papr analysis and simulation for 3gpp lte system

PAPR ANALYSIS AND SIMULATION FOR 3GPP

LTE SYSTEM

A B.Sc Engineering Thesis

by

S.M. Mahmud Hasan

Roll No: 074019

Department of Electronics and Telecommunication Engineering

RAJSHAHI UNIVERSITY OF ENGINEERING & TECHNOLOGY

September 2012

1

PAPR ANALYSIS AND SIMULATION FOR 3GPP LTE

by

S.M. Mahmud Hasan

Roll No.: 074019

A thesis submitted in partial fulfillment of the requirements for the degree of

BACHELOR OF SCIENCE

in

Electronics and Telecommunication Engineering

to the


RAJSHAHI UNIVERSITY OF ENGINEERING & TECHNOLOGY

September 2012

2

Declaration

This is to certify that the thesis work “PAPR Analysis and Simulation for 3GPP LTE

System” by S.M. Mahmud Hasan, bearing Roll no. 074019 has been carried out under my

supervision as a requirement for the degree of Bachelor of Science in Electronics and

Telecommunication Engineering.

Md. Munjure Mowla

Lecturer


Rajshahi University of Engineering & Technology

Rajshahi - 6204.

3

Acknowledgement

On the submission of my thesis report of “PAPR Analysis and Simulation for 3GPP LTE

System”, I would like to extend my gratitude and sincere thanks to my supervisor,

Md. Munjure Mowla, Lecturer, Department of Electronics and Telecommunication

Engineering for his constant inspiration and support during the course of my work in the last

one year. I truly appreciate and value his esteemed guidance and encouragement during

execution of thesis work from the beginning till end of this thesis. He has been great sources

of inspiration to me and I thank him also for imparting me immense knowledge in the field of

communication which made my work a lot easier. I am indebted to his for having helped me

in taking various problem statements and providing methods and techniques for the solution

of it. This thesis would have been difficult to accomplish without his continuous moral

support.

S.M. Mahmud Hasan

Roll No.- 074019

RUET, Rajshahi.

September 09, 2012.

4

Abstract

The highest bit rates in commercially deployed wireless systems are achieved by means of

Orthogonal Frequency Division Multiplexing (OFDM). The next advance in cellular systems,

under investigation by Third Generation Partnership Project (3GPP), also anticipates the

adoption of OFDMA to achieve high data rates. But a modified form of OFDMA i.e.

SCFDMA (Single Carrier FDMA) having similar throughput performance and essentially the

same complexity has been implemented as it has an edge over OFDMA having lower PAPR

(peak to average power ratio). SCFDMA is currently a strong candidate for the uplink

multiple access in the Long Term Evolution of cellular systems under consideration by the

3GPP.

In the thesis, Peak to Average Power Ratio (PAPR) analysis of OFDMA & SCFDMA with

different subcarrier mapping has been performed. Though SCFDMA had larger ISI it has

lower PAPR which help in avoiding the need of an efficient linear power amplifier. Various

modulation techniques and various parameters have been changed to compare the PAPR for

OFDMA & SCFDMA.

Many techniques have been studied for reducing the PAPR of a transmitted OFDM signal. In

general, in LTE the cost and complexity of generating the OFDM signal with acceptable

Error Vector Magnitude (EVM) is left to the eNodeB implementation. As OFDM is not used

for the LTE uplink, such considerations do not directly apply to the transmitter in the UE.

Techniques for PAPR reduction of OFDM signals can be broadly categorized into three main

concepts: Clipping and Filtering, Selected Mapping and Pre-coding Technique.

Clipping & Filtering technique has been introduced for PAPR reduction of OFDM signals.

The effects of high power amplifier and the channel noise on the OFDM signals have been

also analyzed and then introduced clipping & filtering as a PAPR reduction method to reduce

this effect. This technique consists of oversampling the original signal by padding the input

signal with zeros and processing it using a longer IFFT. The oversampled signal is clipped

and then filtered to reduce the out-of-band radiation.

5

Contents

Declaration

Acknowledgement 3

Abstract 4

Contents 5

List of Tables 10

List of Figures 10

Acronyms 13

CHAPTER 1: Introduction

1.1 Introduction 16

1.2 3rd

Generation Partnership Project 17

1.3 LTE in the Mobile Radio Landscape 18

1.4 Evolution of 4G 19

1.5 Requirements for Long Term Evolution 21

1.6 Multi Carrier Modulations 22

1.7 Objective of Thesis 22

1.8 Scope of Thesis 22

Chapter 2: LTE Network Architecture

2.1 Introduction 24

2.2 Overall Architectural Overview 24

2.2.1 The Core Network 26

2.2.1.1 Non-Access Stratum (NAS) Procedures 28

2.2.2 The Access Network 29

2

6

2.3 Roaming Architecture 31

2.4 Inter-Working with other Networks 32

2.5 Inter-Radio Access Technologies (RAT) Mobility 33

2.6 Connected Mode Inter-RAT Mobility 34

2.6.1 Handover to LTE 34

2.6.2 Mobility from LTE 34

Chapter 3: Physical Layer in the LTE Uplink

3.1 Introduction 36

3.2 LTE Uplink Requirements 36

3.3 SC-FDMA Principles 37

3.3.1 SC-FDMA Transmission Structure 37

3.3.2 Time-Domain Signal Generation 37

3.4 SC-FDMA Frame Structure 38

3.5 Uplink SC-FDMA Parameters 39

3.6 Modulation 40

3.7 Implementation of the SC-FDMA Transceiver 40

3.8 LTE Uplink physical channels 41

3.9 LTE uplink transport channels 41

Chapter 4: Physical layer in the LTE downlink

4.1 Introduction 42

4.2 LTE Downlink Requirements 42

4.3 OFDM Principles 43

4.3.1 Orthogonal Multiplexing Principle 43

4.3.2 Importance of Orthogonality 46

7

4.3.3 Guard Interval 48

4.4 OFDM Frame Structure 48

4.5 Downlink OFDM Parameters 49

4.6 Mapping of Subcarriers 50

4.7 Implementation of the OFDM Transceiver 51

4.7.1 Binary Source Generator 51

4.7.2 Modulation 51

4.8 Downlink Data Transmission 52

4.8.1 Modulation 52

4.8.2 Downlink Reference Signal Structure 52

4.8.3 Cell Search 54

4.9 Latency Requirement 54

Chapter 5: PAPR Calculation for SCFDMA & OFDMA

5.1 Introduction 55

5.2 SCFDMA 55

5.2.1 Block Diagram of SC-FDMA 57

5.3 OFDM 58

5.4 OFDMA 59

5.4.1 Block Diagram of OFDMA 61

5.5 Description of Problem Statement 62

5.6 Mathematical Calculation for PAPR 64

5.7 Comparison of PAPR for OFDMA and SCFDMA 65

5.8 Significance of Pulse Shaping Filter in PAPR Analysis 65

5.8.1 Sinc Filter 66

5.8.2 Raised Cosine Filter 67

8

5.8.3 Gaussian Filter 68

5.9 PAPR Reduction Techniques for OFDM signal 68

5.9.1 Clipping and Filtering 69

5.9.2 Selective Mapping 71

5.9.3 Pre-coding Technique 72

Chapter 6: Characteristics of Mobile Radio Channel

6.1 Introduction 73

6.2 Types of Fading 73

6.3 Small-scale Fading 74

6.4 Critical Channel Parameters 74

6.5 Types of Small-scale Fading

6.6 Rayleigh and Ricean Distribution

Chapter 7 Channel Estimation in OFDM

7.1 Introduction 78

7.2 Block type of Pilot Arrangement 79

7.3 Comb type of Pilot Arrangement 79

7.4 Working Environment 79

7.5 Mathematical Analysis of the Channel Estimators 80

7.5.1 Least Square Error (LS) Estimation 81

7.5.2 Minimum Mean Square Error (MMSE) Estimation 82

7.6 Modified MMSE Estimation 83

75

76

9

Chapter 8: Simulations & Results

8.1 OFDM Signal and its spectrum with Guard Interval 84

8.2 Comparison of PAPR for OFDMA and SCFDMA 85

8.3 Investigation of Clipping & Filtering method as PAPR

Reduction Technique for OFDM signals 92

Conclusion & Future Scope 99

Reference 100

Appendix A 102

Appendix B 107

Appendix C 113

10

List of Tables

Table No. Name of Table

3.1 Uplink parameters for SC-FDMA transmission 39

4.1 Downlink parameters for OFDM transmission 50

4.2 Normalization factor for M-QAM modulation

Schemes in E-UTRA downlink 52

List of Figures

Fig No. Name of Figure

1.1 Radio Access Network Milestones 17

1.2 Approximate timeline of the mobile communications standards

Landscape 19

2.1 The EPS network elements 25

2.2 Functional split between E-UTRAN and EPC 27

2.3 Overall E-UTRAN architecture 30

2.4 Roaming architecture for 3GPP accesses with P-GW in home

Network 32

2.5 Architecture for 3G UMTS interworking 33

2.6 Uplink S1 CDMA2000 tunneling procedure. 34

2.7 Mobility from LTE 35

3.1 SC-FDMA time-domain transmit processing 38

3.2 Generic frame structure (TDD or FDD) 38

3.3 Slot structure 39

3.4 Block diagram of the SC-FDMA transmitter in LTE 40

3.5 Block diagram of the SC-FDMA receiver in LTE 40

4.1 Serial-to-parallel conversion operations for OFDM 44

4.2 OFDM Transmitter 44

4.3 OFDM receiver 45

4.4 OFDM cyclic prefix insertion 45

4.5 Insertion of cyclic prefix 48

Page No.

Page No.

11

4.6 OFDM Frame structure in LTE. A radio frame is divided

Into 20 slots of 0.5 ms each having 6 or 7 OFDM symbols 49

4.7 Placement of occupied subcarriers 50

4.8 Block diagram of the OFDM transmitter in LTE 51

4.9 Block diagram of the OFDM receiver in LTE 51

4.10 The reference symbol structure for one slot with 6 OFDM

Symbols using two antennas 53

5.1 Difference between channel representations between OFDMA

And SCFDMA 56

5.2 Tx and Rx structure of SCFDMA (M > N) 57

5.3 Spectral efficiency of OFDM compared to classical multicarrier

Modulation:

(a) Classical multicarrier system spectrum 58

(b) OFDM system spectrum 58

5.4 Difference between OFDM and OFDMA 60

5.5 Sensitivity of OFDM subcarriers with Carrier 60

5.6 OFDM transmission spectrum 61

5.7 Block Diagram of OFDMA 62

5.8 Sub-carrier mapping for 3 users, 12 sub-carriers and 4 sub-carriers

Per user 63

5.9 PAPR distribution for different numbers of OFDM subcarriers 65

5.10 The Transfer Function of Sinc Filter 66

5.11 The Transfer Function of Raised Cosine Filter 67

5.12 The Transfer Function of Gaussian Filter 68

5.13 Simplified clipping and filtering with Optimum value of Υ 69

5.14 The clipping and frequency domain filtering of the input OFDM

Signal 70

5.15 Block diagram of SFBC-OFDM transmitter with two transmitters

Antennas and the selective mapping (SLM) method for PAPR

Reduction 71

5.16 Block diagram of pre-coding technique for PAPR reduction of

OFDM signal 72

6.1 Rayleigh fading channel with two path sine wave input 77

7.1 Two basic types of pilot arrangement for OFDM channel estimation 79

7.2 General estimator structure 80

7.3 SNR vs BER using LSE estimator for an OFDM channel 81

7.4 SNR vs MSE for an OFDM system with MMSE / LSE estimator 82

12

7.5 SNR vs SER for an OFDM system with MMSE / LSE estimator 83

8.1 OFDM signal and its spectrum with Guard Interval

(Graph on time domain) 84

8.2 OFDM signal and its spectrum with Guard Interval

(Graph on frequency domain) 84

8.3 CCDF of PAPR for OFDMA & SCFDMA (N=64, M=512)

With QPSK Modulation 85






With 16-QAM Modulation 88







8.10 Transmitted Data Phase Representation 92

8.11 The representation of the modulated signal (QPSK) 93

8.12 Unclipped OFDM signal 94

8.13 Clipped OFDM signal 94

8.14 Unclipped OFDM signal after passing through H.P.A 95

8.15 Clipped OFDM signal after passing through H.P.A 95

8.16 Comparison between Transmitted Data Phase Representation &

Received unclipped OFDM signal 96

8.17 Comparison between Transmitted Data Phase Representation &

Received clipped OFDM signal 97

13

Acronyms

1G First Generation

2G Second Generation

3G Third Generations

4G Fourth Generations

3GPP 3rd Generation Partnership Project

3GPP2 3rd Generation Partnership Project 2

AMPS Analogue Mobile Phone System

APN Access Point Name

ARIB Association of Radio Industries and Businesses

ATIS Alliance for Telecommunications Industry Solutions

AWGN Additive White Gaussian Noise

BER Bit Error Rate

BPSK Binary Phase Shift Keying

CCDF Complementary Cumulative Density Function

CCO Cell Change Order,

CCSA China Communications Standards Association

CDMA Code Division Multiple Access

CT Core Network & Terminals

CP cyclic prefix

DPSK Differential Phase Shift Keying

ECM-IDLE EPS Connection Management IDLE

EDGE Enhanced Data rates for GSM Evolution

eNodeB evolved NodeB

EPC Evolved Packet Core

EPS Evolved Packet System

ETSI European Telecommunications Standards Institute

E-UTRA Evolved UMTS Terrestrial Radio Access

FDM Frequency Division Multiplexing

FFT Fast Fourier Transform

GPRS General Packet Radio Service

GSM Global System for Mobile communications

14

GERAN GSM EDGE Radio Access Networks

HLR Home Location Register

HSPA High Speed Packet Access

HSS Home Subscriber Server

IDFT Inverse Discrete Fourier Transform

ITU International Telecommunication Union

ITU-R ITU Radio communication sector

IMT International Mobile Telecommunications

IP Internet Protocol

ISI Inter Symbol Interference

IMS IP Multimedia Subsystem

LSE Least Square Estimation

LMMSE Minimum Mean Square Estimation

LTE Long Term Evolution

MME Mobility Management Entity

MMSE Minimum Mean Square Estimation

Mod MMSE Modified Minimum Mean Square Estimation

MSE Mean Square Error

NAS Non-Access Stratum

NACC Network Assisted Cell Change

OS Orthogonal Sequence

OFDM Orthogonal Frequency Division Multiplexing

OFDMA Orthogonal Frequency Division Multiple Access

PAPR Peak to Average Power Ratio

PCRF Policy Control and Charging Rules Function

PSK Phase Shift Keying

P-GW PDN Gateway

PLMN Public Land Mobile Network

PMIP Proxy Mobile Internet Protocol

PRS Pseudo-random Sequence

PSCH Primary Synchronization Channel

QAM Quadrature Amplitude Modulation

QoS Quality-of-Service

QPSK Quadrature Phase Shift Keying

15

RAN Radio Access Networks

RAT Radio Access Technologies

SA Service & Systems Aspects

SINR Signal-to-Interference plus Noise Ratio

SAE System Architecture Evolution

S-GW Serving Gateway

S-TMSI SAE-Temporary Mobile Subscriber Identity

SC-FDMA Single Carrier-Frequency Division Multiple Access

SER Symbol Error Rate

SNR Signal to Noise Ratio

SSCH Secondary Synchronization Channel

TTA Telecommunications Technology Association

TTC Telecommunications Technology Committee

TSG Technical Specification Groups

TDMA Time Division Multiple Access

TD-SCDMA Time Division Synchronous Code Division Multiple Access

TFT Traffic Flow Templates

TTI Transmission Time Interval

TDD Time Division Duplex

UTRA Universal Terrestrial Radio Access

UTRAN Universal Terrestrial Radio Access Network

UMTS Universal Mobile Telecommunications System

VoIP Voice-over-IP

WAN Wide Area Network

WCDMA Wideband Code Division Multiple Access

WiMAX Worldwide interoperability for Microwave Access

16

Chapter 1

Introduction

1.1 Introduction:

LTE (Long Term Evolution), marketed as 3.9G LTE, is a standard for wireless

communication of high-speed data for mobile phones and data terminals. It is based on the

GSM/EDGE and UMTS/HSPA network technologies, increasing the capacity and speed

using new modulation techniques. The standard is developed by the 3GPP (3rd Generation

Partnership Project) and is specified in its Release 8 document series, with minor

enhancements described in Release 9 [1].

LTE is a wireless broadband technology designed to support roaming Internet access via cell

phones and handheld devices. Because LTE offers significant improvements over older

cellular communication standards, some refer to it as a 4G (fourth generation) technology

along with WiMAX [2]. is considered by many to be the obvious successor to the current

generation of UMTS 3G technology, which is based upon WCDMA, HSDPA, HSUPA, and

HSPA. LTE is not a replacement for UMTS in the way that UMTS was a replacement for

GSM, but rather an update to the UMTS technology that will enable it to provide

significantly faster data rates for both uploading and downloading [3]. It is anticipated to

become the first truly global mobile phone standard, although the use of different frequency

bands in different countries will mean that only multi-band phones will be able to utilize LTE

in all countries where it is supported.

Although marketed as a 4G wireless service, LTE as specified in the 3GPP Release 8 and 9

document series does not satisfy the technical requirements the 3GPP consortium has adopted

for its new standard generation, and which are set forth by the ITU-R organization in its IMT-

Advanced specification [1].

17

1.2 3rd

Generation Partnership Project:

The 3rd

Generation Partnership Project (3GPP) unites Six telecommunications standard

development organizations (ARIB, ATIS, CCSA, ETSI, TTA, TTC), known as

“Organizational Partners” and provides their members with a stable environment to produce

the highly successful Reports and Specifications that define 3GPP technologies.

The Four Technical Specification Groups (TSG) in 3GPP are Radio Access Networks

(RAN), Service & Systems Aspects (SA), Core Network & Terminals (CT) and GSM EDGE

Radio Access Networks (GERAN).

Timeline (Year)

1999 2000 01 02 03 04 05 06 07 08 09 10 11 2012

Release 99

Release 4

Release 5

Release 6

Release 7

Release 8

Release 9

Release 10

Release 11+

Fig 1.1: Radio Access Network Milestones.

W-CDMA

1.28Mbps

TDD

HSDPA

HSUPA,

MBMS

HSPA+

(MIMO, HOM, etc )

LTE

LTE

enhancements

LTE –A

Further

LTE enhancements

18

Each of the four TSGs has a set of Working Groups, which meet regularly four to six times a

year. Each TSG has its own quarterly plenary meeting where the work from its WGs is

presented for information, discussion and approval. Each TSG has a particular area of

responsibility for the Reports and Specifications within its own Terms of Reference.

3GPP Technical Specification Group RAN, like other TSGs, ensures that systems based on

3GPP specifications are capable of rapid development and deployment with the provision of

global roaming of equipment. Some of the headline 3GPP radio technologies and systems

over the recent Releases [4] have been shown in the above Fig 1.1.

1.3 LTE in the Mobile Radio Landscape:

The complementary functions of the regulatory authorities and the standardization

organizations can be summarized broadly by the following relationship [5] :

Aggregated Data Rate = Bandwidth × Spectral efficiency

(Regulation & Licenses) (Technology & Standards)

From the technology and standards angle, there are currently three main organizations

responsible for developing the standards meeting IMT requirements, and which are

continuing to shape the landscape of mobile radio systems, as shown in Fig 1.2.

19

Approximate Timeline:

1995 2000 2010 2015

Fig 1.2: Approximate timeline of the mobile communications standards landscape.

1.4 Evolution of 4G:

The evolution of 4G from 1G is described below [6]-[10]:

1G (early 1980s):

- Analog speech communication

- Analog FDMA/FDD

- Ex-AMPS standard by Bell Labs

2G 3G 4G

EDGE

3GPP

GSM

GPRS

TD-SCDMA (China)

HSPA+ R8 HSPA+R7 HSUPA HSDPA UMTS

TDD

FDD

LTE LTE

advanced

IEEE

802.16 e

“mobile WiMAX”

802.16 m 802.16 2004

“fixed WiMAX”

3GPP2

CDMA

2000 IS - 95 CDMA

EVDO

CDMA

EVDO Rev A

CDMA

EVDO Rev B

UMB

TDMA/

FDMA

CDMA

OFDM

EDGE

20

2G (early 1990s):

- Digital speech communication

- Handoff, more secure communication

- TDMA and CDMA schemes

- Ex-Four major standards

- GSM

- IS-136/IS-54 NADC, PDC(Japan)

- IS-95 cdmaOne

2.5G (mid 1990s):

- Improvement of data rate

- Up-gradation of 2G

- Ex-HSCSD, GPRS, EDGE (from GSM)

IS-95B (from cdmaOne)

3G (late 1990s):

- A global standard for communication

- High data rate

- Ex-WCDMA (UMTS), cdma2000, TD-SCDMA

4G (mid 2000s):

- Based on an all-IP packet switched network.

- Peak data rates of up to approximately 100 Mbit/s for high mobility such as mobile access

and up to approximately 1 Gbit/s for low mobility such as nomadic/local wireless access.

- Dynamically share and use the network resources to support more simultaneous users per

cell.

- Scalable channel bandwidth 5–20 MHz, optionally up to 40 MHz.

- Peak link spectral efficiency of 15 bit/s/Hz in the downlink, and 6.75 bit/s/Hz in the uplink

(meaning that 1 Gbit/s in the downlink should be possible over less than 67 MHz band-

width).

- System spectral efficiency of up to 3 bit/s/Hz/cell in the downlink and 2.25 bit/s/Hz/cell

for indoor usage.

- Smooth handovers across heterogeneous networks.

- Ability to offer high quality of service for next generation multimedia support.

21

- Ex- LTE Advanced standardized by the 3GPP and 802.16m standardized by the IEEE

(i.e - WiMAX)

1.5 Requirements for Long Term Evolution:

The requirements for LTE were re-defined and crystallized, being finalized in June 2005.

They can be summarized as follows [5]:

• Reduced delays, in terms of both connection establishment and transmission latency.

• Increased user data rates.

• Increased cell-edge bit-rate, for uniformity of service provision.

• Reduced cost per bit, implying improved spectral efficiency.

• Greater flexibility of spectrum usage, in both new and pre-existing bands.

• Simplified network architecture.

• Seamless mobility, including between different radio-access technologies.

• Reasonable power consumption for the mobile terminal.

The 3GPP LTE (Long Term Evolution) was a recent standard introduced by 3GPP group

which promises high-speed data, multimedia unicast and multimedia broadcast services. The

Specifications [8]-[10] include the following:

Multiple Access Schemes:

DL: OFDMA with CP

UL: SCFDMA with CP

Modulation:

UL/DL: QPSK, 16QAM, 64QAM

Coding:

Convolution code, Rel-6 Turbo code.

22

1.6 Multi Carrier Modulations:

Unlike single carrier systems, OFDM communication systems do not rely on increased

symbol rates in order to achieve higher data rates. OFDM is a multicarrier digital modulation

scheme. OFDM systems break the available bandwidth into many narrower sub-carriers and

transmit the data in parallel streams. Each subcarrier is modulated using varying levels of

QAM modulation, e.g. QPSK, QAM, 64QAM or possibly higher orders depending on signal

quality. Each OFDM symbol is therefore a linear combination of the instantaneous signals on

each of the sub-carriers in the channel .This scheme facilitates efficient use of bandwidth and

reduced Inter Symbol Interference (ISI). But another problem is high Peak to Average Power

Ratio (PAPR) OFDM symbols .To counter this we use a modified scheme called Single

Carrier FDMA (SC-FDMA).The advantages are reduced PAPR and frequency domain

equalization [6].

1.7 Objective of Thesis:

The main objectives of thesis are:

(1) A comparative study of SCFDMA and OFDMA which are used for uplink and downlink

communication in 3GPP LTE system.

(2) Comprising of PAPR analysis for both the techniques under different conditions or

parameters.

(3) Reducing the PAPR of OFDM signal using the clipping and filtering method.

1.8 Scope of Thesis:

The thesis is organized as follows:

Chapter 2 presents the overall architectural overview of the LTE system.

Chapter 3 discusses about the physical layer in the LTE uplink and its multiple access

SCFDMA.

Chapter 4 discusses about the physical layer in the LTE downlink and its multiple access

OFDMA.

Chapter 5 discusses about the basics of PAPR analysis and comparative study of PAPR for

SCFDMA & OFDMA and PAPR reduction techniques for OFDM signal.

23

Chapter 6 provides the characteristics of mobile radio channels and different ways to model

channel impulse responses.

Chapter 7 investigates different channel estimation techniques, they are LS estimator,

LMMSE estimator and modified MMSE estimator.

Chapter 8 deals with simulations and results under different parametric conditions.

Chapter 9 concludes on the entire discussion.

24

Chapter 2

LTE Network Architecture

2.1 Introduction:

In contrast to the circuit-switched model of previous cellular systems, Long Term Evolution

(LTE) has been designed to support only packet-switched services. It aims to provide

seamless Internet Protocol (IP) connectivity between user equipment (UE) and the packet

data network (PDN), without any disruption to the end users‟ applications during mobility.

While the term “LTE” encompasses the evolution of the Universal Mobile

Telecommunications System (UMTS) radio access through the Evolved UTRAN (E-

UTRAN), it is accompanied by an evolution of the non-radio aspects under the term “System

Architecture Evolution” (SAE), which includes the Evolved Packet Core (EPC) network.

Together LTE and SAE comprise the Evolved Packet System (EPS). EPS uses the concept of

EPS bearers to route IP traffic from a gateway in the PDN to the UE. A bearer is an IP

packet flow with a defined quality of service (QoS) between the gateway and the UE. The E-

UTRAN and EPC together set up and release bearers as required by applications.

This paper provides a comprehensive tutorial of the overall EPS network architecture, giving

an overview of the functions provided by the core network (CN) and E-UTRAN. The

protocol stack across the different interfaces is explained, along with an overview of the

functions provided by the different protocol layers. The end-to-end bearer path along with

QoS aspects are also discussed, including a typical procedure for establishing a bearer. The

remainder of this paper presents the network interfaces in detail, with particular focus on the

E-UTRAN interfaces and the procedures used across these interfaces, including those for the

support of user mobility [5].

2.2 Overall Architectural Overview:

EPS provides the user with IP connectivity to a PDN for accessing the Internet, as well as for

running services such as Voice over IP (VoIP). An EPS bearer is typically associated with a

QoS. Multiple bearers can be established for a user in order to provide different QoS streams

or connectivity to different PDNs. For example, a user might be engaged in a voice (VoIP)

25

call while at the same time performing web browsing or FTP download. A VoIP bearer

would provide the necessary QoS for the voice call, while a best-effort bearer would be

suitable for the web browsing or FTP session. The network must also provide sufficient

security and privacy for the user and protection for the network against fraudulent use.

This is achieved by means of several EPS network elements that have different roles. Fig 2.1

shows the overall network architecture, including the network elements and the standardized

interfaces. At a high level, the network is comprised of the CN (EPC) and the access network

E-UTRAN.

While the CN consists of many logical nodes, the access network is made up of essentially

just one node, the evolved NodeB (eNodeB), which connects to the UEs. Each of these

network elements is interconnected by means of interfaces that are standardized in order to

allow multi-vendor interoperability. This gives network operators the possibility to source

different network elements from different vendors. In fact, network operators may choose in

their physical implementations to split or merge these logical network elements depending on

commercial considerations. The functional split between the EPC and E-UTRAN is shown in

Fig 2.2. The EPC and E-UTRAN network elements are described in more detail below [5].

S6a

Rx

LTE - Uu

S1-MME S11 Gx

S1-U S5/S8 SGi

Fig 2.1 The EPS network elements.

eNodeB

UE

PCRF MME

S - GW P - GW

HSS

Operator‟s IP

services ( For

ex- IMS, PSS)

26

2.2.1 The core network:

The CN (called EPC in SAE) is responsible for the overall control of the UE and

establishment of the bearers. The main logical nodes of the EPC are:

• PDN Gateway (P-GW);

• Serving Gateway (S-GW);

• Mobility Management Entity (MME).

In addition to these nodes, EPC also includes other logical nodes and functions such as the

Home Subscriber Server (HSS) and the Policy Control and Charging Rules Function (PCRF).

Since the EPS only provides a bearer path of a certain QoS, control of multimedia

applications such as VoIP is provided by the IP Multimedia Subsystem (IMS) which is

considered to be outside the EPS itself. The logical CN nodes are shown in Figure 2.1 and

discussed in more detail [5] in the following.

• PCRF: It is responsible for policy control decision-making, as well as for controlling the

flow-based charging functionalities in the Policy Control Enforcement Function (PCEF)

which resides in the P-GW. The PCRF provides the QoS authorization (QoS class identifier

and bitrates) that decides how a certain data flow will be treated in the PCEF and ensures that

this is in accordance with the user‟s subscription profile.

• Home Location Register (HLR): The HLR contains users‟ SAE subscription data such as

the EPS-subscribed QoS profile and any access restrictions for roaming. It also holds

information about the PDNs to which the user can connect.

This could be in the form of an Access Point Name (APN) (which is a label according to

DNS1 naming conventions describing the access point to the PDN), or a PDN Address

(indicating subscribed IP address(es). In addition the HLR holds dynamic information such as

the identity of the MME to which the user is currently attached or registered. The HLR may

also integrate the Authentication Centre (AuC) which generates the vectors for authentication

and security keys.

27

S1

E-UTRAN EPC

Fig 2.2: Functional split between E-UTRAN and EPC.

• P-GW: The P-GW is responsible for IP address allocation for the UE, as well as QoS

enforcement and flow-based charging according to rules from the PCRF. The P-GW is

responsible for the filtering of downlink user IP packets into the different QoS based bearers.

This is performed based on Traffic Flow Templates (TFTs). The P-GW performs QoS

enforcement for Guaranteed Bit Rate (GBR) bearers. It also serves as the mobility anchor for

inter-working with non-3GPP technologies such as CDMA2000 and WiMAX networks.

eNodeB

Radio Admission Control

RB Control

Connection Mobility Control

eNodeB Measurement

Configuration & Provision

Dynamic Resource Allocation

(Scheduler)

RRC

PDCP

RLC

MAC

PHY

Inter Cell RRM

MME

S - GW P - GW

NAS Security

Idle State Mobility

Handling

EPS Bearer Control

Mobility

Anchoring

UE IP Address

Allocation

Packet Filtering

Internet

28

• S-GW: All user IP packets are transferred through the S-GW, which serves as the local

mobility anchor for the data bearers when the UE moves between eNodeBs. It also retains the

information about the bearers when the UE is in idle state (known as ECM- IDLE) and

temporarily buffers downlink data while the MME initiates paging of the UE to re-establish

the bearers. In addition, the S-GW performs some administrative functions in the visited

network such as collecting information for charging (e.g. the volume of data sent to or

received from the user), and legal interception. It also serves as the mobility anchor for inter-

working with other 3GPP technologies such as GPRS and UMTS.

• MME: The MME is the control node which processes the signaling between the UE and the

CN. The protocols running between the UE and the CN are known as the Non-Access

Stratum (NAS) protocols. The main functions supported by the MME are classified as:

Functions related to bearer management: This includes the establishment, maintenance

and release of the bearers, and is handled by the session management layer in the NAS

protocol.

Functions related to connection management: This includes the establishment of the

connection and security between the network and UE, and is handled by the connection or

mobility management layer in the NAS protocol layer.

NAS control procedures are discussed in more detail in the following section.

2.2.1.1 Non-Access Stratum (NAS) Procedures:

The NAS procedures, especially the connection management procedures, are fundamentally

similar to UMTS. The main change from UMTS is that EPS allows concatenation of some

procedures to allow faster establishment of the connection and the bearers. The MME creates

a UE context when a UE is turned on and attaches to the network. It assigns a unique short

temporary identity termed the SAE-Temporary Mobile Subscriber Identity (S-TMSI) to the

UE which identifies the UE context in the MME. This UE context holds user subscription

information downloaded from the HSS. The local storage of subscription data in the MME

allows faster execution of procedures such as bearer establishment since it removes the need

to consult the HSS every time. In addition, the UE context also holds dynamic information

such as the list of bearers that are established and the terminal capabilities.

29

To reduce the overhead in the E-UTRAN and processing in the UE, all UE-related

information in the access network can be released during long periods of data inactivity. This

state is called EPS Connection Management IDLE (ECM-IDLE). The MME retains the UE

context and the information about the established bearers during these idle periods. To allow

the network to contact an ECM-IDLE UE, the UE updates the network as to its new location

whenever it moves out of its current Tracking Area (TA); this procedure is called a „Tracking

Area Update‟. The MME is responsible for keeping track of the user location while the UE is

in ECM-IDLE.

When there is a need to deliver downlink data to an ECM-IDLE UE, the MME sends a

paging message to all the eNodeBs in its current TA, and the eNodeBs page the UE over the

radio interface. On receipt of a paging message, the UE performs a service request procedure

which results in moving the UE to ECM-CONNECTED state. UE-related information is

thereby created in the E-UTRAN, and the bearers are re-established. The MME is responsible

for the re-establishment of the radio bearers and updating the UE context in the eNodeB. This

transition between the UE states is called an idle-to-active transition. To speed up the idle-to-

active transition and bearer establishment, EPS supports concatenation of the NAS and AS

procedures for bearer activation. Some inter-relationship between the NAS and AS protocols

is intentionally used to allow procedures to run simultaneously rather than sequentially, as in

UMTS. For example, the bearer establishment procedure can be executed by the network

without waiting for the completion of the security procedure. Security functions are the

responsibility of the MME for both signaling and user data. When a UE attaches with the

network, a mutual authentication of the UE and the network is performed between the UE

and the MME/HSS. This authentication function also establishes the security keys which are

used for encryption of the bearers [5].

2.2.2 The access network:

The Access Network of LTE, E-UTRAN, simply consists of a network of eNodeBs, as

illustrated in Fig 2.3. For normal user traffic (as opposed to broadcast), there is no centralized

controller in E-UTRAN; hence the E-UTRAN architecture is said to be flat. The eNodeBs are

normally inter-connected with each other by means of an interface known as X2, and to the

EPC by means of the S1 interface more specifically, to the MME by means of the S1-MME

interface and to the S-GW by means of the S1-U interface. The protocols which run between

30

the eNodeBs and the UE are known as the Access Stratum (AS) protocols. The E-UTRAN is

responsible for all radio-related functions, which can be summarized briefly [5] as:

• Radio Resource Management: This covers all functions related to the radio bearers, such

as radio bearer control, radio admission control, radio mobility control, scheduling and

dynamic allocation of resources to UEs in both uplink and downlink.

• Header Compression: This helps to ensure efficient use of the radio interface by

compressing the IP packet headers which could otherwise represent a significant overhead,

especially for small packets such as VoIP.

• Security: All data sent over the radio interface is encrypted.

• Connectivity to the EPC: This consists of the signaling towards the MME and the bearer

path towards the S-GW.

S1 S1 S1 S1

X2

E- UTRAN

X2 X2

Fig 2.3: Overall E-UTRAN architecture.

eNodeB#1 eNodeB#3

eNodeB#2

MME / S-GW MME / S-GW

31

On the network side, all of these functions reside in the eNodeBs, each of which can be

responsible for managing multiple cells. Unlike some of the previous second- and third-

generation technologies, LTE integrates the radio controller function into the eNodeB. This

allows tight interaction between the different protocol layers of the radio access network, thus

reducing latency and improving efficiency. Such distributed control eliminates the need for a

high-availability, processing-intensive controller, which in turn has the potential to reduce

costs and avoid „single points of failure‟. Furthermore, as LTE does not support soft handover

there is no need for a centralized data-combining function in the network.

One consequence of the lack of a centralized controller node is that, as the UE moves, the

network must transfer all information related to a UE, i.e. the UE context, together with any

buffered data, from one eNodeB to another. Mechanisms are therefore needed to avoid data

loss during handover.

An important feature of the S1 interface linking the Access Network to the CN is known as

S1-flex. This is a concept whereby multiple CN nodes (MME/S-GWs) can serve a common

geographical area, being connected by a mesh network to the set of eNodeBs in that area. An

eNodeB may thus be served by multiple MME/S-GWs, as is the case for eNodeB#2 in Figure

2.3. The set of MME/S-GW nodes which serves a common area is called an MME/S-GW

pool, and the area covered by such a pool of MME/S-GWs is called a pool area. This concept

allows UEs in the cell(s) controlled by one eNodeB to be shared between multiple CN nodes,

thereby providing a possibility for load sharing and also eliminating single points of failure

for the CN nodes. The UE context normally remains with the same MME as long as the UE is

located within the pool area.

2.3 Roaming Architecture:

A network run by one operator in one country is known as a Public Land Mobile Network

(PLMN). Roaming, where users are allowed to connect to PLMNs other than those to which

they are directly subscribed is a powerful feature for mobile networks, and LTE/SAE is no

exception. A roaming user is connected to the E-UTRAN, MME and S-GW of the visited

LTE network. However, LTE/SAE allows the P-GW of either the visited or the home

network to be used, as shown in Fig 2.4. Using the home network‟s P-GW allows the user to

32

access the home operator‟s services even while in a visited network. A P-GW in the visited

network allows a „local breakout‟ to the Internet in the visited network [5].

Rx

Gx

SGi

HPMN

VPLMN

S8

S1-MME S11

LTE-Uu S1-U

Fig 2.4: Roaming architecture for 3GPP accesses with P-GW in home network.

2.4 Inter-Working with Other Networks: EPS also supports inter-working and mobility (handover) with networks using other Radio

Access Technologies (RATs), notably GSM, UMTS, CDMA2000 and WiMAX. The

architecture for inter-working with 2G and 3G GPRS/UMTS networks is shown in Fig 2.5.

The S-GW acts as the mobility anchor for inter-working with other 3GPP technologies such

as GSM and UMTS, while the P-GW serves as an anchor allowing seamless mobility to non-

3GPP networks such as CDMA2000 or WiMAX. The P-GW may also support a Proxy

HSS

PDN

Gateway

Serving

Gateway

MME

UE

Operator‟s IP

Services (e.g.

IMS, PSS)

E - UTRAN

PCRF

33

Mobile Internet Protocol (PMIP) based interface. More details of the radio interface

procedures for inter-working are specified [5].

S3

S4

S1-MME S11

LTE-Uu S1-U S5/S8

Fig 2.5: Architecture for 3G UMTS interworking.

2.5 Inter-Radio Access Technologies (RAT) Mobility: One key element of the design of the first release of LTE is the need to co-exist with other

technologies. For mobility from LTE towards UMTS, the handover process can reuse the S1-

handover procedures described above, with the exception of the STATUS TRANSFER

message which is not needed at steps 10 and 11 since no PDCP context is continued. For

mobility towards CDMA2000, dedicated uplink and downlink procedures have been

introduced in LTE. They essentially aim at tunneling the CDMA2000 signaling between the

UE and the CDMA2000 system over the S1 interface, without being interpreted by the

eNodeB on the way. The UPLINK S1 CDMA2000 TUNNELLING message presented in Fig

2.6 also includes the RAT type in order to identify which CDMA2000 RAT the tunneled

CDMA2000 message is associated with in order for the message to be routed to the correct

node within the CDMA2000 system.

Serving

Gateway UE E - UTRAN

MME

3G-SGSN

PDN

Gateway

UTRAN

34

UPLINK S1 CDMA2000 TUNNELING

Fig 2.6: Uplink S1 CDMA2000 tunneling procedure.

2.6 Connected Mode Inter-RAT Mobility:

The overall procedure for the control of mobility is explained in this section;

2.6.1 Handover to LTE:

The procedure for handover to LTE is largely the same as the procedure for handover within

LTE, so it is not necessary to repeat the details here. The main difference is that upon

handover to LTE the entire AS-configuration needs to be signaled, whereas within LTE it is

possible to use „delta signaling‟, whereby only the changes to the configuration are signaled.

If ciphering had not yet been activated in the previous RAT, the E-UTRAN activates

ciphering, possibly using the NULL algorithm, as part of the handover procedure. The E-

UTRAN also establishes SRB1, SRB2 and one or more DRBs (i.e. at least the DRB

associated with the default EPS bearer).

2.6.2 Mobility from LTE:

The procedure for mobility from LTE to another RAT supports both handover and Cell

Change Order (CCO), possibly with Network Assistance (NACC – Network Assisted Cell

Change). The CCO/NACC procedure is applicable only for mobility to GERAN. Mobility

eNodeB MME

35

from LTE is performed only after security has been activated. The procedure is illustrated in

Fig 2.7.

Measurement Report

Mobility From EUTRA Command

“Handover Complete” OR

Connection Establishment

Fig 2.7: Mobility from LTE.

1. The UE may send a Measurement Report message.

2. In case of handover (as opposed to CCO), the source eNodeB requests the target RAN

node to prepare for the handover. As part of the „handover preparation request‟ the source

eNodeB provides information about the applicable inter-RAT UE capabilities as well as

information about the currently-established bearers. In response, the target RAN generates

the „handover command‟ and returns this to the source eNodeB.

3. The source eNodeB sends a Mobility From EUTRA Command message to the UE, which

includes either the inter-RAT message received from the target (in case of handover), or the

target cell/frequency and a few inter-RAT parameters (in case of CCO).

4. Upon receiving the Mobility From EUTRA Command message, the UE starts the timer

T304 and connects to the target node, either by using the received radio configuration

(handover) or by initiating connection establishment (CCO) in accordance with the applicable

specifications of the target RAT.

Source

eNodeB

UE Target

RAN

Handover Preparation

36

Chapter 3

Physical Layer in the LTE Uplink

3.1 Introduction:

SC-FDMA combines the desirable characteristics of OFDM with the low PAPR of single-

carrier transmission schemes. Like OFDM, SC-FDMA divides the transmission bandwidth

into multiple parallel subcarriers, with the orthogonality between the subcarriers being

maintained in frequency-selective channels by the use of a Cyclic Prefix (CP) or guard

period. The use of a CP prevents Inter-Symbol Interference (ISI) between SC-FDMA

information blocks. It transforms the linear convolution of the multipath channel into a

circular convolution, enabling the receiver to equalize the channel simply by scaling each

subcarrier by a complex gain factor.

However, unlike OFDM, where the data symbols directly modulate each subcarrier

independently (such that the amplitude of each subcarrier at a given time instant is set by the

constellation points of the digital modulation scheme), in SC-FDMA the signal modulated

onto a given subcarrier is a linear combination of all the data symbols transmitted at the same

time instant. Thus in each symbol period, all the transmitted subcarriers of an SC-FDMA

signal carry a component of each modulated data symbol. This gives SC-FDMA its crucial

single-carrier property, which results in the PAPR being significantly lower than pure

multicarrier transmission schemes such as OFDM [5].

3.2 LTE Uplink Requirements:

While many of the requirements for the design of the LTE uplink physical layer and multiple-

access scheme are similar to those of the downlink, the uplink also poses some unique

challenges. Some of the desirable attributes for the LTE uplink include [5]:

• Orthogonal uplink transmission by different User Equipment (UEs), to minimize

intracellular interference and maximize capacity.

• Flexibility to support a wide range of data rates, and to enable data rate to be adapted to the

SINR (Signal-to-Interference plus Noise Ratio).

• Sufficiently low Peak-to-Average Power Ratio (PAPR) of the transmitted waveform, to

avoid excessive cost, size and power consumption of the UE Power Amplifier (PA).

37

• Ability to exploit the frequency diversity afforded by the wideband channel (up to 20 MHz),

even when transmitting at low data rates.

• Support for frequency-selective scheduling.

• Support for advanced multiple-antenna techniques, to exploit spatial diversity and enhance

uplink capacity.

The multiple-access scheme selected for the LTE uplink so as to fulfil these principle

characteristics is Single-Carrier Frequency Division Multiple Access (SC-FDMA). A major

advantage of SC-FDMA over the Direct-Sequence Code Division Multiple Access (DS-

CDMA) scheme used in LTE is that it achieves intra-cell orthogonality and low PAPR.

3.3 SC-FDMA Principles:

3.3.1 SC-FDMA transmission structure:

An SC-FDMA signal can, in theory, be generated in either the time-domain or the frequency-

domain . Although the two techniques are duals and „functionally‟ equivalent, in practice, the

time-domain generation is less bandwidth-efficient due to time-domain filtering and

associated requirements for filter ramp-up and ramp-down times [5]. Nevertheless, we

describe both approaches here to facilitate understanding of the principles of SC-FDMA in

both domains.

3.3.2 Time-domain signal generation:

Time-domain generation of an SC-FDMA signal is shown in Fig 3.1. It can be seen to be

similar to conventional single-carrier transmission. The input bit stream is mapped into a

single-carrier stream of QPSK or QAM symbols, which are grouped into symbol-blocks of

length M. This may be followed by an optional repetition stage, in which each block is

repeated L times, and a user-specific frequency shift, by which each user‟s transmission may

be translated to a particular part of the available bandwidth. A CP is then inserted. After

filtering (e.g. with a root-raised cosine pulse-shaping filter), the resulting signal is transmitted.

Different users‟ transmissions, using different repetition factors or bandwidths, remain

orthogonal on the uplink when the following conditions are met [5]:

• The users occupy different sets of subcarriers. This may in general be accomplished either

by introducing a user-specific frequency shift (typically for the case of localized

transmissions) or alternatively by arranging for different users to occupy interleaved sets of

38

subcarriers (typically for the case of distributed transmissions). The latter method is known in

the literature as Interleaved Frequency Division Multiple Access (IFDMA).

Incoming bit stream

Fig 3.1: SC-FDMA time-domain transmit processing.

• The received signals are properly synchronized in time and frequency.

• The CP is longer than the sum of the delay spread of the channel and any residual timing

synchronization error between the users. The SC-FDMA time-domain generated signal has a

similar level of CM/PAPR as pulse-shaped single-carrier modulation. ISI in multipath

channels is prevented by the CP, which enables efficient equalization at the receiver by

means of a Frequency Domain Equalizer (FDE).

3.4 SC-FDMA Frame Structure:

The generic frame structure for the SC-FDMA uplink is shown [11] in Fig 3.2.

One Radio Frame, Tf = 10ms

One Slot Tslot = 0.5 ms

One Subframe

Fig 3.2: Generic frame structure (TDD or FDD)

S/P

C

onver

ter

Bit

to

Const

ella

tion

Map

pin

g

DS

-Spre

adin

g

(Opti

onal

)

Use

r-sp

ecif

ic

Blo

ck r

epet

itio

n

Puls

e-sh

ape

filt

er

Tra

nsm

issi

on

circ

uit

ry

Add

CP

# 0 # 1 # 2 # 3 # 18 # 19

User-specific frequency

shift

39

The generic slot structure with a normal cyclic prefix is shown in Fig 3.3. A slot with an

extended cyclic prefix contains only 6 long blocks.

One Slot = 0.5 ms

Fig 3.3: Slot structure

- CP = Cyclic prefix (guard interval)

- LB = Long block (for data symbol)

3.5 Uplink SC-FDMA Parameters:

Table 3.1: Uplink parameters for SC-FDMA transmission [11].

Transmission BW 1.25 MHz 2.5 MHz 5 MHz 10 MHz 15 MHz 20

MHz Slot duration

(generic frame structure) 0.5 ms

Slot duration (alternative

frame structure) 0.675 ms

CP duration

ms / no. of subcarriers

(generic frame structure)

3.65/7

or

7.81/15

3.91/15

or

5.99/23

4.04/31

or

5.08/39

4.1/63

or

4.62/71

4.12/95

or

4.47/103

4.13/127

or

4.39/135

CP duration

ms / no. of subcarriers (alternative frame

structure)

6.25/12

or

10.4/20

6.51/25

or

8.58/33

6.64/51

or

7.67/59

6.71/103

or

7.22/111

6.77/156

or

7.11/164

6.71/206 or

6.97/214

Long block (LB) size

ms 66.67

Occupied subcarriers 75 150 300 600 900 1200

FFT size 128 256 512 1024 1536 2048 Short block (SB) size

ms 33.33

Occupied subcarriers 38 75 150 300 450 600

FFT size 64 128 256 512 768 1024

CP LB0 CP LB0 CP LB0 CP LB0 CP LB0 CP LB0 CP LB0

40

3.6 Modulation:

There are no harmonization problems between the downlink and the uplink in terms of frame

structure and modulation parameters. The modulation scheme that is used can be QPSK,

16QAM or 64QAM according to the channel quality. Specifically, the uplink symbols enter a

serial/ parallel converter and then into a FFT block. The result is mapped onto the available

sub-carriers. Later, a N point IFFT is applied, the cyclic prefix is added and, finally, this

result enters a parallel to serial converter [12].

3.7 Implementation of the SC-FDMA Transceiver:

Different transmitters (users) are assigned different Fourier coefficients. This assignment is

carried out in the mapping and demapping blocks. The transmitter of LTE uplink is designed

as illustrated in fig 3.4. The receiver side includes one demapping block, one IDFT block

and one detection block for each user signal to be received. The receiver of LTE uplink is

designed as illustrated in fig 3.5 [13]. SC-FDMA is a new multiple access technique that

utilizes single carrier modulation, DFT-spread orthogonal frequency multiplexing, and

frequency domain equalization. It has a similar structure and performance as OFDM. SC-

FDMA is currently adopted as the uplink multiple access scheme for 3GPP LTE. Transmitter

and receiver structure for SC-FDMA are given in Figures 3.4 and 3.5. It is evident from the

figures that SC-FDMA transceiver has similar structure as a typical OFDM system except the

addition of a new DFT block before subcarrier mapping. Hence, SC-FDMA can be

considered as an OFDM system with a DFT mapper.

Fig 3.4: Block diagram of the SC-FDMA transmitter in LTE.

Fig 3.5: Block diagram of the SC-FDMA receiver in LTE.

S/P

Conver-

sion

N-FFT

Sub-carrier

mapping

M-IFFT P/S

Conversion

Add

CP

P/S

Conver-

sion

N-IFFT

Sub-carrier

demapping

M-FFT S/P

Conversi

on

Remove

CP

41

3.8 LTE Uplink Physical Channels:

Physical Uplink Control Channel (PUCCH): It provides control signaling information such

as ACK/NACK information, CQI (channel quality indication) reports, RI (rank indication)

and other formats.

Physical Uplink Shared Channel (PUSCH): It is the Uplink counterpart of PDSCH.

Physical Random Access Channel (PRACH): It is used for random access functions. Through

this, the downlink and uplink propagation delays are not known. As a result, the transmission

cannot get synchronized [12].

3.9 LTE Uplink Transport Channels:

Uplink Shared Channel (UL-SCH) : It is the most important channel for uplink data transfer

used by several logical channels.

Random Access Channel (RACH) : It is used for random access requirements [12].

42

Chapter 4

Physical Layer in the LTE Downlink

4.1 Introduction:

One of the main changes in the LTE system compared to 3G-UMTS is the physical layer. In

third generation systems, Wideband Code Division Multiple Access (WCDMA) is the most

widely adopted technology. A highlight of the characteristics of the UMTS before Release 7

is listed below [14]:

- User information bits are spread over a wide bandwidth by multiplying the user data with a

spreading code. The use of variable spreading factor allows a variation of the bit rate.

- The bandwidth is 5 MHz. The chip rate used is 3.84 Mbps. A network operator can deploy

multiple 5 MHz bands to increase capacity.

- The frame length is 10 ms. During this phase, the user data rate is kept constant. However,

the data rate among the users can change from frame to frame.

In the LTE system, this will be very different. The new system will present an OFDM based

structure. The main aspects important for channel estimation in the physical layer are

presented in the following section. In the LTE only packet-switched transmission is utilized.

OFDMA fits perfectly into packet-switched transmission, since different number of

subcarriers (RBs) can be assigned to different users, in order to support differentiated Quality

of Service (QoS). The scheduling is dynamic and performed for each sub-frame, hence the

number of RBs can be adjusted dynamically depending on the channel quality.

4.2 LTE Downlink Requirements:

The technique of OFDM is based on the technique of frequency division multiplexing

(FDM). The OFDM technique differs from traditional FDM by having subcarriers, which are

orthogonal to each other. The modulation technique used in an OFDM system helps to

overcome the effects of a frequency selective channel. A frequency selective channel occurs

when the transmitted signal experiences a multipath environment. Under such conditions, a

given received symbol can be potentially corrupted by a number of previous symbols. This

43

effect is commonly known as inter-symbol interference (ISI). To avoid such interference, the

symbol duration has to be much larger than the delays caused by multipath channel.

Hence each symbol is prolonged with a copy of its tail denoted as cyclic prefix (CP) such that

the ISI is minimized. Also, the spectral efficiency of the OFDM modulation technique is

superior to FDM since the subcarriers are overlapping, but orthogonal. The frequency spacing

between the Subcarriers 𝑓𝑠𝑝𝑎𝑐𝑒 =𝑓𝑠

𝑁𝐼𝐹𝐹𝑇 is either 15 kHz or 7.5 kHz according to working

assumption in Release 8 [5]. In contrast to an OFDM transmission scheme, OFDMA allows

multiple users to share the available bandwidth. Each user is assigned a specific time-

frequency resource referred as resource block (RB). The fundamental principle of the

Evolved UMTS Terrestrial Radio Access (E-UTRA) is that the data channels are shared

channels, i.e. for each transmission time interval (TTI) of 1ms, a new scheduling decision is

made at eNodeB regarding which users are assigned to which time/frequency resources

during this transmission time interval [14].

4.3 OFDM Principles:

4.3.1 Orthogonal multiplexing principle:

A high-rate data stream typically faces a problem in having a symbol period Ts much smaller

than the channel delay spread Td if it is transmitted serially. This generates Inter- symbol

Interference (ISI) which can only be undone by means of a complex equalization procedure.

In general, the equalization complexity grows with the square of the channel impulse

response length. In OFDM, the high-rate stream of data symbols is first serial-to-parallel

converted for modulation onto M parallel subcarriers as shown in Fig 4.1. This increases the

symbol duration on each subcarrier by a factor of approximately M, such that it becomes

significantly longer than the channel delay spread.

This operation has the important advantage of requiring a much less complex equalization

procedure in the receiver, under the assumption that the time-varying channel impulse

response remains substantially constant during the transmission of each modulated OFDM

symbol. This operation has the important advantage of requiring a much less complex

equalization procedure in the receiver, under the assumption that the time-varying channel

impulse response remains substantially constant during the transmission of each modulated

OFDM symbol. Figure 5.3 shows how the resulting long symbol duration is virtually

44

unaffected by ISI compared to the short symbol duration, which is highly corrupted. Figure

5.4 shows the typical block diagram of an OFDM system [5].

𝒆−𝒋𝟐𝝅𝒕𝒇𝟏

Low Symbol Rate

𝒆−𝒋𝟐𝝅𝒕𝒇𝒏

Fig 4.1: Serial-to-parallel conversion operations for OFDM.

xk[N-G]

Cyclic Prefix

xk[N-1] Sk[0] Xk[0]

xk[0]

Sk[1] Xk[1] xk[1]

Sk[N-2] Xk[N-2] xk[N-G]

Sk[N-1] Xk[N-1] xk[N-1]

Fig 4.2: OFDM Transmitter

The signal to be transmitted is defined in the frequency domain. A Serial to Parallel (S/P)

converter collects serial data symbols into a data block Sk = [Sk [0] ,Sk [1] ,...,Sk [M − 1]]T of

dimension M, where the subscript k is the index of an OFDM symbol (spanning the M sub-

carriers). The M parallel data streams are first independently modulated resulting in the

complex vector Xk = [Xk [0] ,Xk [1] , ..., Xk [M − 1]]T . Note that in principle it is possible to

S/P

S/P

IFFT

P/S DAC

45

use different modulations (e.g. QPSK or 16QAM) on each sub-carrier; due to channel

frequency selectivity, the channel gain may differ between sub-carriers, and thus some sub-

carriers can carry higher data-rates than others.

rkCP

[0]

Cyclic Prefix removal

rkCP

[G-1]

rkCP

[G] = rk[0] Yk[0]

rkCP

[G+1] = rk[1] Yk[1]

rkCP

[N+G-2] = rk[N-2]

Yk[N-2]

rk

CP[N+G-1] = rk[N-1] Yk[N-1]

Fig 4.3: OFDM receiver

The vector of data symbols Xk then passes through an Inverse FFT (IFFT) resulting in a set of

N complex time domain samples xk = [xk[0],...,xk[N − 1]]T . In a practical OFDM system, the

number of processed subcarriers is greater than the number of modulated sub-carriers (i.e. N

≥M), with the un-modulated sub-carriers being padded with zeros.

TCP Tu TCP Tu

Fig 4.4: OFDM cyclic prefix insertion.

The next key operation in the generation of an OFDM signal is the creation of a guard period

at the beginning of each OFDM symbol, to eliminate the remaining impact of ISI caused by

S/P ADC

FFT

46

multipath propagation. The guard period is obtained by adding a Cyclic Prefix (CP) at the

beginning of the symbol xk. The CP is generated by duplicating the last G samples of the

IFFT output and appending them at the beginning of xk. This yields the time domain OFDM

symbol [xk[N − G], ..., xk[N − 1], xk[0], ...,xk[N − 1]] T ,as shown in Fig 4.3.

To avoid ISI completely, the CP length G must be chosen to be longer than the longest

channel impulse response to be supported. The CP converts the linear (i.e. a-periodic)

convolution of the channel into a circular (i.e. periodic) one which is suitable for DFT

processing. This important feature of CP used in OFDM is explained more formally later in

this section. The output of the IFFT is then Parallel-to-Serial (P/S) converted for transmission

through the frequency-selective channel.

At the receiver, the reverse operations are performed to demodulate the OFDM signal.

Assuming that time- and frequency-synchronization is achieved, a number of samples

corresponding to the length of the CP are removed, such that only an ISI-free block of

samples is passed to the DFT. If the number of subcarriers N is designed to be a power of 2, a

highly efficient FFT implementation may be used to transform the signal back to the

frequency domain. Among the N parallel streams output from the FFT, the modulated subset

of M subcarriers are selected and further processed by the receiver.

Let x(t) be the signal symbol transmitted at time instant t . The received signal in a multipath

environment is then given by

r(t) = x(t) ∗ h(t) + z(t) (4.1)

where h(t) is the continuous-time impulse response of the channel, ∗ represents the

convolution operation and z(t) is the additive noise. Assuming that x(t) is band-limited to

[−12𝑇𝑠

, 12𝑇𝑠

], the continuous-time signal x(t) can be sampled at sampling rate Ts such

that the Nyquist criterion is satisfied.

As a result of the multipath propagation, several replicas of the transmitted signals arrive at

the receiver at different delays [5].

4.3.2 Importance of orthogonality:

The “orthogonal” part of OFDM name indicates there is some mathematical relationship

between frequencies in sub bands. Introduction of guard bands reduces the spectral

efficiency. So to enhance this efficiency, the carriers in OFDM signals are arranged in a

manner such that individual carriers overlap and the signals can still be received without

carrier interference. Mathematically, two signals are orthogonal if

47

𝑋𝑝 𝑡 . 𝑋𝑞∗ 𝑡 𝑑𝑡

𝑏

𝑎 = K if p = q (4.2)

0 if p ≠ q

Where * denotes the complex conjugate and interval [a b] is a symbol period [16]. An OFDM

signal consists of a sum of subcarriers that are modulated by using BPSK, QPSK or QAM.

Mathematically, each carrier can be described as a complex wave:

𝑋𝑡 𝑡 = 𝐴𝑐 𝑡 𝑒𝑗 {𝜔𝑐 𝑡+𝜑𝑐 (𝑡)} (4.3)

OFDM being carrying many carriers, its signal representation is:

𝑋𝑠 𝑡 =1

𝑁 𝐴𝑛 𝑡 𝑒

𝑗 {𝜔𝑛 𝑡+𝜑𝑛 (𝑡)}𝑛=𝑁−1𝑛=0 (4.4)

Where,

𝜔𝑛 = 𝜔𝑜 + 𝑛∆𝜔

This is a continuous signal. If we consider the waveforms of each component of the signal

over one symbol period, then Ac(t) and fc(t) take on fixed values, which depends on the

frequency of that particular carrier, and so can be rewritten as:

𝜑𝑛 𝑡 = 𝜑𝑛 and 𝐴𝑛 𝑡 = 𝐴𝑛

if now the signal is sampled at T time period, then the resulting signal becomes:

𝑋𝑠 𝑘𝑇 =1

𝑁 𝐴𝑛𝑒

𝑗 {𝜔𝑛 +𝜑𝑛 }𝑛=𝑁−1𝑛=0 (4.5)

At this point, we restricted the time of analysis upto N samples. But it‟s convenient to sample

over one data symbol period. Thus we have:

τ = NT

If we simplify eqn. 4.5, without the loss of generality by letting ωo = 0, then the signal

becomes:

𝑋𝑠 𝑘𝑇 =1

𝑁 𝐴𝑛𝑒

𝑗𝜑𝑛𝑛=𝑁−1𝑛=0 𝑒𝑗 (𝑛∆𝜔)𝑘𝑇 (4.6)

This can now be compared with the general form of inverse Fourier Transform:

𝑔 𝑘𝑇 =1

𝑁 𝐺(

𝑛

𝑁𝑇)𝑛=𝑁−1

𝑛=0 𝑒𝑗2𝜋𝑛𝑘 /𝑁 (4.7)

Eqns 3.5 and 3.6 are equivalent if:

48

∆𝑓 =∆𝜔

2𝜋=

1

𝑁𝑇=

1

𝜏 (4.8)

This is the same condition that was required for orthogonality. Thus, maintaining orthogo-

nality is that the OFDM signal can be defined by using Fourier transform procedures [16].

4.3.3 Guard interval:

Individual sub channels can be completely separated by the FFT at the receiver when there

are no ISI and ICI introduced by channel distortion. Practically these conditions cannot be

obtained. Since the spectra of an OFDM signal is not strictly band limited, linear distortion

such as multipath fading cause sub channel to spread energy in the adjacent channels [16].

This problem can be solved by increasing symbol duration. One way to prevent ISI is to

create a cyclically extended guard interval, where each symbol is preceded by a periodic

extension of the signal itself. The total symbol duration being increased to TTotal = Tg + T.

When Tg is longer than the channel impulse response, the ISI can be eliminated. Since the

insertion of guard interval will reduce data throughput, Tg is usually less than T/4. The main

reasons to use a cyclic prefix for the guard band interval are [16]:

1. To maintain the receiver carrier synchronization.

2. Cyclic convolution can still be applied between the OFDM signal and the channel

response to model the transmission systems.

Fig 4.5: Insertion of cyclic prefix

4.4 OFDM Frame Structure:

The structure of the radio frame, illustrated in Fig 4.6, is described in the current study from

3GPP. It should be noticed that for time division duplex (TDD), sub-frames for uplink and

downlink purpose should be assigned. Other frame structures are proposed in order to make

the structure compatible with the present structure used in 3G. For simplicity it is chosen to

work with the illustrated generic frame structure. The duration of one frame is 10 ms and is

CP Symbol CP Symbol

49

composed of 20 slots of 0.5 ms, where one sub-frame consists of two slots. The number of

OFDM symbols in one slot Nsym depends on the chosen length of the cyclic prefix (CP) and

can be either 6 (long CP) or 7 (short CP).

Tframe = 10ms

20 slots

Tslot = 0.5ms

Tsubframe = 1ms 6 or 7 OFDM symbols

Fig 4.6: OFDM Frame structure in LTE [14]. A radio frame is divided into 20 slots of 0.5 ms

each having 6 or 7 OFDM symbols. Two slots make one sub frame, which corresponds to the

minimum downlink TTI.

4.5 Downlink OFDM Parameters:

The parameters used for downlink are listed in Table 4.1. The subcarrier frequency spacing

𝑓𝑠𝑝𝑎𝑐𝑒 =𝑓𝑠

𝑁𝐼𝐹𝐹𝑇 = 15 kHz is used, and it is always constant, hence fs and NIFFT are proportional.

The downlink parameters for fspace = 7.5 kHz are not yet defined [14]. The number of OFDM

symbols Nsym per slot depends on the length of the CP as described in section 2.2. If 128-

point IFFT and short CP is used, the first 6 OFDM symbols have a CP of 9 samples and the

last symbol a CP of 10 samples, such that the duration of the sub-frame of 0.5ms is preserved.

Not all subcarriers are occupied, in Release 7 [15] approximately 2/3 of the total frequency

band is used. According to technical specifications in Release 8 [14] the number of used

subcarriers (here denoted as NBW) can be varied. The values of NBW however are not

specified. In this project the values NBW are the same as in Release 7. Other downlink

parameters than number of FFT-points and sampling frequency are not yet determined, but

the above assumption is used for evaluation purpose in 3GPP, hence these parameters are

also used in the project.

50

Table 4.1: Downlink parameters for OFDM transmission.

Transmission BW 1.25 MHz 2.5 MHz 5 MHz 10 MHz 15 MHz 20 MHz

Subframe duration Tsub 0.5 ms

Sub-carrier spacing fspace 15 KHz

Sampling frequency fs 1.92 MHz

3.84

MHz 7.68MHz 15.36MHz

23.04

MHz 30.72MHz

FFT size NIFFT 128 256 512 1024 1536 2048

Number of occupied sub-

carriers NBW 75 150 300 600 900 1200

Number of OFDM symbols

per subframe (short/long

CP)

7/6

CP length

(µs / sample)

Short

(4.69/9)×6

(5.21/10)×1

(4.69/18)

×6 (5.21/20)

×1

(4.69/36)

×6 (5.21/40)

×1

(4.69/72)×

6 (5.21/80)×

1

(4.69/108)

×6 (5.21/120)

×1

(4.69/144)

×6 (5.21/160)

×1

Long (16.67/32) (16.67/64

)

(16.67/12

8)

(16.67/25

6)

(16.67/38

4)

(16.67/51

2)

4.6 Mapping of Subcarriers:

The subcarriers are mapped into the frequency spectrum as illustrated in Fig 4.7. According

to Table 2.1, NBW is 75/150/300/600/900/1200 when the transmission bandwidth is

1.25/2.5/5/10/15/20 MHz.

Unused 1 Nn o Nn+1 NBW Unused

Subcarriers Subcarriers

Fig 4.7: Placement of occupied subcarriers [15]. NBW and Nn are the total number of

occupied subcarriers and the number of carriers in the negative spectrum respectively.

Since the occupied subcarriers are centered around the frequency 0, half of the occupied

subcarriers are placed in the negative spectrum and the other half in the positive spectrum.

Let us denote the occupied subcarriers in the negative spectrum as {1, . . . ,Nn} and in the

positive spectrum as {Nn + 1, . . . ,NBW}, where Nn is 37/75/150/300/450/600 [14]. The

unused carriers are placed at the edges of the spectrum such that the utilized bandwidth is less

51

than the specified bandwidth. This can be based on reducing the requirements for the analog

filters at the transmitter and receiver side.

4.7 Implementation of the OFDM Transceiver:

Based on the mentioned information on the physical layer, a structure of the transmitter in

LTE is designed as illustrated on Fig 4.8. The transmitter is based on conventional OFDM

system structure. The structure of the implemented receiver is depicted in Fig 4.9.

Tx

Signal

Figure 4.8: Block diagram of the OFDM transmitter in LTE.

Rx Signal

Fig 4.9: Block diagram of the OFDM receiver in LTE.

4.7.1 Binary Source Generator:

The binary source generator generates the signal randomly. The number of the generated

binary symbols depends on the modulation scheme, i.e. the number of bits per QAM-symbol

and the number of subcarriers [14].

4.7.2 Modulation:

During modulation it is necessary to normalize the transmitted symbols in order to adjust the

signal-to-noise ratio. The normalization is achieved by scaling the symbols as listed in Table

4.2.

Bin

ary S

ourc

e

G

ener

ator

S/P

conver

ter

IFF

T

CP

i

nse

rtio

n

P

/S c

onver

ter

Ref

eren

ce

Sym

bol

Inse

rtio

n

M-Q

AM

Modula

tor

R

aw B

ER

C

om

pu

tati

on

P/S

conver

ter

FF

T

CP

R

emoval

S

/P c

onver

ter

Ref

eren

ce

Sym

bol

Rem

oval

M-Q

AM

D

emodula

tor

Chan

nel

est

ima-

tion &

Equal

iza-

tion

52

Table 4.2: Normalization factor for M-QAM modulation schemes in E-UTRA downlink [14].

Modulation Knorm

4-QAM 1

√2

16-QAM 1

√10

64-QAM 1

√64

4.8 Downlink Data Transmission:

The transmitted signal in each slot is described by a resource grid of NBW subcarriers and

Nsym OFDM symbols. In order to achieve multiple accesses, bandwidth is allocated to the

UEs in terms of resource blocks. A physical resource block, NRB consists of 12 consecutive

subcarriers in the frequency domain. In the time domain, a physical resource block consists of

Nsym consecutive OFDM symbols, Nsym is equal to the number of OFDM symbols in a slot.

The resource block size is the same for all bandwidths; hence the number of available

physical resource blocks depends on the bandwidth. Depending on the required data rate,

each UE can be assigned one or more resource blocks in each transmission time interval of 1

ms. The scheduling decision is done at the NodeB. The user data is carried on the Physical

Downlink Shared Channel (PDSCH). Downlink control signaling on the Physical Downlink

Control Channel (PDCCH) is used to transport the scheduling decisions to individual UEs.

The PDCCH is placed in the first OFDM symbols of a slot [14].

4.8.1 Modulation:

According to the working assumptions for PDSCH in Release 8, the transmitted bits are

modulated using quadrature amplitude modulation (QAM). The available modulation

schemes are 4-QAM, 16-QAM, and 64-QAM [15].

4.8.2 Downlink reference signal structure:

The downlink reference signal structure is important for cell search and channel estimation.

Resource elements in the time-frequency domain are carrying the reference signal sequence,

which is predefined for each cell. The reference symbols are placed in the first OFDM

53

symbol of one slot and on the third last OFDM symbol. The spacing between the reference

symbols is always 6 subcarriers [15] and the norm is always 1 no matter which modulation

scheme is utilized for the data symbols. In the LTE the eNodeBs and UEs can have 2 or 4

antennas and when two or more transmitter antennas are applied, the reference symbols are

transmitted such that they are orthogonal in space.

Subcarriers

……. 1st OFDM symbol

…….

…….

…….

…….

……. 6th OFDM symbol

Reference symbol vacant resource element

Antenna 1

Subcarriers

……… 1st OFDM symbol

………

………

………

………

……… 6th OFDM symbol

Antenna 2

Fig 4.10: The reference symbol structure for one slot with 6 OFDM symbols using two

antennas. Note that only the used subcarriers are depicted. In this thesis we consider one

antenna and makes use of the reference symbol structure depicted for antenna 1.

The orthogonality in space is obtained by letting all other antennas be silent in the resource

element in which one antenna transmits a reference symbol [14]. Figure 2.4 shows the

positions of the reference symbols for transmission with two antennas as an example. When

X X

X X X

X X X

X X

O

ne

Slo

t D

urati

on

TS

lot

O

ne

Slo

t D

ura

tio

n

TS

lot

54

antenna 1 transmits a reference symbol, antenna 2 is silent and vice versa. This thesis

considers one antenna and makes use of the reference symbol structure depicted for antenna 1

on Fig 4.10. The reference signal sequence also carries the cell identity. The reference signal

sequence is generated as a symbol-by-symbol product of an orthogonal sequence (OS) ROS

∈ C340×2 (3 different sequences are predefined) and a pseudo-random sequence (PRS)

RPRS ∈ R340×2 (170 different sequences are predefined).

Each cell identity corresponds to a unique combination of one orthogonal sequence ROS and

one pseudorandom sequence RPRS, allowing 510 different cell identities [14]. Frequency

hopping can also be applied to the downlink reference signals. The frequency hopping pattern

has a period of one frame duration.

4.8.3 Cell search:

During cell search, different types of information need to be identified by the UE such as

radio frame timing, frequency, cell identification, overall transmission bandwidth, antenna

configuration, cyclic prefix length. Besides the reference symbols, synchronization signals are

therefore needed during cell search. In E-UTRA (Evolved UMTS Terrestrial Radio Access)

the synchronization acquisition and the cell group identifier are obtained from different

synchronization channels (SCH). A primary synchronization channel (PSCH) for

synchronization acquisition and a secondary synchronization channel (SSCH) for cell group

identification have a predefined structure. They are transmitted on the 72 subcarriers centered

around subcarrier at frequency f = 0 within the same predefined slots (1st and 11th slot in one

frame). PSCH and SSCH are however placed on the second last and third last OFDM symbol

respectively [14]. Hence cell search is always performed using the 72 central subcarriers

independent of the overall transmission bandwidth.

4.9 Latency Requirement:

The user plane latency should be below 5 ms. For the downlink case the user plane is defined

in terms of a one-way transit time between a packet being available at the IP layer at the

NodeB and the availability of this packet at IP layer at the UE. The NodeB provides the

interface towards the core network. From channel estimation point of view a latency below 5

ms results in a block length less than 5ms for channel estimation purpose [14].

55

Chapter 5

PAPR Calculation for SCFDMA & OFDMA

5.1 Introduction:

In order to transition from today's 3rd generation (3G) communications systems to meet the

needs of 4th generation (4G) systems, the 3rd Generation Partnership Project (3GPP) has

released the Long Term Evolution (LTE) specification. Among the numerous differences

between these generations are changes in the physical layer, specifically in the modulation

and multiple access schemes. While its parent generation relied on variations of Code

Division Multiple Access (CDMA), LTE implements Orthogonal Frequency Division

Multiplexing (OFDM) for its downlink and Single-Carrier Frequency-Division Multiple

Access (SC-FDMA) for its uplink. The purpose of this project is to investigate the reasoning

for this discord between uplink and downlink modulation schemes; specifically, why

Orthogonal Frequency Division Multiple-Access (OFDMA) was not used as the uplink.

OFDMA and SC-FDMA are the multiple-access versions of OFDM and a similar modulation

scheme, Single-Carrier Frequency-Domain Equalization (SC-FDE). In order to compare the

differences between the multiple-access methods, it is important to first cover the differences

between the modulation schemes.

5.2 SCFDMA:

For uplink, SC-FDMA is selected as a basic multiple access scheme for LTE physical

layer. SC-FDMA is also a multi-carrier scheme that re-uses many of the functional blocks of

OFDMA. The main advantage of SC-FDMA is its low PAPR which is a useful parameter for

uplink [15].

OFDMA has small frequency channels, each of which is assigned to a specific symbol. These

symbols are transmitted simultaneously as in figure 2.4. As it was mentioned before, prior to

transmission over the air all the multiple frequency channels are added together which creates

an uncontrollable signal with high peaks. To handle this uncontrollable signal we have to use

more power. Using more power is not a problem for downlink however it is one of the main

issues in uplink since it increases mobile costs and decreases battery life. Because OFDMA

transmits many symbols at a time, we need more power for effective transmission. So as a

56

solution, SC-FDMA decrease the number of symbols transmitted per time, which brings the

uncontrollable signal to a manageable levels. Use of wider bandwidth reduces symbol

transmission time. For more clarity this can be seen in Fig 5.1 [16].

Bs Hz OFDMA

Bs Hz SC-FDMA

T seconds

Fig 5.1: Difference between channel representations between OFDMA and SCFDMA.

3GPP is working on a modified form of OFDMA for uplink transmissions in LTE (long term

evolution) of cellular systems. An alternative approach was sought known as Single Carrier

Frequency Division Multiple Access (SCFDMA). As in OFDMA, the transmitters in an

SCFDMA system use different orthogonal frequencies (subcarriers) to transmit information

symbols. However, they transmit the subcarriers sequentially, rather than in parallel. This

reduces envelope fluctuation relative to OFDMA. So SCFDMA has inherently low PAPR

than OFDMA. But now it has the problem of ISI. It can be removed by adaptive channel

equalization algorithms in the frequency domain [18]. Time domain equalization is very

complex because of long channel impulse response in time domain and large tap size of

filters. But using Discrete Fourier Transform (DFT) in frequency domain it‟s much easier

because DFT size doesn‟t increase linearly with channel response.

57

5.2.1 Block diagram of SC-FDMA:

SC-FDMA uses an additional N-point DFT stage at transmitter and an N-point IDFT stage at

receiver. The basic block diagram of SC-FDMA transmitter and receiver is shown in Fig 5.2.

The input to transmitter is a stream of modulated symbols.

In SC-FDMA, the data is mapped into signal constellation according to the QPSK, 16-QAM,

or 64-QAM modulation, depending upon the channel conditions similarly as in OFDMA.

Whereas, the QPSK/QAM symbols do not directly modulate the subcarriers. These symbols

passes through a serial to parallel converter followed by a DFT block that produce discrete

frequency domain representation of the QPSK/QAM symbols. Pulse shaping is followed by

DFT element, but it is optional and sometimes needs to shape the output signal from DFT. If

pulse shaping is active then in the actual signal, bandwidth extension occurs. The discrete

Fourier symbols from the output of DFT block are then mapped with the subcarriers in

subcarrier mapping block. After mapping this frequency domain modulated subcarriers pass

through IDFT for time domain conversion. The rest of transmitter operation is similar as

OFDMA.

Carrier

Tx

Rx

Carrier

Fig. 5.2: Tx and Rx structure of SCFDMA (M > N)

SC-FDMA receiver is shown in Fig 5.2. It is almost same as conventional OFDMA with

additional blocks of subcarrier demapping, IDFT and optional shaping filter. This filter

corresponds to the spectral shaping used in the transmitter. The subcarrier demapping of M-

mapped subcarrier results N-discrete signals. In the end, IDFT converts the SC-FDMA signal

S/P

Conver- sion

N-FFT

Sub-

carrier mapping

M-IFFT

P/S

Conver- sion

Channel

Add

CP

P/S

Conver-

sion

N-IFFT

Sub-

carrier demapping

M-FFT

S/P

Conver- sion

Remove CP

58

to the signal constellation. In uplink transmission of LTE, there are some additional data

carrying signals such as; reference signal, random access preamble and control signal etc.

These signals are characterized as sequence signaling and have constant amplitude with zero

autocorrelation. In contrast with data carrying signals, these signals are not part of SC-FDMA

modulation scheme [19].

5.3 OFDM:

The choice of an appropriate modulation and multiple-access technique for mobile wireless

data communications is critical to achieving good system performance. In particular, typical

mobile radio channels tend to be dispersive and time-variant, and this has generated interest

in multicarrier modulation. In general, multicarrier schemes subdivide the used channel

bandwidth into a number of parallel sub-channels as shown in Fig 5.3(a). Ideally the

bandwidth of each sub-channel is such that they are each non-frequency-selective (i.e. having

a spectrally-flat gain); this has the advantage that the receiver can easily compensate for the

sub-channel gains individually in the frequency domain.

(a)

Saving in spectrum

(b)

Fig 5.3: Spectral efficiency of OFDM compared to classical multicarrier modulation [5]:

(a) classical multicarrier system spectrum; (b) OFDM system spectrum.

59

Orthogonal Frequency Division Multiplexing (OFDM) is a special case of multicarrier

transmission which is highly attractive for implementation. In OFDM, the non-frequency-

selective narrowband sub-channels into which the frequency-selective wideband channel is

divided are overlapping but orthogonal, as shown in Figure 5.3(b). This avoids the need to

separate the carriers by means of guard-bands, and therefore makes OFDM highly spectrally

efficient. The spacing between the sub-channels in OFDM is such they can be perfectly

separated at the receiver [5].

This allows for a low-complexity receiver implementation, which makes OFDM attractive for

high-rate mobile data transmission such as the LTE downlink. It is worth noting that the

advantage of separating the transmission into multiple narrowband sub-channels cannot itself

translate into robustness against time-variant channels if no channel coding is employed [5].

5.4 OFDMA:

Like OFDM, OFDMA (Orthogonal frequency division multiple access) employs multiple

closely spaced sub-carriers, but the subcarriers are divided into groups of subcarriers. Each

group is named a sub channel. The sub-carriers that form a sub-channel need not be adjacent.

In the downlink, a sub channel may be intended for different receivers. In the uplink, a

transmitter may be assigned one or more sub-channels. Sub-channelization defines sub-

channels that can be allocated to subscriber stations depending on the channel conditions and

data requirements. Using sub-channelization, within the same time slot a mobile base station

can allocate more transmit power to user devices with low SNR and vice-versa. This also

save a user device transmit power as it can concentrate power only on certain sub-channels

allocated to it [6].

Apart from having certain advantages it could have from OFDM, the OFDMA waveform

exhibits very pronounced envelop deviation resulting in a high PAPR (peak to average

power ratio). And the signals having high PAPR requires highly linear power amplifiers like

class A, class AB etc. to avoid excessive inter modulation distortion. To achieve this

linearity, the amplifiers have to operate with a large back off from their peak power, resulting

in decreased power efficiency. Another problem with OFDMA is, while up linking there is an

introduction of frequency offset among the different terminals that transmit simultaneously,

destroying the concept of orthogonality [17].

60

OFDM

Sub-carriers

Time

OFDMA

Sub-channels

Time

Fig 5.4: Difference between OFDM and OFDMA

Fig 5.5: Sensitivity of OFDM subcarriers with Carrier

0 5 10 150.8

1

1.2

1.4

1.6

1.8

2Consecutive OFDM Subcarriers in Time domain

Subcarrier index

Am

plit

ude

61

Fig 5.6: OFDM transmission spectrum

5.4.1 Block diagram of OFDMA:

As we move ahead for higher generation of mobile technology we always encounter the need

of high speed communication. Various multicarrier multiplexing techniques have evolved to

meet these demands, some of them being code division multiple access (CDMA) and

orthogonal frequency division multiplexing (OFDM). OFDM utilizes orthogonal subcarriers

to transmit information parallel. In a conventional serial data transmission, the symbols are

transmitted sequentially, with the frequency spectrum of each data symbol allowed to occupy

the entire bandwidth. In OFDM, the data is divided among large number of closely spaced

carriers (frequency division multiplexing). This is not a multiple access technique, since no

common medium is to be shared. Here only small amount of data is carried by each carrier,

reducing the ISI significantly. Many modulation schemes could be used to modulate the data

at a low bit rate onto each carrier. Bandwidth occupied by the OFDM systems being greater

than the correlation bandwidth of the fading channel gives it an extra edge over serial

communication [6].

0 50 100 150 200 250 3000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8OFDM Transmission Spectrum

Subcarriers

Am

plit

ude

62

Carrier

Info

Symbol

Estima-

ted symbol

Carrier

Fig 5.7: Block Diagram of OFDMA

Dividing an entire channel into many narrow sub bands makes the frequency response

become relatively flat in each individual sub band. Since each sub channel covers only a

small fraction original bandwidth, equalization is quite simple (differential encoding may

even make equalization unnecessary) [19]. Use of guard interval, system‟s reaction to delay

spread can be reduced. OFDM can be finally said as a form of multicarrier modulation where

its carrier spacing is carefully selected so that each subcarrier is orthogonal to the other

subcarriers. The block diagram of OFDMA transmitter & receiver is shown in Fig 5.7.

5.5 Description of Problem Statement:

As it‟s clear from the figure many blocks are common to both OFDMA and SCFDMA. At

the input to the transmitter, a baseband modulator transforms the binary input to a multilevel

sequence of complex numbers xn in one of several possible modulation formats including

quaternary PSK (QPSK), 16-level quadrature amplitude modulation (16-QAM) and 64-QAM

etc. Then serial bit stream is converted to parallel bit stream of N data points. The first step is

to produce a frequency representation Xk of the input symbols. It then maps each of the N

DFT outputs to one of the M (>N) orthogonal subcarriers that can be transmitted, where

M=N*Q ,Q is the bandwidth expansion factor of symbol sequence.

Coding &

modulation S/P

conversion N-IFFT CP

insertion

P/S

conversion

Channel

S/P

conversion

CP

extraction

FFT P/S conversion

Decoding &

demodulation

63

The mapping can be of two types:

1. LFDMA

2. IFDMA

In Localized FDMA each terminal uses a set of adjacent subcarriers to transmit its symbols.

Thus the bandwidth of an LFDMA transmission is confined to a fraction of the system band-

width.

In Interleaved FDMA the subcarriers used by a terminal are spread over the entire signal

band.

Fig 5.8 shows two type of mapping in the frequency domain. There are three terminals, each

transmitting symbols on four subcarriers in a system with a total of 12 subcarriers. SCFDMA

is better against frequency selective fading because its information is spread across the entire

signal band. On the other hand, LFDMA can potentially achieve multi-user diversity in the

presence of frequency selective fading if it assigns each user to subcarriers in a portion of the

signal band where that user has favorable transmission characteristics [17]. After sub-carrier

mapping we get the set of M complex sub-carrier amplitudes X1 frequency domain. Then M-

DFT is performed to convert them into M time domain signals xm . Each xm then modulates a

single frequency carrier and all the modulated symbols are transmitted sequentially.

Terminal 1 Terminal 2 Terminal 3

Interleaved Localized

Fig 5.8: Sub-carrier mapping for 3 users, 12 sub-carriers and 4 sub-carriers per user.

64

5.6 Mathematical Calculation for PAPR:

Let the data block of length N be represented by a vector X= [X0,X1,….,XN-1]T. Duration of

any symbol XK in the set X is T and represents one of the sub-carriers set. As the N sub-

carriers chosen to transmit the signal are orthogonal, so we can have fn = n∆f, where n∆f =

1/NT and NT is the duration of the OFDM data block X. The complex data block for the

OFDM signal to be transmitted is given by

𝑥 𝑡 =1

√𝑁 𝑥𝑛𝑒

𝑗2𝜋𝑛∆𝑓𝑡𝑛=𝑁−1𝑛=0 , 0 ≤ 𝑡 ≤ 𝑁𝑇

The PAPR of the transmitted signal is defined as

PAPR =𝑚𝑎𝑥0≤𝑡<𝑁𝑇 |𝑥(𝑡)|2

1𝑁𝑇 |𝑥 𝑡 |2𝑑𝑡

𝑁𝑇

0

The cumulative distribution function (CDF) is one of the most regularly used parameters,

which is used to measure the efficiency of any PAPR technique. Normally, the

complementary CDF (CCDF) is used instead of CDF, which helps us to measure the

probability that the PAPR of a certain data block exceeds the given threshold [6].

The CDF of the PAPR of the amplitude of a signal sample is given by;

𝐹 𝑧 = 1 − 𝑒𝑧

The CCDF of the PAPR of the data block is desired in our case is to compare outputs of

various reduction techniques. This is given by:

𝑃 𝑃𝐴𝑃𝑅 > 𝑧 = 1 − 𝑃 𝑃𝐴𝑃𝑅 ≤ 𝑧

= 1 − 𝐹 𝑧 𝑁

= 1 − (1 − 𝑒−𝑧)𝑁 (5.1)

Fig 5.9 shows PAPR distribution for different numbers of OFDM subcarriers.

65

Fig 5.9: PAPR distribution for different numbers of OFDM subcarriers [3].

5.7 Comparison of PAPR for OFDMA And SCFDMA:

SC-FDMA offers similar performance and complexity as OFDM. However, the main

advantage of SC-FDMA is the low PAPR (peak-average-power ratio) of the transmit signal.

PAPR is defined as the ratio of the peak power to average power of the transmit signal. As

PAPR is a major concern at the user terminals, low PAPR makes the SC-FDMA the preferred

technology for the uplink transmission. PAPR relates to the power amplifier efficiency at the

transmitter, and the maximum power efficiency is achieved when the amplifier operates at the

saturation point. Lower PAPR allows operation of the power amplifier close to saturation

resulting in higher efficiency. With higher PAPR signal, the power amplifier operating point

has to be backed off to lower the signal distortion, and thereby lowering amplifier efficiency.

As SC-FDMA modulated signal can be viewed as a single carrier signal, a pulse shaping

filter can be applied to transmit signal to further improve PAPR [18].

5.8 Significance of Pulse Shaping Filter in PAPR Analysis:

In digital communication, pulse shaping is one of the methods of changing the waveform of

the transmitted pulse. It helps in limiting the effective bandwidth of the transmission and also

the ISI caused by the channel can also be kept in control. Nyquist ISI criterion is the

commonly used criterion for evaluation of filters. Examples of pulse-shaping filters are [6]:

2 4 6 8 10 12 14

100

101

102

103

104

105

z------------

P(P

AP

R>

z)-

----

----

---

N=16

N=32

N=128

N=512

N=2048

66

- Sinc filter

- Raised cosine filter

- Gaussian filter

5.8.1 Sinc filter:

A sinc filter is an idealized filter that removes all frequency components above a given

bandwidth, leaves the low frequencies alone and has linear phase. The filter's impulse

response is a sinc function in the time domain, and its frequency response is a rectangular

function. The impulse response of such a filter is given by [19];

h t = 2Bsinc(2Bt)

Where, B = arbitrary cutoff frequency.

Fig 5.10: The Transfer Function of Sinc Filter

-5 -4 -3 -2 -1 0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Plot of Sinc Filter Transfer Function

t---->

h(t

)---

->

67

5.8.2 Raised cosine filter:

Raised-cosine filter is practical to implement and it is in wide use. It has a parametrisable

excess bandwidth, so communication systems can choose a trade-off between a more

complex filter and spectral efficiency. The raised-cosine filter is an implementation of a low-

pass Nyquist filter, i.e., one that has the property of vestigial symmetry. This means that its

spectrum exhibits odd symmetry about 1/2T, where T is the symbol-period of the

communications system.

Its frequency-domain description is a piecewise function, given by [20].

𝐻 𝑓 =

𝑇, 𝑓 ≤

1 − 𝛼

2𝑇𝑇

2 1 + cos

𝜋𝑇

𝛼 𝑓 −

1 − 𝛼

2𝑇 ,

1 − 𝛼

2𝑇< 𝑓 ≤

1 + 𝛼

2𝑇

0, 𝑜𝑡𝑕𝑒𝑟𝑤𝑖𝑠𝑒

and characterized by two values‟, “α” the roll-off factor, and “T”, the reciprocal of the

symbol-rate.

Fig 5.11: The Transfer Function of Raised Cosine Filter

0 5 10 15 20 25 30 35 40 45-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

n(Samples)

Am

plit

ude

Plot the transfer function of Raised Cosine filter

alpha=0

alpha=0.5

alpha=1

68

5.8.3 Gaussian filter:

A Gaussian filter is a filter whose impulse response is a Gaussian function. Gaussian filters

are designed to give no overshoot to a step function input while minimizing the rise and fall

time. This behavior is closely connected to the fact that the Gaussian filter has the minimum

possible group delay.

The one-dimensional Gaussian filter has an impulse response given by [21];

g x = a

π . e−a.x2

Fig 5.12: The Transfer Function of Gaussian Filter

5.9 PAPR Reduction Techniques for OFDM Signal:

Many techniques have been studied for reducing the PAPR of a transmitted OFDM signal.

Although no such techniques are specified for the LTE downlink signal generation, an

overview of the possibilities is provided below. In general in LTE the cost and complexity of

generating the OFDM signal with acceptable Error Vector Magnitude (EVM) is left to the

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2Plot of Gaussian Filter Transfer Function

x---->

g(x

)---

->

69

eNodeB implementation. As OFDM is not used for the LTE uplink, such considerations do

not directly apply to the transmitter in the UE.

Techniques for PAPR reduction of OFDM signals [5] can be broadly categorized into three

main concepts:

• Clipping and Filtering

• Selected Mapping

• Pre-coding Technique.

5.9.1 Clipping and filtering:

The time-domain signal is clipped to a predefined level. This causes spectral leakage into

adjacent channels, resulting in reduced spectral efficiency as well as in-band noise degrading

the bit error rate performance. Out-of- band radiation caused by the clipping process can,

however, be reduced by filtering. If discrete signals are clipped directly, the resulting clipping

noise will all fall in band and thus cannot be reduced by filtering. To avoid this problem, one

solution consists of oversampling the original signal by padding the input signal with zeros

and processing it using a longer IFFT. The oversampled signal is clipped and then filtered to

reduce the out-of-band radiation.

We have chosen a concatenation of interleaving with repeated clipping and filtering using

optimum value of Υ and frequency domain filtering. A schematic diagram of the proposed

OFDM transmitter is shown in Fig 5.13.

Input

Fig 5.13: Simplified clipping and filtering with Optimum value of Υ

First, the interleaving approach is used and the signal with lowest PAPR is then passed

through clipping and filtering method. The intention to combine these two methods is to

Encoder

FFT Out-of-Band

Removal

Interleaving

(W)

IFFT (with Over

sampling)

Clipping

IFFT

70

obtain signal with lower PAPR than in the case of interleaving method and with lower

distortion (and thus lower bit error rate) than in the case of standalone Repeated clipping and

filtering. As both methods used in the combination suffer from high complexity, the main

disadvantage of the combined method is above all the complexity. Moreover, side

information (SI) to identify the interleaver with lowest PAPR has to be sent to receiver for

each OFDM symbol. Without this side information, it is not possible to decode the data. As

the correct decoding of side information is fundamental for the performance of OFDM

modem, the side information can thus be either mapped using modulation with lower number

of states or encoded by FEC. The complexity of the presented combined method can be

dramatically reduced using the recently proposed method Simplified clipping and filtering

instead of the repeated clipping and frequency domain filtering method [22]. The clipping

and frequency domain filtering of the input OFDM signal is shown in Fig 5.14.

Sc (1)

Sc (2)

Input 0 Output

0

OFDM OFDM

Sc (9)

Fig 5.14: The clipping and frequency domain filtering of the input OFDM signal.

The modified CF algorithm can be stated as below [22]:

1. Convert the OFDM symbol to time domain as (n) = IFFT (XK).

2. Calculate the optimum value of clipping level and Clip (n) to the threshold A.

3. Convert (n) to frequency domain to obtain Xk by doing FFT of x(n).

4. Clipped the OFDM signal using optimum value and pass through a frequency domain

filter based upon Hanning Windowing to reduce the PAPR of OFDM signal.

5. Convert to time domain and transmit the OFDM Signal.

Clip

FFT

Filtering

IFFT

71

5.9.2 Selected mapping:

Multiple transmit signals which represent the same OFDM data symbol are generated by

multiplying the OFDM symbol by different phase vectors. The representation with the lowest

PAPR is selected. To recover the phase information, it is of course necessary to use separate

control signaling to indicate to the receiver which phase vector was used [5].

The selective mapping (SLM) technique can be applied to SFBC-OFDM systems with two

transmitter antennas and Almouti coding scheme without changing the orthogonality of space

frequency coding. In this method, the optimum phase sequence is applied to the OFDM

frames of two antennas such that the SFBC structure remains constant. In the SLM method,

D different representations of the OFDM frame are generated, and that with minimum PAPR

is transmitted. The main disadvantage of this system is that it increases the complexity of the

system by adding a no of terms [23].

Fig 5.15: Block diagram of SFBC-OFDM transmitter with two transmitter antennas and the

selective mapping (SLM) method for PAPR reduction

72

5.9.3 Pre-coding technique:

These techniques consist of finding the code words with the lowest PAPR from a set of

codeword to map the input data. A look-up table may be used if N is small. It is shown that

complementary codes have good properties to combine both PAPR and forward error

correction. The latter two concepts are not applicable in the context of LTE; selected

mapping would require additional signaling, while techniques based on codeword selection

are not compatible with the data scrambling used in the LTE downlink [5].

A design procedure for good pre-coding schemes is very important. It is possible to reduce

the PAPR of OFDM signals by pre-coding without destroying the detectability property of

the different symbols of the OFDM block . We can use any band efficient modulation like

BPSK, QPSK etc [24].

Noise

Fig 5.16: Block diagram of pre-coding technique for PAPR reduction of OFDM signal

Modulation S/P

conversion IFFT CP

insertion

CFBD

Channel

Turbo

Equalizer Reverse Pre coding

FFT P/S

conversion

Demodulation

Pre

coding

73

Chapter 6

Characteristics of Mobile Radio Channel

6.1 Introduction:

A channel ideally should contain only one copy of transmitted signal coming in the line of

Sight path from transmitter to receiver, so there would be a perfect reconstruction of original

signal. But in reality this doesn‟t happen. Rather the received signal consists of a

combination of attenuated, reflected, refracted and diffracted replicas of original signal . So

the channel gets faded both in time and frequency domain. Also the channel adds noise to the

signal which further complicates the procedure. If there‟s relative motion in the channel then

frequency shift occurs (Doppler Effect). Knowledge of all these phenomena is necessary in

order to model the channel for radio wave propagation [6].

6.2 Types of Fading:

The propagation model mainly focuses on predicting the average received signal strength at a

given T-R (Transmitter-Receiver) separation and radial variation for the specified separation.

So we can classify fading into two types: Large-scale fading and Small scale fading. Large

scale fading attributes for variation in signal strength over large T-R separation distances.

Large scale models try to find out mean signal power attenuation or path loss due motion

over large area around transmitter or receiver. Small scale fading characterizes rapid

fluctuation of received signal strength over short T-R separations and for short period of time.

So the signal is a sum of many signals coming from different directions with different

attenuation which brings dramatic changes in signal amplitude and phase. Various models

exist in literature for large scale fading. They are like empirical models such as Okumura

model, Hata model, cost 136 model etc; indoor models like Log-distance path loss model,

Ericsson multiple breakpoint model, Attenuation factor model etc. Large scale fading models

find applications in wireless network planning for an area and modeling path loss over a large

distance. So, large scale path loss models are more important for cell site planning but less for

communication system design. So we will next discuss small scale fading in a little detail.

74

6.3 Small-Scale Fading:

Fading is caused by interference between two or more forms of transmitted signal that arrive

at receiver at slightly different times. These components are called multipath components.

The complete set of multi paths has to be known for modeling the multipath channel. Each

path is characterized by three parameters namely delay, attenuation and phase shift. The

discrete time variant channel impulse response of the multipath channel is given by [10]

𝑕 𝜏, 𝑡 = 𝛼𝑚 𝑡 𝑒−𝑗2𝜋𝑓𝑐𝜏𝑚 𝑡 𝛿(𝑡 − 𝜏𝑚 (𝑡))𝑚

where,

𝛼𝑚 𝑡 is the attenuation in the mth

path at time t

𝜏𝑚 (𝑡) is the propagation delay in the mth path at time t

𝑒−𝑗2𝜋𝑓𝑐𝜏𝑚 𝑡 is the phase shift for carrier frequency fc for mth

multipath component

( ) is the dirac delta function

The above model takes into all the modifications that a multipath channel can make to the

signal.

6.4 Critical Channel Parameters:

Two kinds of spreading occur when a signal passes through a channel. They are

- Multipath delay spread

- Doppler spread

Multipath delay spread occurs because of time dispersive nature of the channel in local area.

Because delayed versions of original signal is superimposed at the receiver so the received

signal spreads in time domain or shows time dispersion. Parameter used to describe this is

rms delay spread denoted by σt. This is defined as the standard deviation value of the delay

weighed proportional to the energy of waves. Coherence bandwidth (f0) is analogous to delay

spread used to characterize the channel in frequency domain. It‟s the statistical measure of

the range of frequencies for which all components are passed with equal gain and linear

phase. So we can say

𝑓0 ∞1

𝜎𝜏

75

Doppler spread occurs because of relative motion between transmitter and receiver or motion

of objects in the channel. So it occurs because of time variance nature of the channel.

Because of relative motion Doppler shift of frequency occurs which broadens the signal in

frequency domain or shows frequency dispersion. Parameter used to characterize this is

Doppler spread denoted by fd. This is defined as the range of frequencies over which the

Doppler spectrum is non-zero. Coherence time (Tc) is the time domain dual of Doppler

spread and used to characterize the time varying nature of the frequency depressiveness of

channel. It‟s the statistical measure of time duration over which the channel impulse

response is essentially constant. So that we can write

𝑇𝑐 ∞1

𝑓𝑑

6.5 Types of Small-Scale Fading:

Small-scale fading occurs due to two propagation mechanisms as described above [25]. They

are

Due to multipath delay spread

- Flat fading

- Frequency selective fading

Due to Doppler spread

- Fast fading

- Slow fading

If the bandwidth of the channel is less than range of frequency over which the channel has

constant gain and linear phase, then the signal undergoes flat fading. This type of fading is

common in literature as this is analogous to a low pass filter. After passing the spectral

characteristics of the channel remains unchanged but the gain changes with time. So in terms

of channel parameters

If fm < f0 and Ts > στ where fm = signal bandwidth and Ts = symbol period

Then the channel creates flat fading

If the channel has constant gain and linear phase response over range of frequencies which is

less than the signal bandwidth then the channel creates frequency selective fading. That‟s

different frequency components are faded differently. In time domain the received signal is a

distorted because of multiple delayed and faded instances of transmitted signal. As signal gets

76

dispersed in time domain, so channel induces ISI (Inter Symbol Interference). In terms of

channel parameters

If fm < f0 and Ts > στ

Then the channel creates frequency selective fading

In a fast fading channel, the channel characteristics change multiple times within the symbol

duration that‟s it changes at a rate higher than that of the transmitted signal. So this causes

frequency dispersion which happens because of high Doppler spreading. We can say low data

rate signals have more chance of being fast faded. Thus

The signal suffers fast fading if

Ts > Tc and fm < fd

In a slow fading channel, the channel impulse response change at a rate much lower than that

of the transmitted signal. In time domain the channel characteristics remain almost constant

during one symbol time. The Doppler spread here is less as compared bandwidth of the

baseband signal. Thus

The signal suffers fast fading if

Ts < Tc and fm < fd

So we can say the relative motion between mobile and receiver determines the channel to be

slow fading or fast fading.

6.6 Rayleigh and Ricean Distribution:

In a multipath channel if the propagation delays due to multi paths becomes random and the

no of multi paths becomes very large, then central limit theorem applies. So the received

signal envelope becomes Gaussian and can be modeled using various distribution functions

[6].

- Rayleigh distribution:

When phase and quadrature component of received envelope are independent and Gaussian

with zero mean then the pdf of amplitude assumes Rayleigh distribution. There‟s no line of

sight path between transmitter and receiver.

The power is exponentially distributed.

Mostly used as it represents a general case.

77

Fig 6.1 shows an animated effect showing the results of passing an unmodulated carrier

through a simple two path Rayleigh fading channel. The animation shows, input (blue) and

the output (red), the phase shifts, gains, and attenuations of the output sine wave or carrier.

Fig 6.1: Rayleigh fading channel with two path sine wave input.

- Ricean distribution:

Due to deterministic dominant term at least one of in-phase and quadrature component of the

received envelope has non-zero mean. So now the pdf of received envelope assumes Ricean

distribution.

There‟s a dominant line of sight path between transmitter and receiver.

It applies to microcellular systems.

0 1 2 3 4 5 6 7 8 9 10-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

time

am

plit

ude

Rayleigh fading channel with two path sine wave input

78

Chapter 7

Channel Estimation in OFDM

7.1 Introduction:

A wideband radio channel is frequency selective and also time variant. In both the frequency

and time domain, the channel impulse response at different subcarriers, appear unequal. So

we need to estimate the state of the channel at every instant. Pilot based approaches are

widely implemented to estimate the channel characteristics and to correct the corrupt channel

due to multipath fading. We have basically two kinds of pilot arrangement depending on the

nature of channel.

7.2 Block Type of Pilot Arrangement:

The first one, block-type pilot channel estimation, is developed under the assumption of slow

fading channel, and is performed by inserting pilot tones into all subcarriers of OFDM

symbols within a specific period [6]. As the training block contains all the pilots, channel

interpolation in frequency domain is not required. So this type of pilot can be said to be

insensitive to frequency selectivity. As the coherence time is higher than the symbol period in

slow fading due to lower Doppler spread, the channel characteristics remains almost static for

one symbol block time duration. Fig 7.1 shows block-type pilot channel estimation.

7.3 Comb Type of Pilot Arrangement:

The second kind of pilot arrangement is denoted as comb-type pilot arrangement. Assuming

the payloads of the pilot arrangements are the same, the comb type pilot arrangement has

higher re-transmission rate. Thus the comb-type pilot arrangement gives better resistance to

fast fading channels. Since only few subcarriers contain the pilot signal, the channel impulse

response of non-pilot sub-carriers can be estimated by either linear, cubic or spline

interpolation of the neighboring pilot sub-carriers. We can conclude that such pilot

arrangement is sensitive to frequency selectivity. As the coherence time is less than the

symbol period in fast fading due to higher spread, the channel characteristics fluctuates many

time within one symbol block time duration. Fig 7.1 shows comb-type pilot channel

estimation.

79

Block

Pilot

Data

Frequency

Time

Block –type pilot channel estimation

Pilot

Frequency Data

S

Time

Comb-type pilot channel estimation

Fig 7.1: Two basic types of pilot arrangement for OFDM channel estimation.

7.4 Working Environment:

As we are taking a Rayleigh slow fading channel we have stressed on the various block type

pilot arrangement of channel estimation. In block-type pilot based channel estimation, OFDM

channel estimation symbols are transmitted periodically, and all the subcarriers are used as

pilots. So in our work we are using a general model for a slowly fading channel, where we

80

make use of MMSE (minimum mean square error) and LS (least square) estimator and a

method for modifications compromising between complexity and performance.

X0‟

Y0 h0

YN-1 hN-1

XN-1

‟

Fig 7.2: General estimator structure

The use of DPSK (differential phase shift keying) in OFDM systems avoids the tracking of a

time varying channel. However, this limits the number of bits per symbol and results in 3

decibels loss in SNR. If we have a channel estimator in the receiver side, multi amplitude

signaling schemes or M-ary PSK modulation schemes can be used. We have worked on

BPSK, QPSK, 16 QAM modulation schemes for this purpose. Now we will look into the

various estimation techniques in detail and compare the biasedness, complexity and

performance of each. Performance is presented both in terms of Mean Square Error (MSE)

and Symbol Error Rate (SER). The general estimator structure is shown in Fig 7.2 [26].

7.5 Mathematical Analysis of the Channel Estimators:

Let

“g” : the time domain channel vector

“h” : the frequency domain channel vector

“X” : the diagonal matrix containing mapped input symbols

“W” : white gaussian noise vector

Then output symbols in time domain are given by

Y = XFg + W = Xh + W

Where:

X = diag { x0,x1……….xN-1}

IDF

T

Transfo

rmation

DF

T

81

Y= [y0,y1…………..yN-1]T

W=[W0,W1…………..WN-1]T

h = [h0,h1,………….hN-1]T

= DFTN {g}

F = DFT transform block

7.5.1 Least Square Error (LSE) Estimation:

The LS estimator minimizes (Y-XFg)H (Y-XFg) w.r.t g

Time domain LS estimate of g is given by

ĝLS = FHX

-1Y

ĥLS = X-1

Y

So Q block in the fig. 4.2 for LS estimator is given by

QLS = (FHX

HXF)

-1

The MMSE estimator suffers from higher complexity because it requires the calculation of an

N x N matrix QMMSE, whose complexity increases with increase in N. LS doesn‟t use any

channel statistics, has low complexity but estimator gives higher mean square error.

Fig 7.3: SNR vs BER using LSE estimator for an OFDM channel.

0 5 10 15 20 25 3010

-4

10-3

10-2

10-1

100

SNR in dB

Bit E

rror

Rate

SNR vs BER using LSE estimator for an OFDM Channel

82

So we need to move on to another kind of estimator which would overcome the drawback of both the

methods. SNR vs BER using LSE estimator for an OFDM channel is shown in Fig 7.3.

7.5.2 Minimum Mean Square Error (MMSE) Estimation:

If the g is uncorrelated with W then the time domain MMSE estimator is given by [26]

ĝMMSE = RYg RYY-1

Y

where

RYg : cross-covariance matrix of Y and g

RYY : auto-covariance matrix of Y

ĥMMSE = FĝMMSE

So Q block in the fig. 4.2 for MMSE estimator is given by

QMMSE = Rgg[(FHX

HXF)

-1σn

2 + Rgg]

-1(F

HX

HXF)

-1

Rgg = auto-covariance matrix of g

SNR vs MSE for an OFDM system with MMSE / LSE estimator has been shown in Fig 7.4.

SNR vs SER for an OFDM system with MMSE / LSE estimator has been shown in Fig 7.5.

Fig 7.4: SNR vs MSE for an OFDM system with MMSE / LSE estimator.

5 10 15 20 2510

-4

10-3

10-2

10-1

SNR in DB

mean s

quare

d e

rror

PLOT OF SNR V/S MSE FOR AN OFDM SYSTEM WITH MMSE/LSE ESTIMATOR BASED RECEIVERS

MMSE

LSE

83

Fig 7.5: SNR vs SER for an OFDM system with MMSE / LSE estimator.

7.6 Modified MMSE Estimation:

A straightforward way of decreasing the complexity is to reduce the size of QMMSE. As

most of the energy in g is contained in, or near the first L taps as shown in [27] a

modification of MMSE estimator, where only the taps with significant energy are considered.

The components in Rgg corresponding to low energy taps in g are approximated to zero. So

Rgg is an L × L matrix containing the covariance of first L components of g. The DFT matrix

also needs modification for finding DFT of such matrix. Now it would be an N × L matrix by

taking only the first L columns of DFT matrix. If T denotes the modified DFT matrix, then

as shown in [23]

ĥMMSE = TQ‟MMSE THX

HY

Where, Q‟ MMSE = R

‟ gg[(T

HX

HXT)

-1σn

2 + Rgg]

-1(T

HX

HXT)

-1

As L is a very small fraction of N then the computational burden sharply decreases. As we

know the LS estimator doesn‟t use the statistics of channel only depends on input and output.

So modification to LS estimator isn‟t required as it won‟t relieve any computational burden.

5 10 15 20 25 30

10-1.5

10-1.4

10-1.3

10-1.2

SNR in DB

Sym

bol E

rror

Rate

PLOT OF SNR V/S SER FOR AN OFDM SYSTEM WITH MMSE/LSE ESTIMATOR BASED RECEIVERS

MMSE

LSE

84

Chapter 8

Simulations & Results

8.1 OFDM Signal and Its Spectrum with Guard Interval:

Fig 8.1: OFDM signal and its spectrum with guard interval (Graph on time domain)

Fig 8.2: OFDM signal and its spectrum with guard interval (Graph on frequency domain)

-80 -60 -40 -20 0 20 40 60 8010

-3

10-2

10-1

100

OFDM signal and its spectrum with Guard Interval -Graph on time domain-

abs(

z1)--

--->

f----->

-60 -40 -20 0 20 40 60-20

-15

-10

-5

0

5

10

15

20OFDM signal and its spectrum with Guard Interval -Graph on frequency domain-

f----->

Y4-

---->

85

8.2 Comparison of PAPR for OFDMA and SCFDMA for Various Parameters:

Fig 8.3: CCDF of PAPR for OFDMA & SCFDMA (N=64, M=512) with QPSK

Modulation

3 4 5 6 7 8 9 10 11 1210

-3

10-2

10-1

100

PAPR Analysis for OFDMA & SCFDMA'( N=64 & M= 512)

Pr[

PA

PR

>P

AP

R0]

PAPR[dB]

SCFDMA

OFDMA

Parameters Values

Modulation format

Q-PSK

Number of total

subcarriers (M)

512

Data block size (N)

64

System bandwidth

5 MHz

Oversampling factor

4

Number of runs

1000

86

Parameters Values

Modulation format

Q-PSK

Number of total

subcarriers (M)

256

Data block size (N)

64

System bandwidth

5 MHz

Oversampling factor

4

Number of runs

1000

Fig 8.4: CCDF of PAPR for OFDMA & SCFDMA (N=64, M=256) with QPSK Modulation

3 4 5 6 7 8 9 10 11 1210

-3

10-2

10-1

100


Pr[

PA

PR

>P

AP

R0]

PAPR[dB]

SCFDMA

OFDMA

87

Parameters Values

Modulation format

Q-PSK

Number of total

subcarriers.

128

Data block size

64

System bandwidth

5 MHz

Oversampling factor

4

Number of runs

1000

Fig 8.5: CCDF of PAPR for OFDMA & SCFDMA (N=64, M=128) with QPSK Modulation.

3 4 5 6 7 8 9 10 11 1210

-3

10-2

10-1

100


Pr[

PA

PR

>P

AP

R0]

PAPR[dB]

SCFDMA

OFDMA

88

Fig 8.6: CCDF of PAPR for OFDMA & SCFDMA (N=64, M=512) with 16 QAM

Modulation.

3 4 5 6 7 8 9 10 1110

-3

10-2

10-1

100

PAPR Analysis for OFDMA & SCFDMA'( N=64& M= 512)

Pr[

PA

PR

>P

AP

R0]

PAPR[dB]

SCFDMA

OFDMA

Parameters Values

Modulation format

16-QAM

Number of total

subcarriers.

512

Data block size

64

System bandwidth

5 MHz

Oversampling factor

4

Number of runs

1000

89


Modulation.

3 4 5 6 7 8 9 10 1110

-3

10-2

10-1

100


Pr[

PA

PR

>P

AP

R0]

PAPR[dB]

SCFDMA

OFDMA

Parameters Values

Modulation format

16-QAM

Number of total

subcarriers.

256

Data block size

64

System bandwidth

5 MHz

Oversampling factor

4

Number of runs

1000

90


Modulation.

3 4 5 6 7 8 9 10 1110

-3

10-2

10-1

100


Pr[

PA

PR

>P

AP

R0]

PAPR[dB]

SCFDMA

OFDMA

Parameters Values

Modulation format

16-QAM

Number of total

subcarriers.

128

Data block size

64

System bandwidth

5 MHz

Oversampling factor

4

Number of runs

1000

91


Modulation.

2 3 4 5 6 7 8 9 1010

-3

10-2

10-1

100


Pr[

PA

PR

>P

AP

R0]

PAPR[dB]

SCFDMA

OFDMA

Parameters Values

Modulation format

16-QAM

Number of total

subcarriers.

128

Data block size

16

System bandwidth

5 MHz

Oversampling factor

4

Number of runs

1000

92

The above figures clearly shows that the CCDF of PAPR for OFDMA signal contains high

PAPR and the CCDF of PAPR for SCFDMA signal contains low PAPR. PAPR comparison

between OFDMA and SC-FDMA showed that low PAPR makes the SC-FDMA the most

preferred technology for the uplink transmission in LTE system.

8.3 Investigation of Clipping & Filtering Method as PAPR Reduction

Technique for OFDM Signals:

PERFORMANCE CHARACTERISTICS:

Transmitted Data Phase Representation:

The data phase representation of 1*128 randomly generated data points in the transmitter

section is shown above.

Fig 8.10: Transmitted Data Phase Representation

Scatter Plot : Scatter plot help in the representation of the modulated signal in the signal

space by plotting its in-phase components against its quadrature phase.

0 20 40 60 80 100 120 1400

0.5

1

1.5

2

2.5

3

Data Points

transm

itte

d d

ata

phase r

epre

senta

tion

Transmitted Data "O"

93

„M‟ represents the alphabet size and must be an integer power of 2.Since QPSK modulation

technique is being applied therefore the above figure shows the M = 4, i.e, quadrature phase

components.

Fig 8.11: The representation of the modulated signal (QPSK)

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Q

uadra

ture

In-Phase

MODULATED TRANSMITTED DATA

94

Time versus Amplitude plot:

In clipped OFDM signal shown above, the amplitude varies from -0.4 to +0.4 whereas in

unclipped OFDM signal it may exceed this average value.

Fig 8.12: Unclipped OFDM signal

Fig 8.13: Clipped OFDM signal

0 50 100 150-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time

Am

plitu

de

Unclipped OFDM Signal

0 50 100 150-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time

Am

plitu

de

clipped OFDM Signal

95

Unclipped and clipped OFDM signal after passing through high power amplifier:

To show the effect of High Power Amplifier (H.P.A.), random complex noise is added when

the power exceeds the average value ,i.e., -0.4 to +0.4 otherwise no addition is done.

Fig 8.14: Unclipped OFDM signal after passing through H.P.A

Fig 8.15: Clipped OFDM signal after passing through H.P.A

0 50 100 150-4

-3

-2

-1

0

1

2

Time

Am

plitu

de

Unclipped OFDM Signal after HPA

0 50 100 150-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time

Am

plitu

de

clipped OFDM Signal after HPA

96

Comparison between data phase representation of transmitted OFDM signal received

unclipped OFDM signal:

When the data phase representation of the transmitted OFDM signal is compared to that of

data phase representation of the received unclipped OFDM signal, it is found that only few

data points gets matched.

Fig 8.16: Comparison between Transmitted Data Phase Representation & Received unclipped

OFDM signal

0 20 40 60 80 100 120 1400

0.5

1

1.5

2

2.5

3

Data Points

trans

mitt

ed d

ata

phas

e re

pres

enta

tion


0 20 40 60 80 100 120 1400

0.5

1

1.5

2

2.5

3

Data Points

rece

ived

dat

a ph

ase

repr

esen

tatio

n

Received Unclipped OFDM Signal "X"

97

Comparison between data phase representation of transmitted OFDM signal received

clipped OFDM signal:

When the data phase representation of the transmitted OFDM signal is compared to that of

data phase representation of the received clipped OFDM signal ,it is found that large number

of data points gets matched.

Fig 8.17: Comparison between Transmitted Data Phase Representation & Received clipped

OFDM signal

0 20 40 60 80 100 120 1400

0.5

1

1.5

2

2.5

3

Data Points

trans

mitt

ed d

ata

phas

e re

pres

enta

tion


0 20 40 60 80 100 120 1400

0.5

1

1.5

2

2.5

3

Data Points

rece

ived

dat

a ph

ase

repr

esen

tatio

n

Received clipped OFDM Signal "X"

98

This investigation proposes a novel CLIPPING scheme for the reduction of PAPR, when data

phase representation of unclipped OFDM signal and clipped OFDM signal is compared with

the data phase representation of transmitted OFDM signal then it can be concluded that

PAPR get reduced in clipped OFDM signal. Thus, an improved signal is obtained.

99

Conclusion & Future Scope

SC-FDMA offers similar performance and complexity as OFDM. In this thesis, PAPR

comparison between OFDMA and SC-FDMA showed that PAPR is a major concern at the

user terminals, low PAPR makes the SC-FDMA the most preferred technology for the uplink

transmission. PAPR relates to the power amplifier efficiency at the transmitter, and the

maximum power efficiency is achieved when the amplifier operates at the saturation point.

Lower PAPR allows operation of the power amplifier close to saturation resulting in higher

efficiency. With higher PAPR signal, the power amplifier operating point has to be backed

off to lower the signal distortion, and thereby lowering amplifier efficiency.

This thesis also investigated the effects of high power amplifier and the channel noise on the

OFDM signals and then introduces clipping and filtering as a PAPR reduction method to

reduce the PAPR.

As SC-FDMA modulated signal can be viewed as a single carrier signal, a pulse shaping

filter can be applied to transmit signal to further improve PAPR in Future.

Other PAPR reduction techniques for OFDMA can be used in next and compared the

techniques with each other by means of various factors (such as performance, system

configuration or implementation costs and complexity) to select the better one for practical

implementation.

100

References

[1] http://en.wikipedia.org/wiki/LTE_(telecommunication)

[2] http://compnetworking.about.com/od/cellularinternetaccess/g/lte-broadband.htm

[3] http://www.mobileburn.com/definition.jsp?term=LTE

[4] http://www.3gpp.com/About-3GPP

[5] S. Sesia, I. Toufik, and M. Baker, LTE, The UMTS Long Term Evolution: From Theory

to Practice. John Wiley & Sons, 2009.

[6] A thesis paper on “PAPR ANALYSIS AND CHANNEL ESTIMATION TECHNIQUES

FOR 3GPP LTE SYSTEM” by By Abhijeet Sahu & Soumyajyoti Behera.

[7] http://en.wikipedia.org/wiki/1G



[10] http://en.wikipedia.org/wiki/4G,

[11] http://wireless.agilent.com/wireless/helpfiles/n7624a/sc-fdma_frame_structure.htm

[12] http://0el70lte.wordpress.com/2012/06/25/hello-world/

[13] http://en.wikipedia.org/wiki/Single-carrier_FDMA

[14] A project on “CHANNEL ESTIMATION AND PREDICTION IN UMTS LTE”, Aalborg

University, Institute of Electronic Systems Signal and Information Processing for Commu-

nications, 2007.

[15] Performance Evaluation of LTE Physical Layer Using SC-FDMA & OFDMA By Abdul

Samad Shaikh & Khatri Chandan Kumar, Blekinge Institute of Technology, School of

Engineering, Department of Radio Communication, Nov 2010.

[16] PAPR REDUCTION IN OFDM COMMUNICATIONS WITH GENERALIZED

DISCRETE FOURIER TRANSFORM, By Sertac Sayin.

[17] Hyung G. Myung, Junsung Lim, and David J. Goodman, “ Single Carrier FDMA for Uplink

Wireless Transmission”, IEEE Vehicular Technology Magazine, vol. 1, no. 3, Sep. 2006,

pp. 30–38.

[18] Single Carrier FDMA in LTE, IXIA, Rev A Nov, 2009.

[19] http://en.wikipedia.org/wiki/Sinc_filter

[20] http://en.wikipedia.org/wiki/Raised-cosine_filter

[21] http://en.wikipedia.org/wiki/Gaussian_filter

[22] MODIFIED CLIPPING AND FILTERING TECHNIQUE FOR PEAK-TO-AVERAGE

POWER RATIO REDUCTION OF OFDM SIGNALS USED IN WLAN by P.K.Sharma,

Department of Electronics and Communication Engineering, Bhagwan Parshuram Institute

of Technology, GGSIP University, Delhi, India. Vol. 2(10), 2010.

http://en.wikipedia.org/wiki/LTE_(telecommunication)

http://compnetworking.about.com/od/cellularinternetaccess/g/lte-broadband.htm

http://www.mobileburn.com/definition.jsp?term=LTE

http://www.3gpp.com/About-3GPP

http://en.wikipedia.org/wiki/1G




http://wireless.agilent.com/wireless/helpfiles/n7624a/sc-fdma_frame_structure.htm

http://0el70lte.wordpress.com/2012/06/25/hello-world/

http://en.wikipedia.org/wiki/Single-carrier_FDMA

http://en.wikipedia.org/wiki/Sinc_filter

http://en.wikipedia.org/wiki/Raised-cosine_filter

http://en.wikipedia.org/wiki/Gaussian_filter

101

[23] SELECTED MAPPING ALGORITHM FOR PAPR REDUCTION OF SFBC OFDM BY

ADDING DCT by Nisharaj.R.S, P. Thiruvalar Selvan.

[24] Improved Precoding Method for PAPR Reduction in OFDM with Bounded Distortion by

Namitha.A.S & Sudheesh.P, International Journal of Computer Applications (0975 –

8887), June 7, 2010.

[25] Suhas Mathur, “Small Scale Fading in Radio Propagation”, Department of Electrical

Engineering, Rugters University, Lecture Notes for Wireless Communication Technologies,

Spring 2005

[26] O.Edfors, M.Sandell, J.Beek, S. K.Wilson, and P. O. Borjesson, “OFDM channel estimation

by singular value decomposition,” IEEE Transaction on Communications, vol. 46, no. 7,

pp.931-939, July 1998.

[27] J. V. de Beek, O. Edfors, M. Sandel, S. Wilson, and P. Borjesson, “On channel estimation in

ofdm systems”, in IEEE 45th Vehicular Technology Conference, Chicago, USA , Jul. 1995.

102

Appendix A

MATLAB Codes Used for PAPR Analysis

1. SCFDMA PAPR Simulation Matlab Code For QPSK Modulation:

% SCFDMA PAPR Simulation Matlab Code For QPSK Modulation% % Mahmud --------------% function papr(input) totalSubcarriers = 512; % Number of total subcarriers. numSymbols = 64; % Data block size. numRuns = 1000 Fs = 5e6; % System bandwidth. Ts = 1/Fs; % System sampling rate. Nos = 4; % Oversampling factor.; papr=zeros(numRuns,1); table=ones(400,64); input=zeros(numSymbols,1); color=['r'] k=1; for n = 1:numRuns, % Generate random data tmp = round(rand(numSymbols,2)); tmp = tmp*2 - 1; data = (tmp(:,1) + 1i*tmp(:,2))/sqrt(2); X = fft(data); X=X.*exp(1i*pi*input); Y = zeros(totalSubcarriers,1); Y(1:numSymbols) = X; y = ifft(Y); papr(n) =10*log10(max(abs(y).^2) / mean(abs(y).^2)); %-------TO CREATE TABLE----------- table(k,:)=data; k=k+1; %--------------------------------- end save table table [N,X] = hist(papr, 100); semilogy(X,1-cumsum(N)/max(cumsum(N)),color) title(['PAPR Analysis for OFDMA & SCFDMA''( N=' num2str(numSymbols) ' & M=

' num2str(totalSubcarriers),')']); ylabel('Pr[PAPR>PAPR0]'); xlabel('PAPR[dB]') legend('SCFDMA','OFDMA') grid on hold all

103

2. OFDMA PAPR Simulation Matlab Code For QPSK Modulation:

% OFDMA PAPR Simulation Matlab Code For QPSK Modulation% % Mahmud --------------% function paprOFDMA() dataType = 'Q-PSK'; % Modulation format. totalSubcarriers = 512; % Number of total subcarriers. numSymbols = 64; % Data block size. Fs = 5e6; % System bandwidth. Ts = 1/Fs; % System sampling rate. Nos = 4; % Oversampling factor. Nsub = totalSubcarriers; Fsub = [0:Nsub-1]*Fs/Nsub; % Subcarrier spacing. numRuns = 1000; % Number of runs.

papr = zeros(1,numRuns); % Initialize the PAPR results.

for n = 1:numRuns, % Generate random data. if dataType == 'Q-PSK' tmp = round(rand(numSymbols,2)); tmp = tmp*2 - 1; data = (tmp(:,1) + j*tmp(:,2))/sqrt(2); for k = 1:numSymbols, if tmp(k) == 0 tmp(k) = 1; end data(k) = dataSet(tmp(k)); end data = data.'; end

% Time range of the OFDM symbol. t = [0:Ts/Nos:Nsub*Ts];

% OFDM modulation. y = 0; for k = 1:numSymbols, y= y + data(k)*exp(j*2*pi*Fsub(k)*t); end

% Calculate PAPR. papr(n) = 10*log10(max(abs(y).^2) / mean(abs(y).^2)); end

% Plot CCDF. [N,X] = hist(papr, 100); semilogy(X,1-cumsum(N)/max(cumsum(N)),'b') title(['PAPR Analysis for OFDMA & SCFDMA''( N=' num2str(numSymbols) ' & M=

' num2str(totalSubcarriers),')']); ylabel('Pr[PAPR>PAPR0]'); xlabel('PAPR[dB]')

grid on % Save data. save paprOFDMA legend('SCFDMA','OFDMA') grid on hold all

104

3. SCFDMA PAPR Simulation Matlab Code For 16-QAM Modulation:

% SCFDMA PAPR Simulation Matlab Code For 16-QAM Modulation %

% Mahmud-----------% function papr(input) totalSubcarriers = 512; % Number of total subcarriers. numSymbols = 64; % Data block size. Fs = 5e6; % System bandwidth. Ts = 1/Fs; % System sampling rate. Nos = 4; % Oversampling factor ; numRuns = 1000; papr=zeros(numRuns,1); table=ones(numRuns,numSymbols); %---- to see the original performance-- input=zeros(numSymbols,1); color=['b']; %------------------------------------- sertac=1; for n = 1:numRuns, % Generate random data.a data=ones(1,numSymbols); dataSet = [-3+3i -1+3i 1+3i 3+3i ... -3+1i -1+1i 1+1i 3+1i ... -3-1i -1-1i 1-1i 3-1i ... -3-3i -1-3i 1-3i 3-3i]; dataSet = dataSet / sqrt(mean(abs(dataSet).^2)); tmp = ceil(rand(numSymbols,1)*16); for k = 1:numSymbols, if tmp(k) == 0 tmp(k) = 1; end data(1,k) = dataSet(1,tmp(k)); end data = data.'; X = fft(data); X=X.*exp(1i*pi*input); Y = zeros(totalSubcarriers,1); Y(1:numSymbols) = X; y = ifft(Y); papr(n) =10*log10(max(abs(y).^2) / mean(abs(y).^2)); %-------TO CREATE TABLE table(sertac,:)=data; sertac=sertac+1; end save table table [N,X] = hist(papr, 100); semilogy(X,1-cumsum(N)/max(cumsum(N)),color) title(['PAPR Analysis for OFDMA & SCFDMA''( N=' num2str(numSymbols) '& M= '

num2str(totalSubcarriers),')']); ylabel('Pr[PAPR>PAPR0]'); xlabel('PAPR[dB]') legend('SCFDMA','OFDMA') grid on hold on

105

4. OFDMA PAPR Simulation Matlab Code For 16-QAM Modulation:

% OFDMA PAPR Simulation Matlab Code For 16-QAM Modulation% % Mahmud --------------%

function paprOFDMA()

dataType = 'Q-PSK'; % Modulation format. totalSubcarriers = 512; % Number of total subcarriers. numSymbols = 64; % Data block size. Fs = 5e6; % System bandwidth. Ts = 1/Fs; % System sampling rate. Nos = 4; % Oversampling factor. Nsub = totalSubcarriers; Fsub = [0:Nsub-1]*Fs/Nsub; % Subcarrier spacing. numRuns = 1000; % Number of runs.

papr = zeros(1,numRuns); % Initialize the PAPR results.

for n = 1:numRuns, % Generate random data. tmp = round(rand(numSymbols,2)); tmp = tmp*2 - 1; data = (tmp(:,1) + j*tmp(:,2))/sqrt(2); if dataType == '16QAM' dataSet = [-3+3i -1+3i 1+3i 3+3i ... -3+i -1+i 1+i 3+i ... -3-i -1-i 1-i 3-i ... -3-3i -1-3i 1-3i 3-3i]; dataSet = dataSet / sqrt(mean(abs(dataSet).^2)); tmp = ceil(rand(numSymbols,1)*16); for k = 1:numSymbols, if tmp(k) == 0 tmp(k) = 1; end data(k) = dataSet(tmp(k)); end data = data.'; end

% Time range of the OFDM symbol. t = [0:Ts/Nos:Nsub*Ts];

% OFDM modulation. y = 0; for k = 1:numSymbols, y= y + data(k)*exp(j*2*pi*Fsub(k)*t); end

% Calculate PAPR. papr(n) = 10*log10(max(abs(y).^2) / mean(abs(y).^2)); end

% Plot CCDF. [N,X] = hist(papr, 100); semilogy(X,1-cumsum(N)/max(cumsum(N)),'m')

106

title(['PAPR Analysis for OFDMA & SCFDMA''( N=' num2str(numSymbols) '& M= '

num2str(totalSubcarriers),')']); ylabel('Pr[PAPR>PAPR0]'); xlabel('PAPR[dB]') legend('SCFDMA','OFDMA') grid on % Save data. save paprOFDMA hold all;

107

Appendix B

Clipping & Filtering Method

OFDM can be seen as either a modulation technique or a multiplexing technique. It uses the

phenomenon of multicarrier propagation and hence proves to be an important technique for

the transmission of high bit rate data in a radio environment. It provides both TDMA and

FDMA and in it a single channel is further subdivided into a number of sub-channels or

subcarriers so that multiple data bit streams can be sent in parallel simultaneously without

significant losses. Increasing robustness against frequency selective fading or narrowband

interference is one of the most important reasons for the popularity of OFDM. However

OFDM signal suffers from high PAPR or crest factor which might require a large amplifier

power back off. Hence our result oriented investigation show that clipping can improve the

PAPR of OFDM signal transmission.

2. System Description:

Our investigation with the help of MATLAB CODING (m-file) depends on the analysis of

the various sub-

sections as stated below:-

A: Parameter specifications

B: Transmitter section

C: Clipping as a PAPR reduction method

D: Analyzing of effect of high power amplifier

E: Generation of complex multipath channel

F: Receiver section

The detailed analysis of these sections is being listed below:

A: Parameter Specifications:

In this section we have assumed an OFDM signal with following specifications:

- QPSK signal constellation i.e. M=4;

- No _of _data_points=128;

- Size of each OFDM block i.e. block_size=8;

108

- Length of cyclic prefix i.e.cp_length=ceil(0.1*block_size);

Note:-where “ceil” rounds the element to the nearest integer towards infinity.

- no_of _ifft _points and no_of_fft_points is considered to be equal to”block _size” .

- Clipping of transmitted signal is done so that a signal remains between +0.4 to -0.4 average

value.

B: Transmitter Section:

Initially 1*128 random data points are generated and then QPSK modulation technique is

performed which provides the complex envelope of modulating the message signal using the

phase shift keying. Message signal consists of integer values between zero (0) to M-1.

Inverse Fast Fourier Transform (IFFT) is now performed on each block by finding out the

number of columns that will exist after reshaping an empty matrix is created to put the IFFT

data and it operates column wise by appending cyclic prefix which leads to the creation of

OFDM block. Data is converted to serial stream for the purpose of transmission and actual

OFDM signal to be transmitted is generated.

C: Clipping as a PAPR Reduction Method:

OFDM signal suffers from high PAPR or crest factor which may require a large amplifier

power back-off. Hence, clipping of transmitted signal is done so that a signal remains

between +0.4 to -0.4 average value.

D: Analyzing of Effect of High Power Amplifier:

In order to show the effect of power amplifier, random complex noise is generated and then

clipped signal and original OFDM signal (unclipped) are passed through high power

amplifier.

E: Generation of Complex Multipath Channel:

The signals are transmitted through complex multipath channel to the receiver for the purpose

of demodulation.

F: Receiver Section:

In the receiver section clipped and unclipped data is converted back to parallel form in order

to perform Fast Fourier Transform (FFT). Cyclic prefix is removed and data is again

converted to serial stream and demodulated.

109

MATLAB codes for PAPR reduction – Clipping & Filtering -:

%------Mahmud------------% clear all clc close % --------------- % A: Setting Parameters % --------------- M = 4; % QPSK signal constellation no_of_data_points = 128; % have 128 data points block_size = 8; % size of each ofdm block cp_len = ceil(0.1*block_size); % length of cyclic prefix no_of_ifft_points = block_size; % 128 points for the FFT/IFFT no_of_fft_points = block_size; % --------------------------------------------- % B: % +++++ TRANSMITTER +++++ % --------------------------------------------- % 1. Generate 1 x 128 vector of random data points data_source = randsrc(1, no_of_data_points, 0:M-1); figure(1) stem(data_source); grid on; xlabel('Data Points'); ylabel('transmitted data

phase representation') title('Transmitted Data "O"')

% 2. Perform QPSK modulation qpsk_modulated_data = pskmod(data_source, M); scatterplot(qpsk_modulated_data);title('MODULATED TRANSMITTED DATA');

% 3. Do IFFT on each block % Make the serial stream a matrix where each column represents a pre-OFDM % block (w/o cyclic prefixing) % First: Find out the number of colums that will exist after reshaping num_cols=length(qpsk_modulated_data)/block_size; data_matrix = reshape(qpsk_modulated_data, block_size, num_cols);

% Second: Create empty matix to put the IFFT'd data cp_start = block_size-cp_len; cp_end = block_size;

% Third: Operate columnwise & do CP for i=1:num_cols, ifft_data_matrix(:,i) = ifft((data_matrix(:,i)),no_of_ifft_points); % Compute and append Cyclic Prefix for j=1:cp_len, actual_cp(j,i) = ifft_data_matrix(j+cp_start,i); end % Append the CP to the existing block to create the actual OFDM block ifft_data(:,i) = vertcat(actual_cp(:,i),ifft_data_matrix(:,i)); end

% 4. Convert to serial stream for transmission [rows_ifft_data cols_ifft_data]=size(ifft_data); len_ofdm_data = rows_ifft_data*cols_ifft_data;

% Actual OFDM signal to be transmitted ofdm_signal = reshape(ifft_data, 1, len_ofdm_data); figure(3)

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plot(real(ofdm_signal)); xlabel('Time'); ylabel('Amplitude'); title('Unclipped OFDM Signal');grid on;

% --------------------------------------------------------------- % C: % +++++ clipping as a PAPR reduction method +++++ % --------------------------------------------------------------- avg=0.4; clipped=ofdm_signal; for i=1:length(clipped) if clipped(i) > avg clipped(i) = avg; end if clipped(i) < -avg clipped(i) = -avg; end end figure(4) plot(real(clipped)); xlabel('Time'); ylabel('Amplitude'); title('clipped OFDM Signal');grid on;

% ------------------------------------------ % D: % +++++ HPA +++++ % ------------------------------------------ %To show the effect of the PA simply we will add random complex noise %when the power exceeds the avg. value, otherwise it add nothing.

% 1. Generate random complex noise noise = randn(1,len_ofdm_data) + sqrt(-1)*randn(1,len_ofdm_data);

% 2. Transmitted OFDM signal after passing through HPA

%without clipping for i=1:length(ofdm_signal) if ofdm_signal(i) > avg ofdm_signal(i) = ofdm_signal(i)+noise(i); end if ofdm_signal(i) < -avg ofdm_signal(i) = ofdm_signal(i)+noise(i); end end figure(5) plot(real(ofdm_signal)); xlabel('Time'); ylabel('Amplitude'); title('Unclipped OFDM Signal after HPA');grid on;

%with clipping avg=0.4; for i=1:length(clipped) if clipped(i) > avg clipped(i) = clipped(i)+noise(i); end if clipped(i) < -avg clipped(i) = clipped(i)+noise(i); end end figure(6) plot(real(clipped)); xlabel('Time'); ylabel('Amplitude'); title('clipped OFDM Signal after HPA');grid on;

% -------------------------------- % E: % +++++ CHANNEL +++++

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% -------------------------------- % Create a complex multipath channel channel = randn(1,block_size) + sqrt(-1)*randn(1,block_size);

% ------------------------------------------ % F: % +++++ RECEIVER +++++ % ------------------------------------------

% 1. Pass the ofdm signal through the channel after_channel = filter(channel, 1, ofdm_signal);

% 2. Add Noise awgn_noise = awgn(zeros(1,length(after_channel)),0);

% 3. Add noise to signal...

recvd_signal = awgn_noise+after_channel;

% 4. Convert Data back to "parallel" form to perform FFT recvd_signal_matrix = reshape(recvd_signal,rows_ifft_data, cols_ifft_data);

% 5. Remove CP recvd_signal_matrix(1:cp_len,:)=[];

% 6. Perform FFT for i=1:cols_ifft_data, % FFT fft_data_matrix(:,i) = fft(recvd_signal_matrix(:,i),no_of_fft_points); end

% 7. Convert to serial stream recvd_serial_data = reshape(fft_data_matrix, 1,(block_size*num_cols));

% 8. Demodulate the data qpsk_demodulated_data = pskdemod(recvd_serial_data,M);

figure(7) stem(qpsk_demodulated_data,'rx'); grid on;xlabel('Data Points');ylabel('received data phase

representation');title('Received Unclipped OFDM Signal "X"') % ---------------------------------------------------- % F: % +++++ RECEIVER of clipped signal +++++ % ----------------------------------------------------

% 1. Pass the ofdm signal through the channel after_channel = filter(channel, 1, clipped);

% 2. Add Noise awgn_noise = awgn(zeros(1,length(after_channel)),0);

% 3. Add noise to signal...

recvd_signal = awgn_noise+after_channel;

% 4. Convert Data back to "parallel" form to perform FFT recvd_signal_matrix = reshape(recvd_signal,rows_ifft_data, cols_ifft_data);

% 5. Remove CP

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recvd_signal_matrix(1:cp_len,:)=[];

% 6. Perform FFT for i=1:cols_ifft_data, % FFT fft_data_matrix(:,i) = fft(recvd_signal_matrix(:,i),no_of_fft_points); end

% 7. Convert to serial stream recvd_serial_data = reshape(fft_data_matrix, 1,(block_size*num_cols));

% 8. Demodulate the data qpsk_demodulated_data = pskdemod(recvd_serial_data,M); figure(8) stem(qpsk_demodulated_data,'rx'); grid on;xlabel('Data Points');ylabel('received data phase

representation');title('Received clipped OFDM Signal "X"')

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Appendix C

MATLAB Codes Used for Equations & OFDM spectrum

1. MATLAB code for PAPR eqn for different subcarriers (Eqn 5.1):

% PAPR analysis and simulation for 3GPP LTE system % % Author: S.M.Mahmud Hasan % % This program plots PAPR eqn for different subcarriers % %-----------------------------------------------------% x=2:2:14 N=[16] y=1-(1-exp(-x)).^N semilogy(x,y.^-1) hold all grid on xlabel('z------------') ylabel('P(PAPR>z)------------') x=2:2:14 N=[32] y=1-(1-exp(-x)).^N semilogy(x,y.^-1) hold all grid on xlabel('z------------') ylabel('P(PAPR>z)------------') x=2:2:14 N=[128] y=1-(1-exp(-x)).^N semilogy(x,y.^-1) hold all grid on xlabel('z------------') ylabel('P(PAPR>z)------------') x=2:2:14 N=[512] y=1-(1-exp(-x)).^N semilogy(x,y.^-1) hold all grid on xlabel('z------------') ylabel('P(PAPR>z)------------') x=2:2:14 N=[2048] y=1-(1-exp(-x)).^N semilogy(x,y.^-1) hold all grid on xlabel('z------------') ylabel('P(PAPR>z)------------') legend('N=16','N=32','N=128','N=512','N=2048')

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2. MATLAB code for the TF of Sinc Filter:

x = linspace(-5,5); y = sinc(x).^2; plot(x,y) title('Plot of Sinc Filter Transfer Function') xlabel('t---->') ylabel('h(t)---->') grid on

3. MATLAB code for the TF of Raised Cosine Filter:

% PAPR analysis and simulation for 3GPP LTE system %

% Author: S.M.Mahmud Hasan %

% This program plots the Raised Cosine Filter TF %

%------------------------------------------------% L=41; %Filter Length R=1E6; %Data Rate = 1Mbps Fs=8*R; %Oversampling by 8 T=1/R; Ts=1/Fs; alpha =0; % Design Factor for Raised Cosing Filter %---------------------------------------------------------- %Raised Cosing Filter Design %---------------------------------------------------------- if mod(L,2)==0 M=L/2 ; % for even value of L else M=(L-1)/2; % for odd value of L end g=zeros(1,L); %Place holder for RC filter's transfer function for n=-M:M num=sin(pi*n*Ts/T)*cos(alpha*pi*n*Ts/T); den=(pi*n*Ts/T)*(1-(2*alpha*n*Ts/T)^2); g(n+M+1)=num/den; if (1-(2*alpha*n*Ts/T)^2)==0 g(n+M+1)=pi/4*sin(pi*n*Ts/T)/(pi*n*Ts/T); end if n==0 g(n+M+1)=cos(alpha*pi*n*Ts/T)/(1-(2*alpha*n*Ts/T)^2); end end %---------------------------------------------------------- % Plot the transfer function of RC filter plot(g); title('Plot the transfer function of Raised Cosine filter') xlabel('n(Samples)'); ylabel('Amplitude'); grid on; hold all; legend('alpha=0','alpha=0.5','alpha=1')

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4. MATLAB code for the TF of Gaussian Filter:

% PAPR analysis and simulation for 3GPP LTE system % % Author: S.M.Mahmud Hasan % sigma=2; X=-10:10; GAUSS=1/(sqrt(2*pi)*sigma)*exp(-0.5*X.^2/(sigma^2)); plot(GAUSS) title('Plot of Gaussian Filter Transfer Function') xlabel('x---->') ylabel('g(x)---->') grid on

5. MATLAB code for plotting sensitivity of OFDM subcarriers with Carrier:

%% This program plots sensitivity of OFDM subcarriers with Carrier %% frequency offset(CFO) % PAPR analysis and simulation for 3GPP LTE system % % Author: S.M.Mahmud Hasan % clc clear all

e = 0; % Normalized CFO N = 16; % Total Subcarriers Indx = 0.01; % Over sampling index vi = 1; % counter index for k = 0:Indx:N-1 hi = 1; % counter index for l = 0:N-1 % this function calculates effect of CFO. Bias 1 is deliberately % added in order to evaluate function at zero CFO. f(vi,hi) = 1 +(sin(pi*(l+e-k))*exp(1i*pi*(N-1)*(l+e-k)/N))... /(N*sin(pi*(l+e-k)/N)); hi = hi+1; end vi = vi+1; end

plot([0:Indx:N-1],abs(f(:,1)),'r'); hold on; grid on; title('Consecutive OFDM Subcarriers in Time domain'); xlabel('Subcarrier index');ylabel('Amplitude');

for n = 1:N-1 plot([0:Indx:N-1],abs(f(:,n+1))); end

6. MATLAB code for plotting ofdm trasmission spectrum:

%ofdm trasmission spectrum % PAPR analysis and simulation for 3GPP LTE system % % Author: S.M.Mahmud Hasan ([email protected])% clc

N = 16; % Number of subcarriers. a = sign(randn(N, 1)); % Generate BPSK symbols. b = diag(a); % This helps to plot overlapping subcarrier spectrum. c = ifft(b); % Do IFFT along each column--(each column is a subcarrier). f = fft(c, N*16); % Do FFT of 16x resolution.

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plot(abs(f)); % U get the spectrum corresponding to each subcarrier. grid on; hold on; title('OFDM Transmission Spectrum'); xlabel('Subcarriers');ylabel('Amplitude'); plot(abs(sum(f, 2)), '-*');

papr analysis and simulation for 3gpp lte system

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