access attempt.

For one access attempt there are three possibilities for a UE, see Figure 4.9. The

36 Access Delay

first possibility (called possibility A) is that the access attempt fails because ofdetection miss, i.e., the UE’s sent preamble was not detected by the eNB. Thesecond possibility, B, is that the attempt fails because of contention, i.e., the UEhas chosen the same preamble as another UE and looses the contention resolution.The third and last possibility (C) is that the UE gets access. Each of the possibil-ities has a penalty associated with it. This means that if a UE travels down pathA in Figure 4.9 it will be punished with the time penalty α2. The parameters α0until α4 are defined as below.

Definition 4.4 First Attempt DelayThe first attempt delay, denoted as α0, is defined as the time in ms between a UEwants to start a random access attempt until the UE sends its first preamble.

Definition 4.5 Detection DelayThe detection delay, denoted as α1, is defined as the time in ms from a UE sends apreamble until the time the UE gets the RA response associated with the preamble.

Definition 4.6 Detection Miss DelayThe detection miss delay, denoted α2, is defined as the time in ms from a UEsends a preamble until the time the UE sends a preamble in the next attempt,given that the UE did not receive a RA response.

Definition 4.7 Random Access Finished DelayThe random access finished delay, denoted α3, is defined as the time in ms from aUE receives its RA response until the UE gets the contention resolution responsecontaining the unique identity belonging to the UE.

Definition 4.8 Contention Resolution Failed DelayThe contention resolution failed delay, denoted α4, is defined as the time in msfrom when a UE receives its RA response until the UE sends a preamble in the nextattempt, given that the UE did not receive a RA contention resolution responsewith its unique identity.

From Figure 4.9 and the reported number of attempts N we can formulate theexpected access delay, AD for one attempt as

AD(N = 1) = α0 + P (A|Access)α2 + P (B|Access)(α1 + α4) ++P (C|Access)(α1 + α3) = α0 + α1 + α3 (4.3)

where P (A|Access), P (B|Access) and P (C|Access) are the conditional probabil-ities that a UE goes down one of the paths A, B or C given the attempt wassuccessful. The only path a UE can take to get access is path C. Consequently,P (C|Access) = 1 and P (A|Access) = P (B|Access) = 0 which leads to the resultin (4.3). If a UE reports two attempts the expression for AD is altered to

AD(N = 2) = AD(N = 1)+P (A|AccessFailed)α2+P (B|AccessFailed)(α1+α4)(4.4)


where P (A|AccessFailed) and P (B|AccessFailed) are the conditional probabili-ties that a UE goes down one of the paths A or B given the attempt was unsuc-cessful. For an arbitrary great N the following definition to estimate access delayis then defined.

Definition 4.9 Estimated Access DelayThe estimated access delay, denoted with AD for attempt N = n can be definedas

AD(N = n) = α0 + α1 + α3 +(n− 1

)(P (A|AccessFailed)α2 +

+P (B|AccessFailed)(α1 + α4

)).

Using (4.1) and (4.2), the conditional probabilities from Definition 4.9 can bederived from Figure 4.9 to

P (A|AccessFailed) = P (AccessFailed ∩A)P (AccessFailed)

= DMP

1− (1− DMP )(1− CP )(4.5)

P (B|AccessFailed) = P (AccessFailed ∩B)P (AccessFailed)

= (1− DMP )CP1− (1− DMP )(1− CP )

. (4.6)

Combining Definition 4.9, (4.5) and (4.6) gives us an algorithm to base our es-timators of AD on. However, the penalties α0 to α4 still need to be estimated.The following sections describe different estimators for α0 to α4. To separate theestimators from each other each α is expressed with an extra index representingthe estimator it belongs to. For example α0

(1) represents the estimation of α0 forestimator 1.

4.3.2 Penalty Estimator 1In this estimator it is assumed that all events happen at a time uniformly dis-tributed in the time window associated with the event. This means that thesubframe when a UE wants to start its random access attempt is uniformly dis-tributed in the window [0,TconfP − 1] and since we are interested in the averageAD the estimation of α0, denoted as α0

(1) is set to

α0(1) = TconfP − 1

2 .

In the simulator it is assumed that the UEs can make their first RA attemptthe same subframe they are created and thus the window [0,TconfP − 1]. The

38 Access Delay

subframe a UE gets its RA response in is uniformly distributed in the window [1,ra-ResponseWindowSize] and the contention resolution response comes in a subframeuniformly distributed in the window [1,mac-ContentionResolutionTimer]. Thismeans that the estimations of α1 and α3, denoted as α1

(1) and α3(1) can be

written asα1

(1) = 2 + 1 + TrespW2 (4.7)

α3(1) = 5 + 1 + TcontW

2 (4.8)

where TrespW =ra-ResponseWindowSize and TcontW =mac-ContentionResolution-Timer. The 2ms in (4.7) is a standardized waiting time in subframes before theRA response window starts and the 5ms in (4.8) is a standardized waiting timebefore a UE can send its unique identity to the eNB. More information aboutthese constants can be found in Section 3.3.1 and in [2]. If a UE does not geteither a RA response or a RA contention resolution response, it is assumed thatthe UE has to wait until the waiting window has run out plus the time until thenext RA opportunity. It is again assumed that the time after the waiting windowhas run out until the UE can try again is uniformly distributed in the window[0,TconfP −1]. With this assumption α2 and α4 can be estimated as the following:

α2(1) = 2 + TrespW + T

(1)next

α4(1) = 5 + TcontW + T

(1)next

where T (1)next is the time after the waiting window runs out until the UE can try

again, i.e.,

T(1)next = TconfP − 1

2 . (4.9)

4.3.3 Penalty Estimator 2This penalty estimator is in many ways similar to penalty estimator 1. The onlydifference is that the time until the next attempt after a UE does not get a response,Tnext, is estimated differently. Therefore the estimations of α0, α1 and α3 are thesame as in Section 4.3.2, i.e.,

α0(2) = TconfP − 1

2

α1(2) = 2 + 1 + TrespW

2

α3(2) = 5 + 1 + TcontW

2 .

The estimations of α2 and α4 are different in this penalty estimator comparedto penalty estimator 1. The parameter Tnext is calculated in a different way.


Depending on the PRACH configuration and the length of TrespW and TcontW thetime Tnext can be calculated in a more precise way. Thus α2 can be estimated as

α2(2) = 2 + TrespW + T

(2)next,2 (4.10)

where T (2)next,2 is calculated as

T(2)next,2 = TconfP −

((2 + TrespW ) mod TconfP

). (4.11)

This means that the remaining number of subframes can be calculated exactly.The estimation of α4 is done in a similar way. The possible times from the RAattempt until the contention resolution window is over for the UE is given in thevector traResp and can be written as

traResp = 2 +[

1 2 · · · TrespW]

+ 5 + TcontW .

The vector T(2)next,4 can then be expressed as


(traResp mod TconfP

)(4.12)

and α4 is consequently expressed as

α4(2) = 5 + TcontW + T(2)

next,4 (4.13)

where T(2)next,4 is the mean of the vector T(2)

next,4. The mean in (4.13) is neededbecause it is not known when the UE did get its RA response. The estimation ofα4 in (4.13) is not as exact as the estimation of α2 in (4.10) but it is still betterthan α4 for penalty estimator 1. Especially for longer TconfP .

4.3.4 Penalty Estimator 3In this penalty estimator the estimations are done during operation at the basestation. Since it is known when there is an RA opportunity at the eNB and it isalso known when the RA response and the RA contention resolution belonging tothis RA opportunity occurs, it is possible to make better estimations of α1, α2,α3 and α4. The first attempt delay, α0 is estimated in the same way as in penaltyestimators 1 and 2, i.e.,

α0(3) = TconfP − 1

2 .

The estimations of α1 and α3 are set to

α1(3) = traResp − tra

α3(3) = traCont − traResp

where tra, traResp and traCont are the measured times, in the base station, when anRA opportunity, an RA response and an RA contention resolution response have

40 Access Delay

occurred. For all configurations except configurations {9, 10, 11} the estimationsof α2 and α4 are done in the same way as for penalty estimator 2. Howeverfor the estimation of α4 there is no need to use the mean of the RA responsetimes. This means that the estimations of α2 and α4 for all configurations exceptconfigurations {9, 10, 11} can be written as

α2(3) = 2 + TrespW + T

(2)next,2

α4(3) = 5 + TcontW + T

(3)next,4

where T (2)next,2 is defined as in (4.11) and T (3)

next,4 can be defined as


((traCont − tra) mod TconfP

).

For configurations {9, 10, 11} the estimations of α2 and α4 are better describedas Matlab algorithms than equations, see Algorithm 1.

Algorithm 1 Estimation of α2

subframeNr = mod(tra + 2 + TrespW , 10)nextRaSlot = min(raSlots(raSlots− subframeNr > 0))Tnext = nextRaSlot− subframeNralpha2 = 2 + TrespW + Tnext

Algorithm 1 consideres the number the current subframe has (subframeNr) andwhich RA opportunity subframe is the next in line (nextRaSlot). The constantvector raSlots is a vector with the subframe numbers where there are RA oppor-tunities. For example with configuration 9 raSlots would be assigned as

raSlots =[

1 4 7 11]

where the last entry in the array is in fact the first RA opportunity in the nextradio frame. The estimation of α4 for configurations {9, 10, 11} is done in a similarway and is given in Algorithm 2.

Algorithm 2 Estimation of α4

subframeNr = mod(traResp − tra + 5 + TcontW , 10)nextRaSlot = min(raSlots(raSlots− subframeNr > 0))Tnext = nextRaSlot− subframeNralpha4 = 5 + TcontW + Tnext

These estimations of α2 and α4 give better estimates than the estimates in penaltyestimator 2, where the mean of the configuration period is used.


4.3.5 Access Delay Observer ExperimentsTo study how well the observers above perform some experiments need to be ex-ecuted. The experiments test how stable the observers are when different valueson the RACH parameters are used. In the sections below the AD observer withthe different estimators are tested for different power control parameters, config-urations and different loads. The AD observer with penalty estimator 1, 2 and 3will be called AD observer 1, 2 and 3.

4.3.6 Experiment: Accuracy at Varying PRACH Configu-ration and RACH Load

The goal of this experiment is to study the accuracy of the different AD observerswith different penalty estimations at different PRACH configurations and RACHloads. The outline of this experiment can be seen in Table 4.4.

Table 4.4. Setup of PRACH configuration and RACH load observer experiment.

Parameter ValueLoadPUSCH (mean value) 0.5LoadRACH 100, 300, 500, 700, 900 preambles/s/cellRACH Format 0

PRACH Configuration {0, 1, 2}, {3, 4, 5}, {6, 7, 8}, {9, 10, 11},{12 ,13} ,{14}

P0_RACH -120 dBW∆RACH 2 dBM 8ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 100 sSampling Period T 2.5 sInter-site Distance 500 m

To measure the accuracy of the observers the relative residuals, denoted ε, havebeen derived and plotted, where

ε = AD − ADAD

. (4.14)

In (4.14), AD is the measured AD and AD is the estimated AD by the observers.Another way to measure the performance is to measure the root mean squarederror (RMSE) of the measured AD and the observed AD. The RMSE between ameasured signal x and an estimate x with N samples is calculated as

RMSE(x) =

√√√√ 1N

N∑i=1

(xi − xi)2.

42 Access Delay

0 20 40 60 80 100−0.03

−0.02

−0.01

0

0.01

LoadRACH

= 100 preambles/s/cell; Config 0,1,2

Rel

ativ

e R

esid

ual

Time (s)0 20 40 60 80 100

−0.03

−0.02

−0.01

0

0.01

LoadRACH


Rel

ativ

e R

esid

ual

Time (s)

0 20 40 60 80 100−0.03

−0.02

−0.01

0

0.01

LoadRACH


Rel

ativ

e R

esid

ual

Time (s)0 20 40 60 80 100

−0.03

−0.02

−0.01

0

0.01

LoadRACH


Rel

ativ

e R

esid

ual

Time (s)

0 20 40 60 80 100−0.03

−0.02

−0.01

0

0.01

LoadRACH


Rel

ativ

e R

esid

ual

Time (s)

Obs 1Obs 2Obs 3

Figure 4.10. Relative residuals for observers with PRACH configuration {0, 1, 2} anddifferent RACH loads.

The relative residuals for observer 1, 2 and 3 with PRACH configuration {0, 1, 2}and different RACH loads can be seen in Figure 4.10. Here one can get a senseof how the performance of the observers vary in time and it can clearly be seen,that the residual for observer 3 in general has the lowest magnitude. We can alsonotice that the residual magnitude for observer 1 increases as the RACH loadincreases. This can be explained with the fact that more UEs need more attemptswhen the RACH load increases. Recall that the difference between observer 1 and2 is the estimation of Tnext. Therefore the error in observer 1 increases with moreattempts.

If the RMSE in Figure 4.11 is studied, it can also be seen that the RMSE forobserver 3 is the lowest. The difference between observer 1 and 2 is minimal for allconfigurations except configurations {0, 1, 2}. This can be explained by the factthat the configuration period is high, 20ms, for configurations {0, 1, 2}. Thus thedifference between T (1)

next and T(2)next is also great.


0,1,2 3,4,5 6,7,8 9,10,11 12,13 140

0.2

0.4

0.6

0.8

LoadRACH


RM

SE

(AD

) (m

s)

Configuration0,1,2 3,4,5 6,7,8 9,10,11 12,13 140

0.2

0.4

0.6

0.8

LoadRACH


RM

SE

(AD

) (m

s)

Configuration

0,1,2 3,4,5 6,7,8 9,10,11 12,13 140

0.2

0.4

0.6

0.8

LoadRACH


RM

SE

(AD

) (m

s)

Configuration0,1,2 3,4,5 6,7,8 9,10,11 12,13 140

0.2

0.4

0.6

0.8

LoadRACH


RM

SE

(AD

) (m

s)

Configuration

0,1,2 3,4,5 6,7,8 9,10,11 12,13 140

0.2

0.4

0.6

0.8

LoadRACH


RM

SE

(AD

) (m

s)

Configuration

Obs 1Obs 2Obs 3

Figure 4.11. RMSE of measured and observerd AD as a function of PRACH configu-ration and for different RACH loads.

As said before the main reason to the difference between observer 1 and observer 2is the estimation of T (2)

next. This will affect α2 and α4. In Figure 4.12 α0 until α4 forthe different estimations can be seen. It can be seen that α2 and α4 for observer 1differs a lot from observer 2 and observer 3. Here we can also see the reason whyobserver 3 has the best results. In observer 3 the estimations follow the measuredvalues much better, thus leading to a better estimation of AD. It may also benoted that the estimation of α0 is not very accurate for any of the observers.Configurations {9, 10, 11} have varying periods and since α0 is estimated as

α0 = TconfP − 12

a small error is introduced. See Section 3.3.2 for more details regarding the config-uration period for different PRACH configurations. Due to the fact that α0 is onlyused once per estimation it only has a minimal effect on the result. The effects

44 Access Delay

0 20 40 60 80 100

1.16

1.18

1.2

1.22

LoadRACH


α 0 (m

s)

Time (s)0 20 40 60 80 100

4.96

4.98

5

5.02

5.04

5.06

LoadRACH


α 1 (m

s)

Time (s)

0 20 40 60 80 1008

8.5

9

9.5

10

10.5

LoadRACH


α 2 (m

s)

Time (s)0 20 40 60 80 100

17.3

17.4

17.5

17.6

17.7

LoadRACH


α 3 (m

s)

Time (s)

0 20 40 60 80 10030

30.5

31

31.5

LoadRACH


α 4 (m

s)

Time (s)

Meas αObs 1Obs 2Obs 3

Figure 4.12. Measured and observed αs for the observers with RACH load 900 andPRACH configuration {9, 10, 11}.

from using PRACH configurations {9, 10, 11} can also be seen in the estimationsof α4, where the accuracy of observer 2 is not very good. Here we can also see oneof the benefits of using observer 3, namely the better estimation of Tnext.

The conclusion of this experiment is that it is possible to estimate the AD goodenough when varying the PRACH configuration and the RACH load. The RMSEfor observer 2 and 3 are relatively low for all cases, where observer 3 gives slightlybetter estimations than observer 2. Observer 1 has better results for shorter config-uration periods and smaller loads than for longer configuration periods and higherloads. For RACH loads less or equal to 100 preambles/s/cell observer 1 givesacceptable results for all configurations, but as the RACH load increases the per-formance of observer 1 decreases for longer configuration periods. In cases wherethe load continuously is low, 300 preambles/s/cell and lower, observer 1 wouldsuffice. For cases where the load is higher observer 2 or 3 is recommendable. Dueto the fact that α1 and α3 are measured in observer 3, this observer gives the best


results if the working conditions in the base station are changed, for example ifthe distribution of how the UEs are processed is changed.

4.3.7 Experiment: Accuracy at Varying Power Control Pa-rameters

The goal of this experiment is to study the accuracy of observers 1, 2 and 3 whenvarying P0_RACH and ∆RACH . A further goal is also to see how the accuracy ofthe penalty estimates varies with different P0_RACH and ∆RACH . The outline ofthe experiment is seen in Table 4.5.

Table 4.5. Setup of power control observer experiment.

Parameter ValueLoadPUSCH (mean value) 0.5LoadRACH 100 preambles/s/cellRACH Format 0PRACH Configuration {9, 10, 11}P0_RACH -120, -125, -130, -135, -140, -145, -150 dBW∆RACH 0, 2, 4, 6 dBM 8ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 100 sSampling Period T 2.5 sInter-site Distance 500m

In Figure 4.13 the relative residuals for the observers are given. They have beenplotted for the simulations with a P0_RACH of -120, -130, -140 and -150 dBW,and a ∆RACH of 0 dB. As can be seen, the residuals of observer 2 and 3 are rela-tive small and differ very little as P0_RACH is varied. The residual of observer 1however, has an acceptable value, and a very similar value to observer 2, forP0_RACH = −120dBW but for the lower P0_RACH the residual increases rapidly.A lower P0_RACH implies an increase in the number of attempts needed by theUEs to get access. Recall that the difference between observer 1 and observer 2was the estimation of Tnext. The more attempts needed, the more number of timesTnext will be used in the estimation. This explains the large differences betweenobserver 1 and the other two.

In Figure 4.14 the RMSE for the observers are given and they confirm the resultsin Figure 4.13. When looking at the results in Figure 4.14 it can be noted that∆RACH affects the observers much less than P0_RACH .

The estimations for α0 until α4 are seen in Figure 4.15. As can be seen for α2,penalty estimation 1 is almost 2ms under the measured α2. As α2 affects the es-

46 Access Delay

0 20 40 60 80 100−0.02

0

0.02

0.04

0.06

0.08

0.1

∆RACH

= 0 dB; P0_RACH

= −120 dBW

Rel

ativ

e R

esid

ual

Time (s)0 20 40 60 80 100

−0.02

0

0.02

0.04

0.06

0.08

0.1

∆RACH

= 0 dB; P0_RACH

= −130 dBW

Rel

ativ

e R

esid

ual

Time (s)

0 20 40 60 80 100−0.02

0

0.02

0.04

0.06

0.08

0.1

∆RACH

= 0 dB; P0_RACH

= −140 dBW

Rel

ativ

e R

esid

ual

Time (s)0 20 40 60 80 100

−0.02

0

0.02

0.04

0.06

0.08

0.1

∆RACH

= 0 dB; P0_RACH

= −150 dBW

Rel

ativ

e R

esid

ual

Time (s)

Obs 1Obs 2Obs 3

Figure 4.13. Relative residuals for observers with ∆RACH = 0dB and differentP0_RACH .

timation more when the number of attempts increases this explains the high errorfor observer 1.

The conclusion of this experiment is that it is possible to estimate AD good enoughwhen varying P0_RACH and ∆RACH . Observers 2 and 3 have relative good ac-curacy for all simulations, where observer 3 is the better one. It can also benoted that observer 1 has a good accuracy for higher P0_RACH , whereas for lowerP0_RACH it fails to accurately estimate the AD. One of observers 2 or 3 wouldbe to prefer. Even if observer 1 has a good accuracy for high P0_RACH it is notpreferable to always use such high P0_RACH which practically rules out the use ofobserver 1.


−150 −145 −140 −135 −130 −125 −1200

0.5

1

1.5

2

2.5

3

3.5

∆RACH

= 0 dB

RM

SE

(AD

) (m

s)

P0_RACH

(dBW)−150 −145 −140 −135 −130 −125 −120

0

0.5

1

1.5

2

2.5

3

3.5

∆RACH

= 2 dB

RM

SE

(AD

) (m

s)

P0_RACH

(dBW)

−150 −145 −140 −135 −130 −125 −1200

0.5

1

1.5

2

2.5

3

3.5

∆RACH

= 4 dB

RM

SE

(AD

) (m

s)

P0_RACH

(dBW)−150 −145 −140 −135 −130 −125 −120

0

0.5

1

1.5

2

2.5

3

3.5

∆RACH

= 6 dB

RM

SE

(AD

) (m

s)

P0_RACH

(dBW)

Obs 1Obs 2Obs 3

Figure 4.14. RMSE of measured and observerd AD as a function of P0_RACH and fordifferent ∆RACH .

48 Access Delay

0 20 40 60 80 1001.15

1.2

1.25

1.3

∆RACH

= 2 dB; P0_RACH

= −130 dBW

α 0 (m

s)

Time (s)0 20 40 60 80 100

4.95

5

5.05

5.1

5.15

∆RACH

= 2 dB; P0_RACH

= −130 dBW

α 1 (m

s)

Time (s)

0 20 40 60 80 1008

8.5

9

9.5

10

10.5

∆RACH

= 2 dB; P0_RACH

= −130 dBW

α 2 (m

s)

Time (s)0 20 40 60 80 100

17

17.2

17.4

17.6

17.8

∆RACH

= 2 dB; P0_RACH

= −130 dBW

α 3 (m

s)

Time (s)

0 20 40 60 80 10030

30.5

31

31.5

32

32.5

∆RACH

= 2 dB; P0_RACH

= −130 dBW

α 4 (m

s)

Time (s)


Figure 4.15. Measured and observed α0 until α4 for the observers with ∆RACH = 2dBand P0_RACH = −130dBW.


4.3.8 Experiment: Accuracy at Varying PUSCH LoadThe goal of this experiment is to study the accuracy of observers 1, 2 and 3 whenvarying P0_RACH and the PUSCH load. It is also here important to see howthe accuracy of the penalty estimations varies for different P0_RACH and PUSCHloads. The setup of this experiment is given in Table 4.6.

Table 4.6. Setup of PUSCH load observer experiment.

Parameter ValueLoadPUSCH (mean value) 0.0, 0.2, 0.4, 0.6, 0.8, 1.0LoadRACH 100 preambles/s/cellRACH Format 0PRACH Configuration {9, 10, 11}P0_RACH -120, -130, -140, -150 dBW∆RACH 2 dBM 8ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 100 sSampling Period T 2.5 sInter-site Distance 500 m

The results of this experiment are seen in Figure 4.16 and Figure 4.17. As canbe seen observers 2 and 3 show a good accuracy throughout the simulations. Forobserver 1 however the accuracy in general decreases when the PUSCH load in-creases and P0_RACH decreases. In Section 4.3.7 it was already noted that theaccuracy of observer 1 decreases when the P0_RACH decreases. Recall from Sec-tion 4.2.3 that the AD was increased when the PUSCH load was increased. Thereason for this was the increase in uplink inter-cell interference, thus requiring ahigher P0_RACH to keep the same AD. Therefore with a low P0_RACH the numberof attempts needed to get access increases if the PUSCH load increases. This isalso the reason why the accuracy of observer 1 decreases when the PUSCH loadincreases.

In Figure 4.18 the estimation of the penalties can be seen. The results look muchthe same as in the previous sections. The main reason for the error in observer 1is the estimation of α2, which is seen in Figure 4.18. This is why the accuracy ofobserver 1 decreases when the number of attempts increase.

50 Access Delay

0 20 40 60 80 100−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

LoadPUSCH

= 1; P0_RACH

= −120 dBW

Rel

ativ

e R

esid

ual

Time (s)0 20 40 60 80 100

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

LoadPUSCH

= 1; P0_RACH

= −130 dBW

Rel

ativ

e R

esid

ual

Time (s)

0 20 40 60 80 100−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

LoadPUSCH

= 1; P0_RACH

= −140 dBW

Rel

ativ

e R

esid

ual

Time (s)0 20 40 60 80 100

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

LoadPUSCH

= 1; P0_RACH

= −150 dBW

Rel

ativ

e R

esid

ual

Time (s)

Obs 1Obs 2Obs 3

Figure 4.16. Relative residuals for observers with a PUSCH load of 1.0 and differentP0_RACH .


0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

P0_RACH

= −120 dBW

RM

SE

(AD

) (m

s)

LoadPUSCH

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

P0_RACH

= −130 dBW

RM

SE

(AD

) (m

s)

LoadPUSCH

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

P0_RACH

= −140 dBW

RM

SE

(AD

) (m

s)

LoadPUSCH

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

P0_RACH

= −150 dBW

RM

SE

(AD

) (m

s)

LoadPUSCH

Obs 1Obs 2Obs 3

Figure 4.17. RMSE of measured and observerd AD as a function of PUSCH load andfor different P0_RACH .

52 Access Delay

0 20 40 60 80 1001.15

1.2

1.25

1.3

LoadPUSCH

= 0.2; P0_RACH

= −140 dBW

α 0 (m

s)

Time (s)0 20 40 60 80 100

4.9

4.95

5

5.05

5.1

5.15

LoadPUSCH

= 0.2; P0_RACH

= −140 dBW

α 1 (m

s)

Time (s)

0 20 40 60 80 1008

8.5

9

9.5

10

10.5

LoadPUSCH

= 0.2; P0_RACH

= −140 dBW

α 2 (m

s)

Time (s)0 20 40 60 80 100

17.3

17.4

17.5

17.6

17.7

17.8

LoadPUSCH

= 0.2; P0_RACH

= −140 dBW

α 3 (m

s)

Time (s)

0 20 40 60 80 10030

30.5

31

31.5

32

LoadPUSCH

= 0.2; P0_RACH

= −140 dBW

α 4 (m

s)

Time (s)


Figure 4.18. Measured and observed α0 until α4 for the observers with a PUSCH loadof 0.2 and P0_RACH = −140 dBW.


4.3.9 Experiment: Accuracy at Varying RACH Load andP0_RACH

The goal of this experiment is to study the accuracy of the different observerswhen the RACH load and P0_RACH vary. However, due to the fact that this ex-periment did not produce any new information about observer 1 only the resultsfrom observer 2 and 3 are presented. The outline of this experiment is seen inTable 4.7.

Table 4.7. Setup of RACH load observer experiment.

Parameter ValueLoadPUSCH (mean value) 1

LoadRACH10, 50, 100, 300, 500, 700,900 preambles/s/cell

RACH Format 0PRACH Configuration {9, 10, 11}P0_RACH -120, -130, -140, -150 dBW∆RACH 2 dBM 8ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 100 sSampling Period T 2.5 sInter-site Distance 500 m

The results can be seen in Figure 4.19 and Figure 4.20. As can be seen in Fig-ure 4.19, observer 2 and observer 3 follow the measured AD relatively good forP0_RACH = −120,−130 and −140 dBW. When P0_RACH reaches -150 dBW it canclearly be seen that the accuracy of observer 2 and 3 decreases with an increasingRACH load. This can also be seen in Figure 4.20. When P0_RACH = −150 dBWthe residuals for observer 2 and 3 are decreasing in a linear fashion when RACHload increases. It can also be noted in the plot for P0_RACH = −150 dBW inFigure 4.19 that the AD stops increasing after a RACH load of 500. This can beexplained by the fact that more UEs will reach the maximum number of allowedattempts when the RACH load increases and the AD reports of these UEs arenot included in the measured AD. Since the estimations of AD are based on thereported number of sent preambles the estimations follow the mesured AD.

The conclusion of this experiment is that the accuracy of observer 2 and 3 in gen-eral are good, but for higher values of P0_RACH and RACH load the accuracy ofthe observers decreases. The decrease is however not great. The errors are stillunder 1% for RACH loads up to 900 preambles/s/cell. The differences betweenobserver 2 and observer 3 are very small.

54 Access Delay

10 50 100 300 500 700 90023.6

23.8

24

24.2

24.4

24.6

P0_RACH

= −120 dBW

Acc

ess

Del

ay (

ms)

LoadRACH

(preambles/s/cell)10 50 100 300 500 700 900

24

24.2

24.4

24.6

24.8

25

25.2

P0_RACH

= −130 dBW

Acc

ess

Del

ay (

ms)

LoadRACH

(preambles/s/cell)

10 50 100 300 500 700 90033

33.5

34

34.5

35

35.5

P0_RACH

= −140 dBW

Acc

ess

Del

ay (

ms)

LoadRACH

(preambles/s/cell)10 50 100 300 500 700 900

60

61

62

63

64

P0_RACH

= −150 dBW

Acc

ess

Del

ay (

ms)

LoadRACH

(preambles/s/cell)

Meas ADObs2Obs3

Figure 4.19. Measured and observed AD for observers with varying RACH load fordifferent P0_RACH .

10 50 100 300 500 700 900−8

−6

−4

−2

0

2

4

6

8x 10

−3 P0_RACH

= −120 dBW

Rel

ativ

e R

esid

ual

LoadRACH

(preambles/s/cell)10 50 100 300 500 700 900

−8

−6

−4

−2

0

2

4

6

8x 10

−3 P0_RACH

= −130 dBW

Rel

ativ

e R

esid

ual

LoadRACH

(preambles/s/cell)

10 50 100 300 500 700 900−8

−6

−4

−2

0

2

4

6

8x 10

−3 P0_RACH

= −140 dBW

Rel

ativ

e R

esid

ual

LoadRACH

(preambles/s/cell)10 50 100 300 500 700 900

−8

−6

−4

−2

0

2

4

6

8x 10

−3 P0_RACH

= −150 dBW

Rel

ativ

e R

esid

ual

LoadRACH

(preambles/s/cell)

Obs2Obs3

Figure 4.20. Relative residuals for observers with varying RACH load for differentP0_RACH .

4.4 Conclusion 55

4.3.10 Observability SummaryIt has been shown that the AD can be accurately observed when the number ofattempts needed by the UEs is reported to the base station. In all experimentsobserver 3 shows the best results. Even if the distribution of how preambles areprocessed or the distribution of how contention resolution responses are sent ischanged, observer 3 can still esimate the AD good. This is possible because ob-server 3 has access to this information from measurements that are done directlyin the eNB. These measurements are also the reason why observer 3 is the mostcomplex observer. Observer 2 also shows in general a good accuracy for all experi-ments. It accurately estimates the mean AD for all experiments, but does not havethe same accuracy as observer 3. The complexity of observer 2 is however muchlower than observer 3. There is no need for extra measurements in the eNB withobserver 2 and all the estimations can be done offline. This has also the effect thatany changes in processing distribution can not be taken into account when usingobserver 2. As for observer 1 the only time the accuracy can be guarantied to begood enough is if the UEs need few attempts. That is with high power controlparameter values and configurations with a short configuration period.

It can be noted that the observations of AD have been done with regard to themean AD. That is the mean AD for each number of attempts have been calculated.If one wants the distrubution of the AD this has to be calculated by multiplyingthe distribution of the number of attempts with the observed AD for one attempt.This leads to an estimation of the distribution of AD that can differ a bit from thereal distribution. Another way to do this would be to observe the AD by estimat-ing the distribution for one attempt and from this build a complete distributionof AD with help from the number of attempts.

4.4 ConclusionThe conclusion of this chapter is that access delay is both controllable and ob-servable. In the study of the controllability no special assumptions were madebut for the observability study it is assumed that the UEs report the number ofattempts needed to get access and that the backoff parameter B = 0. With theseassumptions it is also possible to use AD in a performance specification model.The study of backoff and the inclusion of backoff in the observer algorithms willbe done in the next chapter.

Chapter 5

Backoff

5.1 Introduction to BackoffThe time a UE waits before it tries to reconnect to a base station after it has faileda random access attempt can be controlled by the backoff indicator. This indicatoris sent to the UE from the eNB with the RA response. This is a possibility for theeNB to reduce the chance of overload and to a certain extent contention. If forexample an eNB receives more preambles than it can handle in an RA opportunity,than the eNB can send a backoff indicator with the RA response. This tells theUEs who will not get access in this attempt to wait with their next attempt. TheUEs choose a backoff time uniformly in the interval [0,B], where B is the backoffparameter identified by the backoff indicator, see Section 3.3.3. A UE can receivean RA response even if it does not include the preamble sent by the UE and cantherefore read the backoff indicator included in these responses. It is therefore stillpossible for a UE whose preamble was not detected to receive the backoff indicator.This chapter will deal with backoff in the sense of how the backoff affects the ADobservers and what possibilities there are to include backoff in the AD observers.The last part of the chapter will be a discussion on whether to include backoffas a control parameter or if it should be seen as an external parameter set by aseparate part of the system.

5.2 Effects of Backoff on Access DelayThe observers that were discussed in Section 4.3 did not include any support forbackoff parameters greater than zero. If AD should be used in a performancespecification model it must be possible to make good observations of AD for allbackoff parameters.

5.2.1 Inclusion of Backoff in ObserversThe observer algorithm from Section 4.3.1 can be used to include support forbackoff. A UE will wait a certain backoff time if the UE can not get access. This

57

58 Backoff

means that α2 and α4 need to be extended to support a backoff parameter greaterthan zero. If the backoff parameter is set to B a UE chooses its backoff timeuniformly in the interval [0,B]. Thus it can be assumed that the average backofftime will be the mean value of the uniform distribution U(0, B). One of the maindifferences between the different penalty estimations for the AD observers wasthe estimation of Tnext. When the backoff parameter is greater than zero it is notpossible to make any special predictions about Tnext as done in penalty estimation2 and 3 described in sections 4.3.3 and 4.3.4. Therefore the best estimation of Tnextis the one in (4.9). This means that for all backoff parameters greater than zeroα2,B and α4,B can be estimated as

α2,B = 2 + TrespW + B

2 + Tnext

α4,B = 5 + TcontW + B

2 + Tnext

where B is the backoff parameter used in the base station and Tnext is defined as

Tnext = TconfP − 12 .

5.2.2 Experiment: Accuracy at Varying RACH LoadThe goal of this experiment is to study the accuracy of the different observerswhen using a backoff parameter greater than zero and when the RACH load andP0_RACH vary. The setup of this experiment can be seen in Table 5.1.

Table 5.1. Setup of RACH load backoff experiment.

Parameter ValueLoadPUSCH (mean value) 1

LoadRACH10, 50, 100, 300, 500, 700,900 preambles/s/cell

RACH Format 0PRACH Configuration {9, 10, 11}P0_RACH -120, -130, -140, -150 dBW∆RACH 2 dBM 8B 0, 80 msra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 100 sSampling Period T 2.5 sInter-site Distance 500 m

The result of this experiment can be seen in Figure 5.1, Figure 5.2 and Figure 5.3.

5.2 Effects of Backoff on Access Delay 59

10 50 100 300 500 700 90023.5

24

24.5

25

25.5

26

P0_RACH

= −120 dBW

Acc

ess

Del

ay (

ms)

LoadRACH

(preambles/s/cell)10 50 100 300 500 700 900

24

25

26

27

28

29

P0_RACH

= −130 dBW

Acc

ess

Del

ay (

ms)

LoadRACH

(preambles/s/cell)

10 50 100 300 500 700 90030

40

50

60

70

80

P0_RACH

= −140 dBW

Acc

ess

Del

ay (

ms)

LoadRACH

(preambles/s/cell)10 50 100 300 500 700 900

60

80

100

120

140

160

180

200

220

P0_RACH

= −150 dBWA

cces

s D

elay

(m

s)

LoadRACH

(preambles/s/cell)

Meas AD; B = 0 msObs 2; B = 0 msMeas AD; B = 80 msObs 2; B = 80 ms

Figure 5.1. AD and estimated AD from observer 2 as a function of RACH load fordifferent P0_RACH .

In Figure 5.1 and Figure 5.2 the measured AD and the observed AD are plottedagainst the RACH load and in Figure 5.3 the RMSE of the measured AD and theobserved AD at different RACH loads are presented. As can be seen in figures5.1 and 5.2 the overall accuracy of the observations decrease when the P0_RACHdecreases. What is interesting to notice is that the accuracy of the observations isgood for all P0_RACH when the RACH load is above 300 preambles/s/cell. Thiscan also be seen in Figure 5.3 where the errors of the observers decreases with anincreasing RACH load. When the RACH load is low there is a higher probabilitythat there is only one UE who sends a preamble at a RA opportunity. If this singleUE is not detected there will be no answer from the eNB. The UE will therefore notknow the true backoff parameter and will instead use a backoff parameter of zero.This leads to a false assumption on the average backoff time used in the observers,which leads to the low accuracy at low RACH loads. An interesting thing to noticeis that when the accuracy of the observations is low the estimations are alwayshigher than the measured AD.

60 Backoff

10 50 100 300 500 700 90023.5

24

24.5

25

25.5

26

P0_RACH

= −120 dBW

Acc

ess

Del

ay (

ms)

LoadRACH

(preambles/s/cell)10 50 100 300 500 700 900

24

25

26

27

28

29

P0_RACH

= −130 dBW

Acc

ess

Del

ay (

ms)

LoadRACH

(preambles/s/cell)

10 50 100 300 500 700 90030

40

50

60

70

80

P0_RACH

= −140 dBW

Acc

ess

Del

ay (

ms)

LoadRACH

(preambles/s/cell)10 50 100 300 500 700 900

60

80

100

120

140

160

180

200

220

P0_RACH

= −150 dBWA

cces

s D

elay

(m

s)

LoadRACH

(preambles/s/cell)

Meas AD; B = 0 msObs 3; B = 0 msMeas AD; B = 80 msObs 3; B = 80 ms

Figure 5.2. AD and estimated AD from observer 3 as a function of RACH load fordifferent P0_RACH .

The conclusion of this experiment is that the accuracy of the observers are verylow at low RACH loads. This has the effect that these observers cannot be usedto accurately estimate AD when a backoff parameter greater than zero is used andthe RACH load is low. Because of the dependency the RACH load has on the ADwhen a backoff parameter greater than zero is used it could be possible to increasethe accuracy of the observers if the RACH load could be estimated. The resultsfrom this experiment also suggest that there is a upper limit to the RACH loadwhen the accuracy of these observers are low. If the RACH load at a base stationis known to be higher than this limit the use of these observers could be possible.

5.3 ConclusionAs could be seen in Section 5.2.2 a backoff parameter greater than zero has a greateffect on the accuracy of the estimated AD. The poor performance of the observers

5.3 Conclusion 61

10 50 100 300 500 700 9000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

P0_RACH

= −120 dBW

RM

SE

(AD

) (m

s)

LoadRACH

(preambles/s/cell)10 50 100 300 500 700 900

0

0.5

1

1.5

2

2.5

P0_RACH

= −130 dBW

RM

SE

(AD

) (m

s)

LoadRACH

(preambles/s/cell)

10 50 100 300 500 700 9000

5

10

15

20

25

30

35

40

P0_RACH

= −140 dBW

RM

SE

(AD

) (m

s)

LoadRACH

(preambles/s/cell)10 50 100 300 500 700 900

0

20

40

60

80

100

120

P0_RACH

= −150 dBWR

MS

E(A

D)

(ms)

LoadRACH

(preambles/s/cell)

Obs 2; B = 0 msObs 3; B = 0 msObs 2; B = 80 msObs 3; B = 80 ms

Figure 5.3. RMSE of measured and observed AD, in ms, as a function of RACH loadfor different P0_RACH .

at low RACH loads could be an indicator that the only way AD can be used ina performance specification model is if the AD measured by the UEs is sent tothe eNB. On the other hand, the results also suggest that it could be possible toincrease the accuracy of the estimations if the RACH load could be measured orobserved. If a measurement of the RACH load was at hand the AD observer couldbe extended to only include backoff if the measured RACH load is high. Thishowever, does not lead to a complete observability of AD.

One other factor of great importance is the way backoff is used. It is possible thata backoff parameter greater than zero will only be used if there is an overload atthe base station, i.e., there are more received preambles in one RA opportunitythan the eNB can process. If this is the case, then the number of UEs that usea backoff greater than zero is limited to a known amount and this could be usedin the estimations. For example, if overloads happen seldom no consideration tobackoff needs to be taken when estimating the average AD.

62 Backoff

The results also show that the observed AD is correct if B > 0 and the RACHload is high. This could be used in an environment where B > 0 only if the RACHload is high. In cases like this an AD observer following the algorithm above couldbe used without any extra measurements or assumptions.

The conclusion of this chapter is that the AD can be estimated well for a B > 0and a relative high RACH load. If the RACH load is low and B > 0, AD cannotbe estimated well. The backoff indicator will therefore not be seen as controlparameter in the rest of this thesis, but instead as a parameter set by anotherlayer out of our control. The backoff parameter is however known by our observersand control system. Despite the great errors in the observers when the RACHload is low the AD is always over-estimated. The error in the estimated AD ishowever decreased as DMP is decreased, i.e., P0_RACH is increased. This indicatesthat a controller using P0_RACH would drive the error of the estimators towardzero. That is a controller using the AD observer would see a high AD and thusincreasing P0_RACH attempting to lower the AD. Increasing the P0_RACH wouldlead to better estimations of the AD and thus the controller will end up in a stablestate. It is also highly possible that backoff will only be used to resolve overloadand thus not significantly affecting the total average of the AD, assuming thatoverloads happen seldom.

Chapter 6

Sampling Period

6.1 IntroductionWhen designing a control system it is very important to know how different sam-pling periods affect the accuracy of the sampled signal. In the case of the randomaccess procedure in LTE this sampled signal is AD, which in this chapter is as-sumed to be measured by the UEs and then reported to the eNB. This chapterincludes a study on how different sampling periods affect the accuracy of the sam-pled AD.

It should be mentioned how the sampling of the RA procedure works. Reports ofAD from UEs are collected in the eNB between two sample points. When the nextsample takes place a percentile is calculated from these collected reports of ADs.After this the list of reported UEs are cleared and the procedure starts over. Notethat in the following sections we assume a stationary condition, where the RACHload, PUSCH load and other parameters are assumed to be constant.

6.2 Experiment: Accuracy of Sampled AccessDelay

The goal of this experiment is to study how different sampling periods affect theaccuracy of the AD. To measure how well the measurements of AD are withdifferent sampling periods a true AD is needed. To find this true AD a longsimulation is carried out. From the data collected during this long simulation anAD for different percentiles is calculated and seen as the true AD. After this thedata was divided into smaller parts representing the different sampling periods.The results from these sampling periods are then compared to the true AD. Thesetup of the experiment can be seen in Table 6.1.

In Figure 6.1 the RMSE of AD for different sampling periods can be seen. Thedashed lines represent the 95% confidence interval for each percentile. As can be

63

64 Sampling Period

Table 6.1. Setup of sampling period experiment.

Parameter ValueLoadPUSCH (mean value) 0.5LoadRACH 10 preambles/s/cellRACH Format 0PRACH Configuration {6, 7, 8}P0_RACH -120, -150 dBW∆RACH 4 dBM 8B 0msra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 3000 s

Sampling Period T 1, 10, 20, 50, 75, 100, 125, 200, 300, 500,1000, 1500 s

Inter-site Distance 500m

1 10 20 50 75 100 125 200 300 500 1000 15000

5

10

15

Sample Time (s)

RM

SE

(AD

) (m

s)

P0_RACH

= −120 dBW

1 10 20 50 75 100 125 200 300 500 1000 15000

5000

10000

15000

Sample Time (s)

Nr

of a

cces

sed

UE

s

50th percentile80th percentile99th percentile99.9th percentile

Figure 6.1. RMSE of AD, in ms, for different sampling periods at P0_RACH =−120 dbW.

6.2 Experiment: Accuracy of Sampled AccessDelay 65

1 10 20 50 75 100 125 200 300 500 1000 15000

5

10

15

20

25

Sample Time (s)

RM

SE

(AD

) (m

s)

P0_RACH

= −150 dBW

1 10 20 50 75 100 125 200 300 500 1000 15000

5000

10000

15000

Sample Time (s)

Nr

of a

cces

sed

UE

s

50th percentile80th percentile99th percentile99.9th percentile

Figure 6.2. RMSE of AD, in ms, for different sampling periods at P0_RACH =−150dbW.

seen for percentiles 50 to 99 the RMSE is high for shorter sampling periods andin general decreases as the sampling period increases.

What is interesting to notice is that the RMSE for the 99.9th percentile increaseat a sampling period of 10 s peaks at 75 s and decrease until 500 s. The increaseat 10 s can be explained by the fact that there are very few UEs who need morethan one attempt to get access. The few UEs who need two attempts are howeverevenly spread out over the simulation in time. This means that for samplingperiods under 10 s there will be few samples including an AD reported from a UEneeding two attempts. Therefore when the RMSE is calculated these few sampleswill have less effect on the result. For sampling periods between 10 and 500 s onthe other hand there will be many samples which includes an AD report from aUE needing two attempts. When the RMSE is calculated from these samples theresulting value will be higher. For even higher sampling periods, above 500 s thereis also one or more AD reports from UEs with two attempts, but the reason whythe RMSE is low here is the number of UE reports in each sample. If the UEreports in a sample is sorted in a list with size N , then the index n of the p-thpercentile can be calculated as

n = N

100p+ 12

66 Sampling Period

and rounded to the nearest integer. This means that if there are enough reportsin a sample the 99.9th percentile are more likely to be from a UE that needs oneattempt. This explains why the RMSE is lower for sampling periods higher than500 s.

The same result can be seen in Figure 6.2. The RMSE for percentiles 50 to 99are high for short sampling periods but decrease fast when the sampling periodincreases. For P0_RACH = −150 dBW the elevation is not as pronounced as forP0_RACH = −120 dBW. When P0_RACH = −150dBW the number of attemptsneeded by the UEs to get access are more evenly spread out in the interval from1 attempt to 8 attempts, leading to a wider range of reported ADs. This explainsthe lower elevation.

The conclusion of this experiment is that a good enough accuracy of the sampledAD can be reached as long as the sampling period is long enough. In this exper-iment this would correspond to a sampling period above 500 s, but this is highlydepending on the percentile that is studied. For all percentiles except the 99th itcould be seen that the accuracy in general increases considerably from a samplingperiod of 1 s to 10 s and then reaches a steady state for sampling periods around50 s and above. For the 99.9th percentile the accuracy is worse for sampling pe-riods from 10 s to 500 s. This must be kept in mind if the 99.9th percentile iswanted in a performance specification. If the 99.9th percentile is not used, thenthe experiment indicates that it is enough with sampling periods around 20 s.

6.3 ConclusionAccording to the experiment in Section 6.2, it is possible to get good measurementsof AD if a sampling period around 20 seconds is used. This is however not truefor percentile 99.9 where sampling periods over 500 seconds should be used to getthe same accuracy as for the other percentiles. If the 99.9th percentile is sampledit must be kept in mind that the accuracy of the sampled AD is not as good asfor the other percentiles.

If a faster system is needed, then a filter could improve the accuracy of the sampledAD. Another possibility is to use an aperiodic sample method. This would meanthat the system samples when enough UE reports are collected. Enough reportsare collected when the confidence interval of the data in the sample is low enough,for example |CI| ≤ ε, where CI is the confidence interval and ε is a positiv number.With this method the accuracy of the samples will always be the same, but thespeed of the controller will be unknown. If the timing of the system is critical anunknown speed of the controller can lead to unwanted effects.

Chapter 7

Control Structures

7.1 IntroductionWhen controlling with multiple variables there are many different control struc-tures that can be applied. Some of the control structures require a good modelof the system to be setup, whereas other structures can be setup manually with-out involving a model. The first thing to do when designing a controller is todecide what parameters to use and for what purpose. Which should the controlparameters be, which parameter(s) should be used for reference and so on. In thischapter we will first discuss how to define our control system and its parametersand after this three different control structures will be presented. Thirdly, someexperiments will be run to show the performance of the control structures and atlast there will be a conclusion of the results.

7.2 Definition of Control ParametersAt first the parameters to use in the controller must be chosen. Access delay ischosen to be part of the reference or performance specification. One advantage ofusing AD instead of for example AP is that AD is more intuitive for the operatorto set than AP. It is important that the performance specification is specified ina way that is possible for the controllers to use. If the reference is only specifiedlike AD = 30ms it is difficult to verify if the specification is held, since it is notspecified if it is the average AD that should be 30ms or if all UEs should havean AD under 30ms. In this thesis the AD is therefore specified for a certain per-centile, like P (AD < 30ms) = 0.5. This means that the the 50th percentile of themeasured ADs should be 30ms.

For controlling the random access procedure P0_RACH , ∆RACH and the PRACHconfiguration will be used. These three parameters offer a wide range for control-ling AD according to the experiments in Chapter 4. Another parameter that couldbe used is the backoff parameter B. However in the experiments below B is seen

67

68 Control Structures

as a parameter that is set by another layer when the RACH load is too high, andis therefore out of our control. The basic principle of our controller can then besummarized and seen in Figure 7.1.

P0_RACH

∆ RACH

Config.Controller RACH-

rAD AD

Figure 7.1. Basic principle of the RACH with a controller.

The box named Controller in Figure 7.1 can be designed in different ways. Threedifferent structures have been designed and tested in this thesis. The first twoare based on a so-called mid-range controller, and the third is a structure whereP0_RACH , ∆RACH and the PRACH configuration are controlled in separate loops.These three control structures will be explained more in detail below.

7.3 ModellingDue to the high complexity of the system the derivation of a physical model wouldbe too time consuming. Therefore we will instead use an autoregressive modelcalled an ARX-model, [14]:

A(q)y(t) = B(q)u(t) + e(t). (7.1)

In (7.1) u(t) and y(t) represent the input and the output respectively and q rep-resents the shift-operator which means that q−1u(t) = u(t − 1). The term e(t)represents white noise. The rational functions A(q) and B(q) can be written as

A(q) = 1 + a1q−1 + . . .+ anaq

−na

B(q) = b1 + b2q−1 + . . .+ bnbq

−nb+1

where ai and bi are the parameters of the model, which need to be estimated. Thiscan be done by sampling input-output data from a simulation and then calculatethe prediction error

ε(t, θ) = y(t)− y(t|θ)

where θ is the parameter vector and y(t|θ) is the prediction created with our model.By using the following fitness metric

VN (θ) = 1N

N∑t=1

ε2(t, θ) (7.2)

7.3 Modelling 69

we can see how good the parameter vector θ is. We can thus find our modelparameters by choosing the value of θ that minimizes (7.2):

θN = arg minθVN (θ). (7.3)

By finding the correct grade for the system we can find a parameter vector θ thatsuits our system.

7.3.1 Modelling with regard to P0_RACH

The modelling was done by running a simulation where the value of P0_RACH waschanged rapidly during a time interval of 200 seconds. After this (7.3) was usedto find the parameters that best suited the model. The outline of this experimentcan be seen in Table 7.1.

Table 7.1. Setup of modelling with regard to P0_RACH .

Parameter ValueLoadPUSCH (mean value) 0.5LoadRACH 100 preambles/s/cellRACH Format 0PRACH Configuration {6, 7, 8}P0_RACH -120, -150 dBW∆RACH 4 dBM 50ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 200 sSampling Period T 1 sInter-site Distance 500m

In Figure 7.2 the values of VN , calculated from (7.2) are presented. As can beseen the lowest value is reached when na = 2 and nb = 1. However the differencebetween the simplest model, where na = 0 and nb = 1, and the best model islow in comparison to the gain from using the simple model. The system fromP0_RACH to AD is therefore modelled as

y(t) = b1u(t) + c+ e(t) (7.4)

where b1 = −0.63 and c = −44.44 constants. The signal u(t) is in this caseP0_RACH . In Figure 7.3 the model compared to the sampled data can be seen.


0 1 2 3 40

5

10

15

20

25

30

35

na

VN

(θ)

nb = 1nb = 2nb = 3nb = 4nb = 5

Figure 7.2. Value of VN for different values on na and nb, when modelling with regardto P0_RACH . On the x-axis we have na. For each na, the most left bar represents nb = 1and the most right bar nb = 5.

0 20 40 60 80 100 120 140 160 180 200

30

40

50

60

Time (s)

AD

, 80%

Per

cent

ile (

ms)

0 20 40 60 80 100 120 140 160 180 200

−150

−140

−130

−120

Time (s)

P0_

RA

CH (

dBW

)

Predicted ADSampled AD

Figure 7.3. Sampled and predicted data with na = 0 and nb = 1, when modelling withregard to P0_RACH .

7.3 Modelling 71

7.3.2 Modelling with regard to ∆RACH

The modelling was done similarly to the experiment in Section 7.3.1 but the param-eter ∆RACH was changed. The outline of the experiment can be seen in Table 7.2.

Table 7.2. Setup of modelling with regard to ∆RACH .

Parameter ValueLoadPUSCH (mean value) 0.5LoadRACH 100 preambles/s/cellRACH Format 0PRACH Configuration {6, 7, 8}P0_RACH -150 dBW∆RACH 0, 6 dBM 50ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 200 sSampling Period T 1 sInter-site Distance 500m

0 1 2 3 40

50

100

150

200

250

na

VN

(θ)

nb = 1nb = 2nb = 3nb = 4nb = 5

Figure 7.4. Value of VN for different values on na and nb, when modelling with regardto ∆RACH . On the x-axis we have na. For each na, the most left bar represents nb = 1and the most right bar nb = 5.


0 20 40 60 80 100 120 140 160 180 20040

60

80

100

120

140

Time (s)

AD

, 80%

Per

cent

ile (

ms)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3

4

5

6

Time (s)

∆ RA

CH (

dB)


Figure 7.5. Sampled and predicted data with na = 0 and nb = 1, when modelling withregard to ∆RACH .

In Figure 7.4 the values of VN can be seen for different degrees on the model. Ascan be seen the lowest value of VN is reached when na = 2 and nb = 4, but also herethere is such a small difference between VN for this model and the simplest model,that there is more to gain from using the simpler model. Therefore the modelis also here written as in (7.4) with b1 = −6.60, c = 89.20 and u(t) = ∆RACH .The result when comparing the prediction to the sampled data can be seen inFigure 7.5.

7.3.3 Modelling with regard to PRACH Configuration

The goal of this experiment is to study how a prediction of AD best can be modeledwith regard to the PRACH Configuration. The outline of the experiment can beseen in Table 7.3.

The values of VN for different degrees can be seen in Figure 7.6. It can be noticedthat the lowest value of VN is reached when na = 3 and nb = 2. Still, as in sections7.3.1 and 7.3.2 the simplest model is chosen because of its simplicity. Thereforethe model will be the same as in (7.4) with b1 = −5.31, c = 56.28 and u(t) is thePRACH configuration. The result when comparing the prediction to the sampleddata can be seen in Figure 7.7.

7.3 Modelling 73

Table 7.3. Setup of modelling with regard to the PRACH Configuration.

Parameter ValueLoadPUSCH (mean value) 0.5LoadRACH 100 preambles/s/cellRACH Format 0PRACH Configuration {0, 1, 2}, {14}P0_RACH -138 dBW∆RACH 2 dBM 50ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 200 sSampling Period T 1 sInter-site Distance 500m

0 1 2 3 40

5

10

15

20

25

30

na

VN

(θ)

nb = 1nb = 2nb = 3nb = 4nb = 5

Figure 7.6. Value of VN for different values on na and nb, when modelling with regardto the PRACH configuration. On the x-axis we have na. For each na, the most left barrepresents nb = 1 and the most right bar nb = 5.

7.3.4 Modelling SummaryAll the experiments show that the RACH system is static when only one of thecontrol parameters is changed. The sampling period used in all the experimentswas set to 1 s. In the experiments in Section 4.2 the longest AD for the 80thpercentile was registered around 250ms. This means that a step response willhave reached its final state within one second and this is an explanation of thestatic behavior of the system. It is also important to remember that the models


0 20 40 60 80 100 120 140 160 180 200

30

40

50

60

70

80

Time (s)

AD

, 80%

Per

cent

ile (

ms)

0 20 40 60 80 100 120 140 160 180 200

0,1,2

3,4,5

6,7,8

9,10,11

12,13

14

Time (s)

PR

AC

H C

onfig

urat

ion


Figure 7.7. PRACH Configuration. Sampled and predicted data with na = 0 andnb = 1, when modelling with regard to the PRACH configuration.

derived above only apply to the assumptions made in the simulator.

7.4 Description of ControllersWhen controlling with more than one control parameter there are many ways tocombine these. In this thesis three different control structures have been tested:two control structures of the Mid-Range type [15] and one control structure wherethe controllers work separately without any knowledge of each other. The actualcontrollers are simple PI-controllers and are also explained below. These controlstructures can all be tuned manually and do not require a model of the systemwhen calculating the tuning parameters. Because only simulated data is available,the models derived in Section 7.3 can only be seen as approximations of the truesystem and therefore no control structures requiring a model of the system havebeen tested.

7.4.1 I-ControllerIn Section 7.3 the dynamics of the system was derived. It could be seen thatthe RACH system is a static system when only one of the control parameters ischanged. To remove the steady-state error a controller with an integrator part

7.4 Description of Controllers 75

- GFr u ye

Figure 7.8. A controller and system with the name of the signals.

is used. It is also important that the control system is not too fast, since sucha system is very sensitive to noise. With the definitions of the signals as seen inFigure 7.8, an I-controller can, according to [15], be expressed as

U(s) = KI

sE(s) = F (s)E(s)⇔ F (s) = KI

s(7.5)

in the Laplace domain. In (7.5) KI is the tuning parameter that defines thecontroller. By using Euler’s method we can change the variable s to

s = 1T

(1− q−1). (7.6)

If we put (7.6) into (7.5) we can write our time discrete controller Fd(q) as

Fd(q) = KIT

1− q−1

which represents the difference equation

u(kT ) = u(kT − T ) +KITe(kT ). (7.7)

This type of controller also has an integrated anti-windup function, see [15]. Theexpression in (7.7) can be translated into pseudo code which can be seen in Algo-rithm 3.

The controller in (7.7) can be used together with the models derived in Section 7.3

Algorithm 3 PI-controllere = r − yv = uk−1 +KI ∗ T ∗ eif v > umax thenu = umax

else if v < umin thenu = umin

elseu = v

end ifuk−1 = u


- GFwrr u w

c c

y-

Figure 7.9. Example of a control system with a removal of a constant.

to calculate KI . The details are only shown for the P0_RACH model in Sec-tion 7.3.1 since the calculations are done similarly for the other models.

First of all the constant c needs to be removed from (7.4) to avoid problems whencombining it with the controller. Therefore we create the new control variablew(t):

w(t) = y(t)− c = b1u.

By making a Laplace transformation we get

W (s) = b1U(s) = G(s)U(s).

Our system now has the form that can be seen in Figure 7.9. If F in Figure 7.9is the same as F (s) in (7.5), the closed loop system from rw to w can be derivedfrom Figure 7.9, i.e.,

GC(s) = F (s)G(s)1 + F (s)G(s) = KIb1

s+KIb1. (7.8)

By pole placing the wanted dynamics of the system can be found. To avoid asystem that is too fast the pole is placed at s = −0.3 which means that the tuningparameter KI is computed as

KIb1 = 0.3⇔ KI = 0.3b1

= −0.48.

If the similar is done for the ∆RACH model in Section 7.3.2 and the pole is placedin s = −0.2 the parameter KI is calculated to −0.03. If the PRACH configurationmodel in Section 7.3.3 is combined with the controller in (7.5) and the pole isplaced in s = −0.2 the parameter KI for the configuration controller is calculatedto −0.038. The placement of the poles for the ∆RACH controller and the con-figuration controller can be motivated by the working intervals for ∆RACH andthe PRACH configuration. They are both highly discretized and have short work-ing intervals and a too fast controller could therefore make the system unstable.Therefore the poles for the ∆RACH controller and the configuration controller areplaced closer to the origin than for the P0_RACH controller.


7.4.2 Double-Percentile ControllerAs the name suggests this controller has two percentiles as reference. The thoughtbehind this concept is that by specifying the reference for two percentiles it makesit easier for the operator. Thus the percentile that requires the highest valuesof the control parameters will have higher priority than the other percentile. Thecontroller can be seen in Figure 7.10. From the experiment in Section 4.2.2 it couldbe seen that ∆RACH affects the higher percentiles more than the lower percentiles.This controller is therefore designed to control a lower percentile with P0_RACHand a higher percentile with ∆RACH , i.e., rPerc1 < rPerc2. What is lost in rangeof possible AD values from not using both control parameters together is gainedwith the possibility to use two percentiles as reference.

rPerc1

rPerc2RACH

FP0_RACH RACH

AD

P0_RACH

-

-

ΔRACHFΔRACH

Alarm

Figure 7.10. Double-Percentile Controller

The controllers in Figure 7.10 operate separately from each other. This meansthat the effect from one controller will be seen as a disturbance by the other.Because of this the controllers operate with different sample times. The controllerfor P0_RACH operates faster than the controller for ∆RACH . The controllersFP0_RACH

and F∆RACHare the same as described in Section 7.4.1. Outside of

these two controllers is a PUSCH controller that controls the assigned RBs forPUSCH by altering the PRACH configuration. The PUSCH controller is describedin Section 7.4.5.

The dotted line in Figure 7.10 named Alarm is a communication possibility forthe controllers to raise an alarm if their measured AD percentile is higher thantheir reference and their control signal has reached its limit. If, for example,P0_RACH = −120 dBW and the measured AD percentile is higher than rPerc1,than the controller FP0_RACH

will send an alarm to the controller F∆RACH. This

will cause F∆RACHto increase ∆RACH with 2 dB if possible. If rPerc1 still cannot

be reached then ∆RACH is increased with another 2 dB and so on. The controllerF∆RACH

has a timer that starts when the alarm from FP0_RACHis received. When

this timer expires F∆RACHwill return to its normal controlling of the second

percentile. If both P0_RACH and ∆RACH have reached their highest limit andone of the target rPerc1 or rPerc2 still cannot be reached an alarm will be sent to


the PUSCH controller that causes the PUSCH controller to increase the PRACHconfiguration.

7.4.3 Mid-Range Controller 1

In a control problem where two different control signals affect the same processvariable it can sometimes be interesting to use a mid-range controller. Especially ifthe two control signals have different working ranges. The control signal with thesmallest working range can then be used to control the process variable and thecontrol signal with the larger working range can be used to keep the first controlsignal in the middle of its working area. The mid-range controller used in this casecan be seen in Figure 7.11. The reason why this structure has been chosen, is thatboth PRACH configuration and P0_RACH is used to control the AD. This leads toa wider range of possible values for AD. Another reason is that the working pointof the PRACH configuration can be controlled by an external PUSCH controller,see Section 7.4.5.

FConfig

rConfig

rADRACH

FP0_RACH RACH

AD

Config

P0_RACH

-

-

Fffu1

u2

u1,ff

Figure 7.11. Mid-Range Controller 1

In Figure 7.11 the PRACH configuration is used to control one percentile of ADand P0_RACH is used to keep the PRACH configuration in its working area. Thereference to the PRACH configuration controller is thus the wanted AD and thereference to the P0_RACH controller is the wanted working point for the PRACHconfiguration. An internal feed-forward connection is also included to keep thePRACH configuration from varying to much. The expression for the feed-forwardcontrol, named Fff in the figure, is expressed as

u1,ff (kT ) = u1(kT ) +Kff

(u2(kT − T )− u2(kT )

)(7.9)

where u1,ff , u1 and u2 is the signal as they are defined in Figure 7.11. The tuningparameter Kff in (7.9) represents the gain of the feed-forward connection. Thecontrol parameter ∆RACH is not used in this structure and thus set to a fix value.The controller used in the boxes FP0_RACH

and FConfig is the same as describedin Section 7.4.1.


7.4.4 Mid-Range Controller 2To use all three control parameters the mid-range controller from Section 7.4.3has be modified to the one that can be seen in Figure 7.12. As for mid-rangecontroller 1 a wider range of values for AD is reached by using all three controlparameters. The reference for the PRACH configuration, rConfig, can also here becontrolled by an external PUSCH controller, see Section 7.4.5. From the experi-ment in Section 4.2.2 it could be noticed that the range for AD varies with different∆RACH . Still the lowest possible AD is the same for all ∆RACH . Therefore thereference for ∆RACH can be set to a value that gives the highest possible range ofAD. This would be equivalent to ∆RACH = 0 dB, but this is not a wanted valuebecause of the high AD at low values of P0_RACH . ∆RACH = 2dB is a good valuefor ∆RACH , which also gives a wide range but not too high values on AD.

FConfig

rConfig

rADRACH

FP0_RACH RACH

AD

Config

P0_RACH

-

-

FΔRACH ΔRACH

ΔRACHr

RACH-

Fff

Fff

Figure 7.12. Mid-Range Controller 2

This controller has three levels where the first one is PRACH configuration, whichis used to control AD. The second level is ∆RACH which is then used to controlthe working point of the PRACH configuration. Level three is P0_RACH , and isused to control the working point of ∆RACH . As can be seen in Figure 7.12 twointernal feed-forward connections have been included in this mid-range controlleras well. The feed-forward control in the Fff boxes use the same expression as in(7.9). Here u1 is the control signal from the same level as the Fff box and u2 is thecontrol signal from the level above. The controller used in the boxes FP0_RACH

,F∆RACH

and FConfig is the same as described in Section 7.4.1.

If both ∆RACH and P0_RACH are at their limits an alarm will be raised. If thishappens the configuration target, rConfig will be raised one level. After a certaintime the rConfig will be reset and once again controlled by the PUSCH controller.

7.4.5 PUSCH ControllerEven if the main purpose of this thesis is to control the AD of the random accessprocedure, it is still important not to forget that the PRACH and the PUSCH


share resources. This means that if PUSCH needs a lot of resources, it is wantedto change the PRACH configuration to a configuration with a longer opportunityperiod, TconfP . For this purpose a PUSCH controller is used. The concept of thecontroller can be seen in Figure 7.13. The PUSCH controller is used differentlyfor the controllers described above. For the double-percentile controller in Sec-tion 7.4.2 the signal u in Figure 7.13 represents the PRACH configuration and forthe mid-range controllers in Section 7.4.3 and Section 7.4.4 u represents the targetconfiguration, rConfig.

- GRBavailable

uRBneeded

FPUSCH

Figure 7.13. PUSCH Controller

If the number of resource blocks needed for PUSCH in average, RBneeded, ishigher than the resource blocks available, RBavailable, i.e., RBneeded > RBavailable,the PRACH configuration is decreased one step and opposite if RBneeded <RBavailable.

As mentioned in Section 7.4.2 and Section 7.4.4 the double-percentile controllerand the mid-range controller 2 have a connection between them and the PUSCHcontroller. If the PUSCH controller receives an alarm it will give away the controlto the controller who sent the alarm. After a certain time the PUSCH controllerautomatically takes back the control.

Since this report is focused on the random access procedure of LTE and notPUSCH, no complex controller is used. This is only meant to show how it ispossible to include a protection of the PUSCH resources when controlling the ADof the random access procedure.

7.5 Controller Experiments

To compare the controllers, described in Section 7.4, with each other they need tobe tested in experiments. These experiments are presented in this section.

It should be mentioned that not all of the controllers use the same sampling period,but a sampling period of 2 s is chosen as shortest. Compared to the results inChapter 6 the sampling period should be around 10 s to get a low RMSE. Ashorter sampling period is however chosen to speed up the simulations. To easeup the oscillations of the measured AD, a low-pass filtered version of the measured

7.5 Controller Experiments 81

AD is fed to the controllers. The filter is calculated as

yk = βxk + (1− β)yk−1

where y is the filtered signal and x is the measured signal. The parameter βdecides how much trust is put on the measured signal x and is calculated as

β = σyσx + σy

(7.10)

where σx is the estimated standard deviation of the AD reports during the lastsample and σy is the standard deviation from the previous filtered measurements.It is wanted that samples with many AD reports should be considered more reliablethan samples with few reports. In a sample where a change in AD is documentedwith many reports, σx will be small. If on the other hand a change in AD isdocumented with few reports, σx will be large. With a β as in (7.10), all sampleswhere σx ≤ σy will be considered as reliable samples. Only the measured AD isshown in the experiments below.

7.5.1 Simulation ScenarioThe scenario that has been simulated represents a wave of UEs wanting to senddata and connect to the eNB. This means that PUSCH load and RACH load isincreased in steps and after some time decreased again. The scenario can be seenin Figure 7.14.

This scenario has been simulated for different references of AD and for differentinter-site distances (ISDs). It should be noted that the loads shown in Figure 7.14are average values of the loads at each base station.

The performance specification for the experiments is specified with an AD per-centile and its target/reference like rAD =

[Percentile Target

]. For the double-

percentile controller this will be written as

rAD =[rPerc1rPerc2

]=[Percentile1 Target1Percentile2 Target2

].

This means that with a demand of P (AD < 30ms) = 0.5 and P (AD < 70ms) =0.99 the performance specification is written as

rAD =[

0.5 300.99 70

].

7.5.2 Experiment: Double-Percentile ControllerThe goal of this experiment is to evaluate the performance of the double-percentilecontroller. The scenario that was simulated can be seen in Figure 7.14 and thesetup of the experiment can be seen in Table 7.4 and Table 7.5. The double-percentile controller described in Section 7.4.2 was combined with the PUSCH-controller described in Section 7.4.5 to get a controller sensitive to the needs of


0 50 100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

1

Load

PU

SC

H

Time (s)

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

Load

RA

CH (

prea

mbl

es/s

/cel

l)

Time (s)

Figure 7.14. Simulation scenario where the PUSCH load and the RACH load arealtered.

PUSCH as well. In this experiment a PUSCH-controller was used, that changedthe PRACH configuration directly. Three different sampling periods were used,one for each controller. This enables the controller with shorter sampling periodsto react on any changes made in the other controller. Only two of the nine simu-lations are presented here. The results of the other simulations are similar to theones presented.

Table 7.4. Setup of double-percentile controller experiment.

Parameter ValueInter-site Distance 500, 1700, 5000m

rAD

[0.5 300.99 70

],[0.5 300.5 30

],[0.5 300.8 40

]Sampling Period TP0_RACH

2 sSampling Period T∆RACH

4 sSampling Period TConfig 8 sRACH Format 0M 50ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesSimulation Time 500 sChannel Bandwidth 15 resource blocks = 2.7MHz


Table 7.5. Setup of double-percentile tuning parameters

Parameter FP0_RACHF∆RACH

KI -0.4 -0.02

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50

100

150

AD

(m

s)

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3,4,5

6,7,8

9,10,11

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14

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AC

H C

onfig

urat

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−140

−130

−120

P0_

RA

CH (

dBW

)

50 100 150 200 250 300 350 400 450 5000

2

4

6

∆ RA

CH (

dB)

Time (s)

50th percentile99th percentileTarget

Figure 7.15. Simulation with double-Percentile controller for an inter-site distance of

500m and with rAD =[

0.5 300.99 70

].

In Figure 7.15 the simulation with ISD 500m and rAD =[

0.5 300.99 70

]can be seen.

Some of the parts in the figure might need a bit of explanation. For the first100 seconds really low ADs are received, even though P0_RACH and ∆RACH areat their lowest values (-150 dBW and 0 dB). This is explained by the PRACHconfiguration during this time, i.e., since the PUSCH load is low the PRACH con-figuration with the shortest TconfP can be used. This is PRACH configuration


50 100 150 200 250 300 350 400 450 50020

30

40

50

60A

D (

ms)

50 100 150 200 250 300 350 400 450 5000,1,2

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AC

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50 100 150 200 250 300 350 400 450 500−150

−140

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P0_

RA

CH (

dBW

)

50 100 150 200 250 300 350 400 450 5000

2

4

6

∆ RA

CH (

dB)

Time (s)

50th percentile80th percentileTarget

Figure 7.16. Simulation with double-Percentile controller for an inter-site distance of

5000m and with rAD =[

0.5 300.80 40

].

{14} which implies that there is a RA opportunity at every subframe. This affectsthe AD in two ways. Firstly the AD will be shorter because the UEs do not haveto wait for the next RA opportunity. Secondly when all eNBs in the network useconfiguration {14} there will be no or very little uplink inter-cell interference thatcan affect the AD negatively. This explains why the AD is so low during the first100 seconds. As soon as the PRACH configuration, at 100 s, changes from {14}to {12, 13} a sudden high increase in AD is seen.

At 150 s the PUSCH load increases to 1, which can be seen in Figure 7.14. Thishas the affect that the PRACH configuration is decreased to {0, 1, 2}. After thisthe two controllers have difficulties to reach their targets. This will cause them totake help from the PRACH configuration, which explains why the PRACH con-


15 20 25 30 35 4020

30

40

50

60

70

80

90

100

Time (s)

AD

(m

s)

50th percentile99th percentile

Figure 7.17. Step response from double-Percentile controller for an inter-site distanceof 500m controlling the 50th and the 99th percentile.

figuration is increased one step at 200 s and one more step at around 225 s, seeSection 7.4.2 and Section 7.4.5. In this experiment the PUSCH controller waitsaround 40 s before it takes back the control of the configuration. This can be seenin Figure 7.15 at around 240 s where the PRACH configuration decreases.

During the time when the PRACH configuration is in the interval [{3, 4, 5}, {12, 13}],it can be noticed that the targets are held with relative small variations onP0_RACH and ∆RACH . Since only an integrator part is used for both controllersit can be expected that the control signal varies a bit.

As a comparison, the simulation with rAD =[

0.5 300.80 40

]and an ISD of 5000m

can be seen in Figure 7.16. One can see here that the power control parametersare low during the whole simulation except when the PUSCH load is close to 1and the PRACH configuration is {0, 1, 2}. In this simulation it is even more clearthat the P0_RACH and ∆RACH controllers cannot reach their target, starting ataround 175 s, and thus take help from the PRACH configuration at 225 s. Whenthe PRACH configuration is increased at 225 s one can see a great decrease inP0_RACH , which can be explained by the fact that the ISD is 5000m. This hasthe effect that the uplink inter-cell interference between the eNBs will be lowerthan ISD = 500m even if the PUSCH load is high and the AP for low values ofP0_RACH is therefore almost as high as for high values of P0_RACH .

Step Response

A step response of the double-percentile controller can be seen in Figure 7.17.From this some commonly used KPMs can be calculated. The rise time, Tr is


around 2.5 s for the 50th percentile and around 4 s for the 99th percentile. Theovershoot, AM can be found as 90% for the 50th percentile and 33% for the99th percentile. Because of a high uncertainty in the measurements of AD, themeasurements of Tr and AM can vary a lot between different step responses. Thismeans that the values here cannot be seen as the true values of Tr and AM , butmore as an estimation. The high uncertainty in the measurements of AD is alsothe reason why the settling time cannot be measured. Even if the results fromthis step resonse are not exact, still the step response shows the trend of what toexpect from the controller.

Conclusion

The conclusion of this experiment is that the double-percentile controller togetherwith the PUSCH-controller performes well. The targets for the AD are followedas wanted. Because of the opportunity to specify the target of two percentiles theoperator gets a more detailed insight in how well the random access procedure iscarried out. Both a mean and a sort of maximum in AD can be controlled. Thecalculated KPMs from the step resonse might seem high, especially AM , but onemust keep in mind that with the short sample interval of 2 s the measurements ofAD will have a RMSE around 5ms, see Chapter 6.

To improve the performance of the double-percentile controller one method wouldbe to work on the cooperation between the control of AD and the control ofresources for PUSCH. For example, the order of control can be switched, so thePUSCH would only be assigned more resources if a higher PRACH configurationis not needed to reach the AD target. That is the PUSCH control is started by theP0_RACH and the ∆RACH controller when no increases in P0_RACH and ∆RACH

have been done for a certain time and P0_RACH and ∆RACH are saturated.

7.5.3 Experiment: Mid-Range Controller 1The goal of this experiment is to study and evaluate the performance of the mid-range controller 1. The structure of the mid-range controller 1 can be seen inSection 7.4.3. This controller was combined with the PUSCH-controller in Sec-tion 7.4.5. The PUSCH-controller was set to control the target configuration,rConfig. In this experiment, only one sampling period was used. Since the con-trollers are connected with output to input it is difficult to use different samplingperiods for the two controllers. In Table 7.6 and Table 7.7 the setup of this exper-iment is seen.

In Figure 7.14 the scenario that was simulated is seen. The results from the sim-ulation where the ISD was 500m and rAD =

[0.80 40

]is seen in Figure 7.18. In

general the AD follows its target, even if it oscillates quite a lot. However with anI-controller this is normal and the average AD is close to the target of 40ms.

During the first 100 s the PUSCH load is low enough for the PUSCH-controller tokeep rConfig at PRACH configuration {14}. Because of this P0_RACH is set to its


Table 7.6. Setup of mid-range controller 1 experiment.

Parameter ValueInter-site Distance 500, 1700, 5000mrAD

[0.80 40

],[0.5 30

],[0.99 70

]Sampling Period T 2 s∆RACH 2 dBRACH Format 0M 50ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesChannel Bandwidth 15 resource blocks = 2.7MHzSimulation Time 500 s

Table 7.7. Setup of mid-range 1 tuning parameters

Parameter FConfig FP0_RACH

KI -0.04 -1Kff 0.25 n/a

lowest value (-150 dBW) to drive the PRACH configuration up towards the valueof rConfig. Since the PRACH configuration controller only is focused on reachingthe AD target the PRACH configuration will only be set to rConfig if the ADtarget is reachable with this configuration. In the time interval from 120 s until150 s one part is seen where the PRACH configuration is held at its reference.

One interesting thing to notice in Figure 7.18 is that the AD is relatively low thefirst 50 s even if P0_RACH = −150 dBW and the PRACH configuration is under{6, 7, 8}. This is explained by the low PUSCH load during this time. The PUSCHload has an average of 0.1 during this time and this has the effect that the PUSCHgenerates very low uplink inter-cell interference. A low interference enables theUEs to get access using a low P0_RACH .

The other simulations had similar results to the simulation with rAD =[0.80 40

].

As a comparison one other simulation is discussed here, seen in Figure 7.19. Thissimulation was done with ISD = 5000m and rAD =

[0.99 70

]. In general the

AD follows its target well except for some high peaks with ADs over 100ms, butthe interesting thing to notice here is the difference in the cooperation betweenPRACH configuration and P0_RACH in this simulation and in the one above,seen in Figure 7.18. In Figure 7.19 the configuration oscillates much more andP0_RACH has either the value -150 dBW or -120 dBW. Since this simulation wasdone with an ISD of 5000m the uplink inter-cell interference is much lower thanwith an ISD of 500m. For this reason the altering of P0_RACH has less effect onAD, thus forcing the control of the PRACH configuration to step in.


50 100 150 200 250 300 350 400 450 50030

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50

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80A

D (

ms)

50 100 150 200 250 300 350 400 450 5000,1,2

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H C

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−140

−130

−120

P0_

RA

CH (

dBW

)

50 100 150 200 250 300 350 400 450 5000,1,2

3,4,5

6,7,8

9,10,11

12,13

14

r Con

fig

Time (s)

80th percentileTarget

Figure 7.18. Simulation with mid-range controller 1 for an inter-site distance of 500mand with rAD =

[0.80 40

].

Step Response

The step response of the mide-range controller 1 can be seen in Figure 7.20. Fromthis, a Tr of about 8 s and a AM of 40% can be found. Due to a low precision causedby the short sampling period these values can not be seen as exact values. Becauseof this it is also not possible to find the settling time of the step response. Thestep-response can however be seen as a indication of how the controller performswith regard to speed and overshoot.

Conclusion

The conclusion of this experiment is that mid-range controller 1 in general performswell. The AD is kept around its target value except for some peaks that occurwhen the configuration is at {0, 1, 2}. Because the PUSCH-controller changes theconfiguration target, rConfig, a higher priority will be set on reaching the AD tar-get of the random access procedure than the priority of how many resource blocks


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

AD

(m

s)

50 100 150 200 250 300 350 400 450 5000,1,2

3,4,5

6,7,8

9,10,11

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14

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AC

H C

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50 100 150 200 250 300 350 400 450 500−150

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P0_

RA

CH (

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)

50 100 150 200 250 300 350 400 450 5000,1,2

3,4,5

6,7,8

9,10,11

12,13

14

r Con

fig

Time (s)



[0.99 70

].

are assigned to PUSCH. This can be compared to the double-percentile controllerin Section 7.5.2, where the needs of PUSCH has a higher priority than to reachthe AD target. In the step response a Tr could be found that is almost 4 timesas long as the Tr for the double-percentile controller. Because of the feed-forwardconnection in the mid-range controller this controller is a bit slower, since mostof the controlling is done using P0_RACH . The amount of feed-forward can becontrolled by changing the tuning parameter Kff .

The main disadvantage of the mid-range controller 1 is that the control parameter∆RACH is not used. Using ∆RACH would allow for a wider range of possible valuesfor AD, but would also increase the complexity of the controller. Another way touse ∆RACH is to control a second percentile, like is done for the double-percentilecontroller. It should also be noted that KI for P0_RACH and Kff for the config-uration in this controller has been derived manually and not using modelling andpole placement. The complexity of the controller makes a theoretical derivation of


5 10 15 20 25 30 35 4022

24

26

28

30

32

34

36

38

40

Time (s)

AD

(m

s)

50th percentile

Figure 7.20. Step response from mid-range controller 1 for an inter-site distance of5000m controlling the 50th percentile.

KI and Kff problematic and modelling and pole placement of the system wouldbe too time consuming and was therefore not done.

7.5.4 Experiment: Mid-Range Controller 2The goal of this experiment is to study the performance of the mid-range con-troller 2, described in Section 7.4.4. As in the other experiments the scenarioin Section 7.5.1 has been run. The PUSCH-controller from Section 7.4.5 hasbeen used to control the configuration target, rConfig, and the target for ∆RACH ,r∆RACH

, was fixed during the whole experiment. As in the experiment for mid-range controller 1 only one sampling period has been used. The setup of theexperiment is seen in tables 7.8 and 7.9.

Table 7.8. Setup of mid-range controller 2 experiment.

Parameter ValueInter-site Distance 500, 5000mrAD

[0.80 40

],[0.99 70

]r∆RACH

2 dBSampling Period T 2 sRACH Format 0M 50ra-ResponseWindowSize 5 subframesmac-ContentionResolutionTimer 24 subframesChannel Bandwidth 15 resource blocks = 2.7MHzSimulation Time 500 s


Table 7.9. Setup of mid-range 2 tuning parameters

Parameter FConfig F∆RACHFP0_RACH

KI -0.04 -1 -3Kff 0.25 0.5 n/a

The results from the simulation with rAD =[0.80 40

]and an ISD of 500m can

be seen in Figure 7.21. As can be noticed does the control signals ∆RACH andP0_RACH oscillate a lot. Despite this is the AD held around its target. The reasonfor the oscillating control signals is badly set tuning parameters. First of all, KI

for P0_RACH should be closer to zero. Secondly is Kff for ∆RACH to high. If∆RACH differs from its target, r∆RACH

, it will have the effect that P0_RACH willtry and compensate. Due to the large KI for P0_RACH , the compensation madeby P0_RACH will be relative large. The compensation from P0_RACH will be fedforward to ∆RACH where the badly set Kff will result in an over compensationon ∆RACH . Therefore ∆RACH and P0_RACH will force themselves into an oscil-lation. This can be seen clearly in Figure 7.21(a) in the time interval from 100 to175 s. After this P0_RACH reaches its maximum thus allowing the oscillation tostop.

If rConfig in Figure 7.21(b) and Figure 7.18 are compared in the time intervals0-100 s, 200-300 s and 375-500 s, one can see that the two figures are not equal. Inmid-range controller 2 there is an alarm function included which takes over thecontrol of rConfig if both ∆RACH and P0_RACH are at their maximum or mini-mum values. The PRACH configuration target is therefore altered to compensatefor this.

Conclusion

The conclusion of this experiment is that the mid-range controller 2 performspoorly. Even if the AD is held around its target the control signal ∆RACH andP0_RACH oscillates to much. The reason for this are bad tuning parameters. Ifmore time and effort were spent on optimizing the tuning parameters a betterresult might be reached. The complexity of the controller makes this however atime consuming task and the gain would be relatively low. This type of controllercan be difficult to tune since an extensive modelling would probably be necessary,to find good tuning parameters. Another reason not to continue with this controlleris that the mid-range controller 2 only controls one percentile, whereas the double-percentile controller controls two percentiles and the mid-range conntroller 1 canbe extended to control two percentiles.

Due to the bad performance of the mid-range controller 2 fewer simulations weremade and no step response was done. No additional results were found in theother simulations and as such they will not be presented here.


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P0_

RA

CH (

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)

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4

6

∆ RA

CH (

dB)

Time (s)


(a) AD and control signals.

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6,7,8

9,10,11

12,13

14

r Con

fig

Time (s)

(b) PRACH configuration target, rConfig .


[0.80 40

].

7.6 Conclusion 93

7.6 ConclusionThe results from the sections above have shown that it is possible to control theAD around a wanted target. The performace for the double-percentile controllerand the mid-range controller 1 was good. Both controllers manage to keep theAD around its target without exposing the control signals to too much stress.Except from the fact that two percentiles are controlled by the double-percentilecontroller and only one with the mid-range controller 1 the greatest differencesbetween the two are seen in the beginning and in the end of the simulations inFigure 7.15 and Figure 7.18. In Figure 7.15 the AD is really low during the first100 s and the last 100 s. The reason for this is the short configuration period usedduring this time. The focus of the double-percentile controller is to always providePUSCH with the resources it needs and this is done by explicitly changing thePRACH configuration. With the mid-range controller 1 the needs for PUSCH arecontrolled by implicitly changing the PRACH configuration through rConfig. Assuch the priority of the mid-range controller 1 lies more on the AD which can beseen during the first 100 s and the last 100 s in Figure 7.18.

The possibility of controlling two percentiles is probably the strongest feature ofthe double-percentile controller. This provides one more level of control since boththe average and the upper boundary of AD can be controlled. This is also thegreatest disadvantage of the mid-range controller 1. It is however possible to up-grade the mid-range controller 1 with an external control loop where a secondpercentile is controlled by ∆RACH . From the step responses in Figure 7.17 andFigure 7.20 it could be seen that the mid-range controller 1 is slower than thedouble-percentile controller.

The results from the experiment with the mid-range controller 2 were not as sat-isfactory as for the other two controllers. It could however be possible to improvethese results by finding better tuning parameters. Due to lack of time and extraeffort it would take to derive these tuning parameters properly, it was not done. Awell tuned mid-range controller 2 would probably not have a much better perfor-mance than the other two controller in this thesis which was also another factorwhy the mid-range controller 2 was not further developed.

Chapter 8

Summary and Future Work

The first part of this thesis was a discussion about access delay and the goalswere to study the controllability and observability of AD. The controllability ex-periments were done with regard to P0_RACH , ∆RACH , PRACH configuration,PUSCH load and RACH load and they showed that AD is controllable. The ex-periments with regard to P0_RACH , ∆RACH and the PRACH configuration gavethe most important results since these parameters are possible control parameters.These experiments also showed that P0_RACH had the greatest influence on ADwhereas the PRACH configuration had the least influence on AD. The influencefrom ∆RACH were high for the 80th percentile and above and low for the 50thpercentile and below.

In the observability experiments three different observers were studied by simu-lating different scenarios. The observers can be ordered by complexity with ob-server 1 being the least complex and observer 3 the most complex. From theseexperiments it was shown that observer 3 had the best results. On second placecame observer 2 with results almost as good as the results from observer 3. Theresults from observer 1 were by far the worst, since it could only estimate AD wellif few access attempts were needed by the UEs. If the accuracy of the estimatesare of absolute importance observer 3 should be used. Observer 3 does howeverrequire measurements to be done in the base station which also requires that thereare enough free processing opportunities to make these measurements. This meansthat if the little extra accuracy delivered by observer 3 is not needed observer 2 isto recommend.

In the study of access delay it was assumed that the backoff parameter, B wasalways set to zero. The second goal of this thesis was to investigate how the ob-servability of AD was affected with B > 0 and if support for backoff was neededin the observer algorithm. It was shown that the observers performed well if theRACH load was high or if P0_RACH was high. At low RACH loads fewer UEsreceived the backoff parameter than was estimated. This lead to an overestimationof the AD in the eNB. If it is not known that the RACH load is constantly high it

95

96 Summary and Future Work

is not recommended to use the observer of AD when B > 0. If AD is wanted in aperformance specification and B > 0, then reports of the measured AD from theUEs are needed.

The third part of this thesis was to design one or more controllers to control theAD of the random access process. To do this, a study on how different samplingperiods affect the accuracy of the measured AD was first done. This study showedthat when using sampling periods from 20 s and above the RMSE of the AD, forpercentiles 99 and under, is under 5ms. The experiments also showed that if the99.9th percentile is measured it is very important to choose a sampling period highenough. In this experiment sampling periods above 300 s were needed to get anaccuracy under 5ms.

Three different controllers were tested in this thesis. One controller was designedto control two percentiles of AD, using P0_RACH and ∆RACH and using PRACHconfiguration to control resources needed by PUSCH. The other two controllerswere based on the mid-ranging technique to control one percentile of AD. Themid-range controller 1 used PRACH configuration and P0_RACH to control ADand the mid-range controller 2 used PRACH configuration, ∆RACH and P0_RACHto control AD. In the case of the two mid-range controllers the needs of PUSCHwere controlled by changing the reference of PRACH configuration. The con-trollers were tested in a scenario representing a wave of incoming UEs wantingto get access and send more data through the PUSCH. The experiments showthat the double-percentile controller and the mid-range controller 1 have the bestresults. Their performance were similar in the simulated scenario but the double-percentile controller showed somewhat better results in a step response. The mid-range controller 2 did not show any good results. The reason for this were badlyset tuning parameters. Due to the complexity of mid-range controller 2 and lackof time no effort was made to improve these constants. Both the double-percentilecontroller and the mid-range controller 1 performed well, but they have other dif-ferences that should be taken into consideration when choosing a controller. Thedouble-percentile controller can control two percentiles which gives the possibilityto control an average and a maximum AD at the same time. It also gives theneeds of PUSCH a higher priority than to reach the target AD. The mid-rangecontroller 1 cannot control two percentiles but it prioritises on the other hand toreach the target AD more, than the needs of PUSCH.

The main goal of this thesis was to see how well the random access procedure couldbe optimized with regard to access delay. It has been shown that it is possibleto optimize the random access procedure with regard to AD and by tuning theRACH parameters P0_RACH , ∆RACH and PRACH configuration an AD targetcan be reached.

8.1 Future Work 97

FConfig

rConfig

RACH

FP0_RACH RACHAD

Config

P0_RACH

-

-

Fff

rPerc2RACH

-ΔRACHFΔRACH

rPerc1

Figure 8.1. Example of how mid-range controller 1 can be extended with an extracontrol loop where ∆RACH is used to control a second percentile.

8.1 Future WorkDuring the work on this thesis there were parts that were not finished, eitherbecause there was not enough time or because of practical problems. Here followsa list of issues that can be studied further.

• Improve the estimations of AD when B > 0. This could for example bedone by running tests in a real base station and from these test derive anestimator for the RACH load. With a known RACH load it could be possibleto estimate AD in a better way. For example by not including backoff in theestimator if the RACH load is under a certain limit.

• Extend mid-range controller 1 to control two percentiles. By adding anexternal control loop where ∆RACH is used it could be possible to use thisloop to control one extra percentile, see Figure 8.1.

• Continue the work with optimizing the tuning parameters in mid-range con-troller 2, for example by modelling of how the outer loops affect the innerloops.

• Introduce self-tuning controllers. To avoid the problem of manually settingthe tuning parameters of the controllers self-tuning controllers can be used.This means that the controllers, during operation, optimize their own tuningparameters.

• Study other parts of the random access procedure to see how they affect theAD. As mentioned in Chapter 1, there are many different parameters thatcan be changed to affect the state of the random access procedure. Someparameters that could be interesting to study are for example:

– PRACH formatDetermine if UEs are power limited and change the PRACH formataccordingly.

98 Summary and Future Work

– Preamble splitStudy how the ratio between preambles dedicated for contention freeRA and for non-contention free RA affects AD.

Bibliography

[1] 3GPP TS 36.211. E-UTRA; Physical Channels and Modulation, (Release 8).

[2] 3GPP TS 36.213. E-UTRA; Physical layer procedures, (Release 8).

[3] 3GPP TS 36.300. E-UTRA and E-UTRAN; Overall description; stage 2,(Release 8).

[4] 3GPP TS 36.321. E-UTRA; Medium Access Control (MAC) protocol speci-fication, (Release 8).

[5] 3GPP TS 36.331. E-UTRA; Physical layer procedures, (Release 8).

[6] 3GPP TR 36.902. E-UTRAN; Self-configuring and self-optimizing networkuse cases and solutions, (Release 8).

[7] 3GPP. URL: http://www.3gpp.org, 1 September 2009.

[8] M. Amirijoo. Private communication.

[9] M. Amirijoo, P. Frenger, F. Gunnarsson, J. Moe, and K. Zetterberg. On Self-Optimization of the Random Access Procedure in 3G Long Term Evolution.Vehicular Technology Conference, 2009. VTC 2009-Spring, to appear, 2009.

[10] Y. Choi, S. Park, and S. Bahk. Multichannel Random Access in OFDMAWireless Networks. IEEE Journal on Selected Areas in Communication, Vol.24, No. 3, 2006.

[11] E. Dahlman, S. Parkvall, J. Sköld, and P. Beming. 3G Evolution. AcademicPress, second edition, 2008. ISBN 978-0-012-374538-5.

[12] S. Kim, Y. So, D. Hong, J. Kim, S. Moon, K. Lee, and S. Oh. Uplink Capac-ity Maximization based on Random Access Channel (RACH) Parameters inWCDMA. Vehicular Technology Conference, 2006. VTC 2006-Spring. IEEE63rd, 2006.

[13] I. Koo, S. Shin, and K. Kim. Performance Analysis of Random Access Chan-nel in OFDMA Systems. Procedings of the 2005 Systems Communications(ICW’05), 2005.

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100 Bibliography

[14] L. Ljung and T. Glad. Modellbygge och Simulering. Studentlitteratur, secondedition, 2004. ISBN 91-44-02443-6.

[15] Linköpings universitet Reglerteknik, ISY. Industriell reglerteknik, Kurskom-pendium. Bokab, 2008.

[16] J. Reig, O. López-Jiménez, L. Rubio, and N. Cardona. Random Access Chan-nel (RACH) Parameters Optimization in WCDMA Systems. IEEE 60th Ve-hicular Technology Conference, VTC2004-Fall, 2004.

[17] P. Zhou, H. Hu, H. Wang, and H. Chen. An Efficient Random Access Schemefor OFDMA Systems with Implicit Message Transmission. IEEE Transactionson Wireless Communications, Vol. 7, No. 7, 2008.

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Optimization of Random Access in 3G Long Term Evolution

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