KATHMANDU UNIVERSITY

SCHOOL OF ENGINEERING

DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING

FINAL YEAR

PROJECT REPORT

Modeling and Simulation

Of

WiMAX/IEEE 802.16e Physical Layer

A final year project report submitted in partial fulfilment

of the requirements for the degree of Bachelor of Engineering

Submitted By:

Amar Shrestha (Regd. No.010617-09)

Shashi Raj Pandey (Regd. No. 010608-09)

June, 2013

CERTIFICATION

FINAL YEAR PROJECT REPORT

On

MODELING AND SIMULATION OF WIMAX/IEEE 802.16e PHYSICAL LAYER

by:

Amar Shrestha (Regd. No. 010617-09)

Shashi Raj Pandey (Regd. No. 010608-09)

Approved by:

1. Project Supervisor

___________________ ____________________________ __________

(Signature) (Name) (Date)

2. Head/In-Charge of the Department

___________________ ____________________________ __________

(Signature) (Name) (Date)

i

ABSTRACT

WiMAX is a wireless transmission infrastructure that allows a fast deployment as well as low

maintenance costs. Based on the IEEE 802.16-2004 standard, WiMAX allows for an efficient

use of bandwidth in a wide frequency range, and can be used as a last mile solution for

broadband internet access. To increase data rate of wireless medium with higher performance;

better spectral efficient Orthogonal Frequency Division Multiplexing (OFDM) technique is used.

Modulation schemes such as 16-QAM, 32-QAM, 64-QAM and 128-QAM (Quadrature

amplitude modulation) have been used in the developed OFDM system for FFT based model.

This research report discusses the model building of the WiMAX Physical layer using Simulink

in Matlab. This model is a useful tool for performance evaluation of the WiMAX Physical layer

under different modulation schemes and channel conditions. And utilizing tools such as BER and

SNR, this research helps to find suitable modulation schemes for different channel condition

regarding WiMAX.

ii

ACKNOWLEDGEMENT

We would like to express sincere gratitude to our project coordinator, Mr. Brajesh Mishra, for

granting us the permission to work on this project “MODELING AND SIMULATION OF

WIMAX/IEEE 802.16e PHYSICAL LAYER”. We are grateful to have Mr. Subodh Ghimire as

our project supervisor. It is due to his constant support, supervision and guidance we have been

able to successfully complete the project. Our special thanks to all the faculty members of the

Department of Electrical and Electronics Engineering for their provision of a sound ambience

and of all the facilities required for the working of our project.

Last but not the least; we would like to thank all our friends for the help they have given us in

innumerable way.

iii

ABBREVIATIONS

AWGN Additive Gaussian White Noise

BER Bit Error Rate

BPSK Binary Phase Shift Keying

BS Base Station

BWA Broadband Wireless Access

CP Cyclic Prefix

CRC Cyclic Redundancy Check

DSL Digital Subscribers Line

FDD Frequency Division Duplexing

FEC Forward Error Correction

FFT Fast Fourier Transform

GT Guard Time

HCS Header Check Sequence

IFFT Inverse Fast Fourier Transform

ISI Inter symbol Interference

ICI Inter carrier Interference

NLOS Non Line of Sight

OFDM Orthogonal Frequency Division Multiplexing

OFDMA Orthogonal Frequency Division Multiple Access

PHY Physical

QAM Quadrature Amplitude Modulation

QPSK Quadrature Phase Shift Keying

SC Single Carrier

iv

SNR Signal to Noise Ratio

SS Subscriber Station

TDD Time Division Duplexing

WiMAX Worldwide Interoperability for Microwave Access

v

LIST OF FIGURES

Figure1.1: Basic Communication System....................................................................................... 2

Figure1.2 Simulation Setup ............................................................................................................ 2

Figure1.3: Simulation Overview ..................................................................................................... 3

Figure2.1 Digital Modulation Principle .......................................................................................... 9

Figure2.2 The BPSK and QPSK constellation ............................................................................... 9

Figure2.3 Possible Phase Value for QPSK modulation .................................................................. 9

Figure2.4 A 64-QAM constellation .............................................................................................. 10

Figure2.5 Time and frequency representation of the SC and OFDM ........................................... 12

Figure2.6 Generation of an OFDM signal (simplified) ................................................................ 13

Figure2.7 Presentation of the OFDM subcarrier frequency.......................................................... 13

Figure2.8 Cyclic Prefix insertion in an OFDM symbol ................................................................ 14

Figure2.9 WiMAX OFDM subcarriers types ............................................................................... 15

Figure2.10 OFDM PHY data rates in Mb/s. ................................................................................. 17

Figure2.11 Model of an OFDM system ........................................................................................ 18

Figure3.1 BER for different modulation scheme in AWGN channel ........................................... 24

Figure3.2 Effect of Doppler shift on BER in QPSK ..................................................................... 25

Figure3.3 BER for QPSK for different values of Doppler shift ................................................... 26

Figure3.4 BER for QPSK for different delay spread .................................................................... 27

Figure3.5 BER for QPSK for different multipath gains ............................................................... 28

vi

LIST OF TABLES

Table 1 Simulation Parameters ....................................................................................................... 4

Table 2 Normalization Factors...................................................................................................... 11

Table 3 Modulation alphabet for the constellation map ............................................................... 11

vii

TABLE OF CONTENTS ABSTRACT .................................................................................................................................... i

ACKNOWLEDGEMENT ............................................................................................................ ii

ABBREVIATIONS ...................................................................................................................... iii

LIST OF FIGURES ...................................................................................................................... v

Chapter 1 ....................................................................................................................................... 1

INTRODUCTION......................................................................................................................... 1

1.1 Background and Objectives ............................................................................................... 1

1.2 System Overview .............................................................................................................. 2

1.3 Methodology ..................................................................................................................... 3

1.4 Overview of Report ........................................................................................................... 7

Chapter 2 ....................................................................................................................................... 8

LITERATURE REVIEW ............................................................................................................ 8

2.1 Literature Survey ............................................................................................................... 8

2.2 Technological Survey ...................................................................................................... 22

Chapter 3 ..................................................................................................................................... 24

SIMULATION RESULTS AND ANALYSIS .......................................................................... 24

3.1 AWGN ............................................................................................................................. 24

3.2 Multipath Fading: ............................................................................................................ 25

Chapter 4 ..................................................................................................................................... 29

DISCUSSION AND CONCLUSION ........................................................................................ 29

4.1 Discussion and Conclusion ............................................................................................. 29

4.2 Recommendations ........................................................................................................... 29

Bibliography ................................................................................................................................ 30

Appendix ...................................................................................................................................... 31

1

Chapter 1

INTRODUCTION

1.1 Background and Objectives

1.1.1 Background

Broadband Wireless Access (BWA) has emerged as a promising solution for last mile access

technology to provide high speed internet access in the residential as well as small and medium

sized enterprise sectors. At this moment, cable and digital subscriber line (DSL) technologies are

providing broadband service in this sectors. But the practical difficulties in deployment have

prevented them from reaching many potential broadband internet customers. Many areas

throughout the world currently are not under broadband access facilities. Even many urban and

suburban loations may not be served by DSL connectivity as it can only reach about three miles

from the central office switch. On the other side many older cable networks do not have return

channel which will prevent to offer internet access and many commercial areas are often not

covered by cable network. But with BWA this difficulties can be overcome. Because of its

wireless nature, it can be faster to deploy, easier to scale and more flexible, thereby giving it the

potential to serve customers not served or not satisfied by their wired broadband alternatives.

IEEE 802.16e standard for BWA and its associated industry consortium, Worldwide

Interoperability for Microwave Access (WiMAX) forum promise to offer high data rate over

large areas to a large number of users where broadband is unavailable. This is the first industry-

wide standard that can be used for fixed as well as mobile wireless access with substantially

higher bandwidth than most cellular networks. Wireless broadband systems have been in use for

many years, but the development of this standard enables economy of scale that can bring down

the cost of equipment, ensure interoperability, and reduce investment risk for operators.

1.1.2 Objectives

This research project mainly focuses on the following topics

Analyze the basic concept of WiMAX including its standards and relationship with other

technologies.

Modeling and Simulation of WiMAX/IEEE 802.16e Physical Layer and its performance

evaluation implementing various modulation techniques.

2

1.2 System Overview

Physical layer set up the connection between the communicating devices and is responsible for

transmitting the bit sequence. It also defines the type of modulation and demodulation as well as

transmission power. WiMAX 802.16e PHY-layer considers two types of transmission techniques

OFDM and OFDMA. Both of these techniques have frequency band below 11GHz and use TDD

and FDD as its duplexing technology. WiMAX physical layer is based on the orthogonal

frequency division multiplexing (OFDM). OFDM is a good choice of high speed data

transmission, multimedia communication and digital video services. It even can maintain very

fast data rate in a non-line of sight (NLOS) condition and multipath environment. The role of the

PHY-layer is to encode the binary digits that represent MAC frames into signals and to transmit

and receive these signals across the communication media. The basic communication system is

shown in Figure1.1.

.

Figure1.1: Basic Communication System

We have implemented the transmitter and receiver of the baseband part of the PHY-layer as in

Figure1.2. This structure corresponds to the phyical layer of the standard. In this setup we have

just implemented the mandatory features of the specification while leaving the implementation of

optimal features for future work.The complementary operations are applied in the reverse order

at channel decoding in the receiver end.

Figure1.2 Simulation Setup

Random

Data Mapping Cyclic Prefix

Insertion IFFT

De-Mapping FFT Output Cyclic Prefix

Removal

Transmitter Channel Receiver

3

1.3 Methodology

1.3.1 Simulation strategy

Figure1.3: Simulation Overview

Our simulation study is based on the standard of OFDM model with parameters based on IEEE

802.16e with changes in the channel according to the environment and as per the requirement for

analysis. And Simulink being a block based design tool, it seemed the best option to implement

the model. So the simulation model was developed model by module in Simulink based on the

basic structure of an OFDM system .Then the standard parameters are provided to the models to

direct the simulation in the direction that the standard permits.

After gaining knowledge about the simulation platform, the model was simulated following the

procedures given below.

At first we perform initialization of the model parameters.

The models are run via Bertool function or directly through Simulink model.

The results are plotted out in number of ways: BER versus SNR plot when AWGN channel is

involved and BER versus Doppler spread/Doppler shift/Multipath gain vector for Rayleigh

fading channel.

Then on the basis of plots and our literature survey analysis is made.

Execute

Initializing

Matlab File

(final.m)

Execute Simulink

Model (.mdl

extension file)

Output Graph Plotting

(Matlab)

Bertool

(.ber file)

4

1.3.2 Simulation Model

Scenario:

For the simulation scenario, we have considered basic models available. As we are working

under wireless communication network for WiMAX, we have taken into account AWGN

(Additive White Gaussian Noise) channel in which noise components just adds up, fading

channel due to multipath environment and a combination of both AWGN and fading channels for

the purpose of simulation. Similarly for the simulation model, we have chosen different

parameters as per the IEEE 802.16e standard.

Table 1 Simulation Parameters

Parameter Value

Ndata 192

Npilot 8

Ntrain 3

BW Variable,from1.25 to 20 MHz being an integer multiple of 1.25, 1.5, or 1.75 MHz

nf 8/7

G 1/4, 1/8, 1/16, 1/32

Number of lower frequency guard subcarriers

28

Number of higher frequency guard subcarriers

27

Frequency offset indices of guard subcarriers

-128,-127,…, -101 +101,+102, …, +127

Frequency offset indices of pilot carriers -88,-63,-38,-13 +13,+38,+63,+88

Tframe(msec) 2.5,4,5,8,10,12.5,20

Beside the parameters that describe the OFDM symbol, other parameters are required in order to

define parameters for the transmission, such as the frame duration, the packet size, or the total

number of transmitted OFDM frame duration, the packet size, or the total number of transmitted

OFDM symbols.

The five primitive parameters that characterize the OFDM symbol are:

BW: nominal channel bandwidth.

Ndata: number of data subcarriers.

5

Npilot: number of pilot subcarriers.

nf: sampling factor, used with BW and Nused (number of non-zero subcarriers) to

determine the subcarrier spacing and the useful symbol time.

G: ratio of CP time to useful time.

Next, derived parameters, which are dependent of the primitive parameters, are listed:

Nused: number of used non-zero subcarriers.

Nused = Ndata + Npilot

NFFT: number of points used to perform the FFT. It is specified to be the smallest power

of two, and greater than Nused.

NFFT = 2[()]

Fs: sampling frequency.

Fs =

8000

∆: subcarrier spacing.

∆ =

Tb:usefulsymboltime.

Tb =

∆

Tg:CPtime.

Tg =

Tsym: OFDM symbol time.

Tsym = Tb+ Tg

Ts: sampling time.

Ts=

6

1.3.3 Performance Metrics

The following different performance metrics are evaluated to analyze the performance of OFDM

in different channels with different modulation scheme for WiMAX.

Signal to Noise Ratio (SNR)

SNR is the ratio of signal power to noise power. SNR value provides the general information

about the channel condition and helps in evaluating the channel capacity for the provided

bandwidth.

=

=

=

Where,

Fs = symbol rate (1/sec)

B= bandwidth (Hz=1/sec)≥ Fs

No = noise power spectral density

Es = Energy per symbol (Joules)

Eb = Energy per bit (Joules)

Nb = bits per symbol

Bit Error Rate (BER)

Bit error rate (BER) also called as bit error probability simply is the ratio of lost bits to the total

number of transmitted bit in a channel.

=

For AWGN channel the BER can be calculated using following equations.

BPSK: = 2

7

4-QAM: ≈ 2 2

M-QAM: ≈ 4

32

− 1

Where

() =1

√ 2

=

√

1.4 Overview of Report

This project is divided into four different chapters, each one illustrating the description of the

project in detail. The report highlights the system overview and the technology and literature

review conducted for the completion of the project.

Chapter 1 discusses the introduction part regarding the project. The background of the project

and its objective initiate the report. The system overview defines the components of the system

for simulation. The simulation strategy and different parameters considered for simulation are

classified under methodology heading.

Chapter 2 deals with the Literature Survey and Technological survey where we have tried to put

all necessary details that help to understand technical terminologies of the project. The research

and survey done during the project time are also included in the survey which could be referred

to understand the project.

Chapter 3 focuses on Simulation Results and Analysis.

Chapter 4 emphasizes on the conclusion of the project. The outcome of the project under

different parameter is highlighted under this section.

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Chapter 2

LITERATURE REVIEW

2.1 Literature Survey

2.1.1 Digital Modulation

As for all recent communication systems, WiMAX/802.16 uses digital modulation. The now

well-known principle of a digital modulation is to modulate an analogue signal with a digital

sequence in order to transport this digital sequence over a given medium: fiber, radio link, etc

(Figure2.1). This has great advantages with regard to classical analogue modulation: better

resistance to noise, use of high-performance digital communication and coding algorithms, etc.

Many digital modulations can be used in a telecommunication system. The variants are obtained

by adjusting the physical characteristics of a sinusoidal carrier, the frequency, phase or

amplitude, or a combination of some of these. Four modulations are supported by the IEEE

802.16 standard: BPSK, QPSK, 16-QAM and 64-QAM. In this section the modulations used in

the OFDM and OFDMA PHYsical layers are introduced with a short explanation for each of

these modulations.

Binary Phase Shift Keying (BPSK)

The BPSK is a binary digital modulation; i.e. one modulation symbol is one bit. This gives high

immunity against noise and interference and a very robust modulation. A digital phase

modulation, which is the case for BPSK modulation, uses phase variation to encode bits: each

modulation symbol is equivalent to one phase. The phase of the BPSK modulated signal is π or –

π according to the value of the data bit. An often used illustration for digital modulation is the

constellation. Figure2.2 shows the BPSK constellation; the values that the signal phase can take

are 0 or π.

Quadrature Phase Shift Keying (QPSK)

When a higher spectral efficiency modulation is needed, i.e. more b/s/Hz, greater modulation

symbols can be used. For example, QPSK considers two-bit modulation symbols. Figure 6 shows

the possible phase values as a function of the modulation symbol. Many variants of QPSK can be

used but QPSK always has a four-point constellation (Figure 5). The decision at the receiver, e.g.

between symbol ‘00’ and symbol ‘01’, is less easy than a decision between ‘0’ and ‘1’. The

QPSK modulation is therefore less noise- resistant than BPSK as it has a smaller immunity

9

against interference. A well-known digital communication principle must be kept in mind: ‘A

greater data symbol modulation is more spectrum efficient but also less robust.’

Figure2.1 Digital Modulation Principle

Figure2.2 The BPSK and QPSK constellation

Figure2.3 Possible Phase Value for QPSK modulation

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Quadrature Amplitude Modulation (QAM): 16-QAM and 64-QAM

The QAM changes the amplitudes of two sinusoidal carriers depending on the digital sequence

that must be transmitted; the two carriers being out of phase of π/2, this amplitude modulation is

called quadrature. It should be mentioned that according to digital communication theory, QAM-

4 and QPSK are the same modulation (considering complex data symbols). Both 16-QAM (4

bits/modulation symbol) and 64-QAM (6 bits/modulation symbol) modulations are included in

the IEEE 802.16 standard. The 64-QAM is the most efficient modulation of 802.16 (Figure2.4).

Indeed, 6 bits are transmitted with each modulation symbol. The 64-QAM modulation is optional

in some cases:

•license-exempt bands, when the OFDM PHYsical Layer is used

•for OFDMA PHY, yet the Mobile WiMAX profiles indicate that 64-QAM is mandatory in the

downlink.

Figure2.4 A 64-QAM constellation

The modulation mapping is built in the simulator by a Simulink block implemented as a Matlab

m-file. The normalization factors and the symbol alphabet (As) that represent the coordinate

points in the constellation map are defined in Table 2 and Table 3 respectively.

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Table 2 Normalization Factors

Modulation scheme Normalization constant for unit average power

BPSK Cm= 1

QPSK Cm= 1/√ 2

16-QAM Cm= 1/√ 10

64-QAM Cm= 1/42

Table 3 Modulation alphabet for the constellation map

Modulation scheme Symbol alphabet

BPSK As= (1, −1)

QPSK As = (1 + j, 1 − j, −1 + j, −1 − j )

16-QAM A = (j, 3j, −j, −3j ) As= (A + 1, A + 3, A − 1, A − 3)

64-QAM A = (j, 3j, 5j, 7j − j, −3j, −5j, −7j ) As= (A + 1, A + 3, A + 5, A + 7, A − 1, A − 3, A − 5,

A− 7

2.1.2 OFDM

OFDM is a very powerful transmission technique. It is based on the principle of transmitting

simultaneously many narrow-band orthogonal frequencies, often also called OFDM subcarriers

or subcarriers. The number of subcarriers is often noted N. These frequencies are orthogonal to

each other which (in theory) eliminates the interference between channels. Each frequency

channel is modulated with a possibly different digital modulation (usually the same in the first

simple versions). The frequency bandwidth associated with each of these channels is then much

smaller than if the total bandwidth was occupied by a single modulation. This is known as the

Single Carrier (SC) (Figure2.5). A data symbol time is N times longer, with OFDM providing a

much better multipath resistance. Having a smaller frequency bandwidth for each channel is

equivalent to greater time periods and then better resistance to multipath propagation (with

regard to the SC). Better resistance to multipath and the fact that the carriers are orthogonal

12

allows a high spectral efficiency. OFDM is often presented as the best performing transmission

technique used for wireless systems.

Basic Principle: Use the IFFT Operator

The FFT is the Fast Fourier Transform operator. This is a matrix computation that allows the

discrete Fourier transform to be computed (while respecting certain conditions). The FFT works

for any number of points.

Figure2.5 Time and frequency representation of the SC and OFDM

The operation is simpler when applied for a number N which is a power of 2 (e.g. N =256). The

IFFT is the Inverse Fast Fourier Transform operator and realizes the reverse operation. OFDM

theory shows that the IFFT of magnitude N, applied on N symbols, realizes an OFDM signal,

where each symbol is transmitted on one of the N orthogonal frequencies. The symbols are the

data symbols of the type BPSK, QPSK, QAM-16 and QAM-64 introduced in the previous

section. Figure2.6 shows an illustration of the simplified principle of the generation of an OFDM

signal. In fact, generation of this signal includes more details that are not shown here for the sake

of simplicity.

13

Figure2.6 Generation of an OFDM signal (simplified)

Figure2.7 Presentation of the OFDM subcarrier frequency

If the duration of one transmitted modulation data symbol is Td, then Td=1/∆f, where ∆f is the

frequency bandwidth of the orthogonal frequencies. As the modulation symbols are transmitted

simultaneously,

Td=duration of one OFDM symbol

=duration of one transmitted modulation data symbol.

14

This duration, ∆f, the frequency distance between the maximums of two adjacent OFDM

subcarriers, can be seen in Figure 2.7. This figure shows how the neighboring OFDM sub-

carriers have values equal to zero at a given OFDM subcarrier maximum, which is why they are

considered to be orthogonal. In fact, duration of the real OFDM symbol is a little greater due to

the addition of the Cyclic Prefix (CP).

Time Domain OFDM Considerations

After application of the IFFT, the OFDM theory requires that a Cyclic Prefix (CP) must be added

at the beginning of the OFDM symbol (Figure2.8). Without getting into mathematical details of

OFDM, it can be said that the CP allows the receiver to absorb much more efficiently the delay

spread due to the multipath and to maintain frequency orthogonality.

Figure2.8 Cyclic Prefix insertion in an OFDM symbol

The CP that occupies a duration called the Guard Time (GT), often denoted TG, is a temporal

redundancy that must be taken into account in data rate computations. The ratio TG/Td is very

often denoted G in WiMAX/802.16 documents. The choice of G is made according to the

following considerations: if the multipath effect is important (a bad radio channel), a high value

of G is needed, which increases the redundancy and then decreases the useful data rate; if the

multipath effect is lighter (a good radio channel), a relatively smaller value of G can be used. For

OFDM and OFDMA PHY layers, 802.16 defined the following values for G: 1/4, 1/8, 1/16 and

1/32. For the mobile (OFDMA) WiMAX profiles presently defined, only the value 1/8 is

mandatory. The standard indicates that, for OFDM and OFDMA PHY layers, SS searches, on

initialization, for all possible values of the CP until it finds the CP being used by the BS. The SS

then uses the same CP on the uplink. Once a specific CP duration has been selected by the BS for

15

operation on the downlink, it cannot be changed. Changing the CP would force all the SSs to

resynchronize to the BS.

Frequency Domain OFDM Considerations

All the subcarriers of an OFDM symbol do not carry useful data. There are four subcarrier types

(Figure2.9):

•Data subcarriers: useful data transmission.

•Pilot subcarriers: mainly for channel estimation and synchronization. For OFDM PHY,

there are eight pilot subcarriers.

•Null subcarriers: no transmission. These are frequency guard bands.

•Another null subcarrier is the DC (Direct Current) subcarrier. In OFDM and OFDMA

PHY layers, the DC subcarrier is the subcarrier whose frequency is equal to the RF center

frequency of the transmitting station. It corresponds to frequency zero (Direct Current) if the

FFT signal is not modulated. In order to simplify Digital-to-Analogue and Analogue-to-Digital

Converter operations, the DC subcarrier is null.

Figure2.9 WiMAX OFDM subcarriers types

16

OFDM Symbol Parameters and Some Simple Computations

The main WiMAX OFDM symbol parameters are the following:

•The total number of subcarriers or, equivalently, the IFFT magnitude. For OFDM PHY,

NFFT=256, the number of lower-frequency guard subcarriers is 28 and the number of higher

frequency guard subcarriers is 27. Considering also the DC subcarrier, there remains Nused, the

number of used subcarriers, excluding the null subcarriers. Hence, Nused=200 for OFDM PHY,

of which 192 are used for useful data transmission, after deducing the pilot subcarriers.

•BW, the nominal channel bandwidth

•n, the sampling factor.

The sampling frequency, denoted fs, is related to the occupied channel bandwidth by the

following (simplified) formula: fs=nBW.

This is a simplified formula because, according to the standard, fs is truncated to an 8 kHz

multiple. According to the 802.16 standard, the numerical value of n depends of the channel

bandwidths. Possible values are 8/7, 86/75, 144/125, 316/275 and 57/50 for OFDM PHY and 8/7

and 28/25 for OFDMA PHY.

Duration of an OFDM Symbol

Based on the above-defined parameters, the time duration of an OFDM symbol can be

computed:

OFDM symbol duration = useful symbol time + guard time (CP time)

=1/ (one subcarrier spacing) +G × useful symbol time

= (1/∆f) (1+G)

= [1/ ( fs/ NFFT)] (1+G)

= [1/ ( nBW / NFFT)] (1+G).

The OFDM symbol duration is a basic parameter for data rate computations.

17

Data Rate Values

In OFDM PHY, one OFDM symbol represents 192 subcarriers, each transmitting a modulation

data symbol (see above). One can then compute the number of data transmitted for the duration

of an OFDM symbol (which value is already known). Knowing the coding rate, the number of

uncoded bits can be computed. Figure2.10 shows the data rates for different Modulation and

Coding Schemes (MCSs) and G values. The occupied bandwidth considered is 7 MHz and the

sampling factor is 8/7 (the value corresponding to 7 MHz according to the standard).Consider the

following case in Figure 12: 16-QAM, coding rate 3/4 and G 1/16. It can be verified that the data

rate is equal to:

Data rate =number of uncoded bits per OFDM symbol/OFDM symbol duration

=192 ×4 × (3/4)/ [256/ (7 MHz ×8/7)] (1 + 1/16)

=16.94 Mb/s.

Figure2.10 OFDM PHY data rates in Mb/s

18

The OFDM Model

Figure2.11 Model of an OFDM system

OFDM signals are typically generated digitally due to the difficulty increasing large banks of

phase lock oscillators and receivers in the analog domain. Figure2.11 shows the block diagram of

such an OFDM system .In the transmitter, the incoming data stream is grouped in blocks of Nc

data symbols, which are the OFDM symbols, and can be represented by a vector Xm. Next, an

IFFT is performed on each data symbol block and acyclic prefix of length Ng is added.

The received signal is, generally, the sum of a linear convolution with the discrete channel

impulse response, h (n), and an additive white Gaussian noise, w (n). It has to be said that it is

implicitly assumed that the channel fading is slow enough to consider it constant during one

symbol, and both, transmitter and receiver, are perfectly synchronized. At the receiver, the cyclic

prefix is removed, and then, the data symbol yk,m(frequency index k, OFDM symbol m) is

obtained by performing the FFT operation.

2.1.3 CHANNEL

AWGN

Additive white Gaussian noise (AWGN) is a channel model in which the only impairment to

communication is a linear addition of wideband or white noise with a constant spectral density

(expressed as watts per hertz of bandwidth) and a Gaussian distribution of amplitude. The model

does not account for fading, frequency selectivity, interference, nonlinearity or dispersion.

19

However, it produces simple and tractable mathematical models which are useful for gaining

insight into the underlying behavior of a system before these other phenomena are considered.

Multipath Fading Channel

A fading channel is a communication channel comprising fading. In wireless systems, fading

may either be due to multipath propagation, referred to as multipath induced fading, or due to

shadowing from obstacles affecting the wave propagation, sometimes referred to as shadow

fading. The presence of reflectors in the environment surrounding a transmitter and receiver

create multiple paths that a transmitted signal can traverse. As a result, the receiver sees the

superposition of multiple copies of the transmitted signal, each traversing a different path. Each

signal copy will experience differences in attenuation, delay and phase shift while travelling

from the source to the receiver. This can result in either constructive or destructive interference,

amplifying or attenuating the signal power seen at the receiver. Strong destructive interference is

frequently referred to as a deep fade and may result in temporary failure of communication due

to a severe drop in the channel signal-to-noise ratio.

Doppler spread and Delay spread

When the receiver and the transmitter are in relative motion, the received signal is subject to a

constant frequency shift, called the Doppler shift Therefore, as it occurs in the time domain, the

Doppler spread is defined as the difference between the largest and the smallest among these

frequency shifts,

fd = fM cos ϕ

Where

• fM = fc( v/c) is the maximum Doppler shift,

• v is the vehicle speed,

• fc is the carrier frequency,

• c is the speed of light, and

• ϕ is the arrival angle of the received signal component.

20

Thus we have,

fd = fc( v/c) cos ϕ

Furthermore, a time-varying Doppler shift is induced on each multipath component if the

reflecting objects and scatters in the propagation channel are in motion, causing frequency

dispersion.

The two manifestations of the channel time variations are the delay spread and the Doppler

spread. Depending on their values, the signal transmitted through the channel will undergo flat or

frequency selective fading. On one hand, the delay spread is a measure of the spreading time

over which the multipath signals arrive. It is a measure of the time dispersion of a channel, and is

very important in determining how fast the symbol rate can be in digital communications. One of

the most widely used measurement for characterizing the delay spread of a multipath channel is

the rms delay spread στ. Furthermore, the inverse of the delay spread defines the coherence

bandwidth, Bcoh. It is the frequency separation at which two frequency components of the signal

undergo independent attenuations and a measure of the range of frequencies over which the

multipath fading channel frequency response can be considered to be flat or not. On the other

hand, the Doppler spread Bd, is a measure of the spectral broadening caused by the time rate of

change of the multipath components due to the relative motion between transmitter and receiver.

Depending on how rapidly the multipath components change, the channel may be classified

either as a fast or a slow fading channel. Inversely proportional to one another rare the Doppler

spread and the coherence time. The coherence time Tcoh, is the time domain dual of Doppler

spread and is used to characterize the time-varying nature of the frequency dispersiveness of the

channel in the time domain. It is a statistical measure of the time duration over which the channel

impulse response is essentially invariant quantifying the similarity of the channel response at

different times.

Rayleigh fading

Rayleigh fading models assume that the magnitude of a signal that has passed through such a

transmission medium (also called a communications channel) will vary randomly, or fade,

according to a Rayleigh distribution — the radial component of the sum of two uncorrelated

Gaussian random variables.

21

Rayleigh fading is a reasonable model when there are many objects in the environment that

scatter the radio signal before it arrives at the receiver. The central limit theorem holds that, if

there is sufficiently much scatter, the channel impulse response will be well-modeled as a

Gaussian process irrespective of the distribution of the individual components. If there is no

dominant component to the scatter, then such a process will have zero mean and phase evenly

distributed between 0 and 2π radians. The envelope of the channel response will therefore be

Rayleigh distributed.

Calling this random variable R, it will have a probability density function:

() =

Ω/Ω, r≥ 0

Where

Ω=E ()

Often, the gain and phase elements of a channel's distortion are conveniently represented as a

complex number. In this case, Rayleigh fading is exhibited by the assumption that the real and

imaginary parts of the response are modeled by independent and identically distributed zero-

mean Gaussian processes so that the amplitude of the response is the sum of two such processes.

Rician fading

Rician fading is a stochastic model for radio propagation anomaly caused by partial cancellation

of a radio signal by itself — the signal arrives at the receiver by several different paths (hence

exhibiting multipath interference), and at least one of the paths is changing (lengthening or

shortening). Rician fading occurs when one of the paths, typically a line of sight signal, is much

stronger than the others. In Rician fading, the amplitude gain is characterized by a distribution.

Rayleigh is the specialized model for stochastic fading when there is no line of sight signal, and

is sometimes considered as a special case of the more generalized concept of Rician fading. In

Rayleigh fading, the amplitude gain is characterized by a Rayleigh distribution.

22

2.2 Technological Survey

2.2.1 Matlab

Matlab (Matrix Laboratory) is an interactive system whose basic data element is an ARRAY. It

was intended for use in Matrix theory, Linear algebra and Numerical analysis. Later and with the

addition of several toolboxes the capabilities of Matlab were expanded and today it is a very

powerful tool at the hands of an engineer. Its typical uses include:

•Math and Computation

•Algorithm development

•Modeling, simulation and prototyping

•Data analysis, exploration and visualization

•Scientific and engineering graphics

•Application development, including graphical user interface building.

2.2.2 Simulink

Simulink (Simulation and Link) is an extension of MATLAB by Math works Inc. It is a platform

for multi domain simulation and Model-Based Design of dynamic systems. It works with

MATLAB to offer modeling, simulation, and analysis of dynamical systems under a graphical

user interface (GUI) environment. The construction of a model is simplified with click-and-drag

mouse operations. Simulink includes a comprehensive block library of toolboxes for both linear

and nonlinear analyses. Models are hierarchical, which allow using both top-down and bottom-

up approaches. As Simulink is an integral part of MATLAB, it is easy to switch back and forth

during the analysis process and thus, the user may take full advantage of features offered in both

environments. Also, control logic can be tested and evaluated with-out the need to do time

consuming hardware experiments.

Key Features

• Extensive and expandable libraries of predefined blocks

• Interactive graphical editor for assembling and managing intuitive block diagrams

• Ability to manage complex designs by segmenting models into hierarchies of design

components

23

• Model Explorer to navigate, create, configure, and search all signals, parameters, and

properties of the model

• Ability to interface with other simulation programs and incorporate hand-written code,

including MATLAB algorithms

• Option to run fixed- or variable-step simulations of time-varying systems interactively

or through batch simulation

• Functions for interactively defining inputs and viewing outputs to evaluate model

behavior

• Graphical debugger to examine simulation results and diagnose unexpected behavior

in the design

• Full access to MATLAB for analyzing and visualizing data, developing graphical user

interfaces, and creating model data and parameters

• Model analysis and diagnostics tools to ensure model consistency and identify

modeling errors

24

Chapter 3

SIMULATION RESULTS AND ANALYSIS

3.1 AWGN

This section gives a comparison between the different modulation schemes used in the simulator.

These results have been obtained in an AWGN channel.

Figure3.1 BER for different modulation scheme in AWGN channel

The curves show the BER as a function of the bit energy to noise rate (Eb/N0), which is a

measure of the energy efficiency of a modulation scheme. If a higher Eb/N0 is needed to transfer

data for a given modulation scheme, it means that more energy is required for each bit transfer.

Low spectral efficiency modulation schemes, such as BPSK and QPSK, require a lower Eb/N0,

and hence, are more energy efficient and less vulnerable to bit errors than the high spectral

efficiency modulation schemes, such as 16-QAM and 64-QAM. And it is clearly visible in the

figure 3.1 which shows BPSK and QPSK with same curves and 16-QAM and 64-QAM with

progressively higher BER curves.

.

25

3.2 Multipath Fading:

As discussed earlier, the Rayleigh fading channel was used to implement the multipath fading.

And the analysis for the three main parameters for the fading channel is done from the obtained

simulation results.

Effect of Doppler shift

.

Figure3.2 Effect of Doppler shift on BER in QPSK

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter; with frequency deviation the sub-carriers will no longer be orthogonal, causing inter-

carrier interference (ICI) (i.e., cross-talk between the sub-carriers). Frequency offsets are caused

by Doppler shift due to movement. While Doppler shift alone may be compensated for by the

receiver, the situation is worsened when combined with multipath, as reflections will appear at

various frequency offsets. This effect typically worsens as speed increases, and it can be easily

seen from the simulation results in figure 3.2 and figure 3.3.

26

Figure3.3 BER for QPSK for different values of Doppler shift

Keeping the delay spread and multipath gain constant, the above simulation results for the

change in Doppler shift for QPSK modulation scheme was determined. In the figure 3.2, the bit

error rate increases as the relative velocity increases. This is also presented in the BER vs. SNR

plot which displays that with increasing Doppler shift, the curves have also shifted showing

higher BER at certain SNR point for higher Doppler shifts.

27

Effect of delay spread:

Figure3.4 BER for QPSK for different delay spread

The simulation result showing the effect of delay spread of the Rayleigh fading channel

presented in the figure3.4.

When the delay spread is less than the sample period, the signal bandwidth is smaller than the

coherence bandwidth causing only flat fading and the delayed samples interfere only with the

own sample itself. The result is that there is no Inter Symbol Interference (ISI). But when the

delay spread increases such that it is higher than the sample period, and the signal bandwidth

becomes larger than the coherence bandwidth causing the delayed samples interfere with the

adjacent samples. This results in ISI and thus bit error. And this can easily be seen in the above

figure. For a delay spread less than sample period, the BER vs. SNR curve shows no effect of

multipath fading and almost represents the AWGN result. But for when delay spread is greater

than sample period, the effect of multipath fading is clearly seen with the increase in BER.

28

Effect of multipath gain

Figure3.5 BER for QPSK for different multipath gains

The figure3.5 shows the effect of the gains of the multipath components.

The amount a multipath component interferes with a transmitting signal depends on the power

that the component reaches the receiver. When the gain of the component is higher, the

interference is higher causing loss in performance. Similarly, low multipath gain leads to less

interference and thus higher performance. And this is clearly seen in the figure3.5.

29

Chapter 4

DISCUSSION AND CONCLUSION

4.1 Discussion and Conclusion

In this wireless communication industry, WiMAX is an attractive alternative for fulfilling needs

higher range and data rates. And the physical layer defined in the standard IEEE 802.16e

describes the use of the Orthogonal Frequency Division Multiplexing (OFDM) which is a

technique based on multi carrier modulation (MCM) and frequency division multiplexing

(FDM). So this research helps to analyze the characteristic behavior of this technique in

different channels with different modulation schemes. BER and SNR are the main metrics used

to perform the analysis. This research helps to find suitable modulation schemes for different

channel conditions.

This research discusses the introduction of the WiMAX physical layer, its components and its

characteristics. The flexible and parameterizeable OFDM was studied, then simulated in

Simulink and analyzed, deriving its characters at different parameters.

Based on the analysis we can conclude that in AWGN channel, modulation schemes with low

spectral efficiency like BPSK and QPSK are better. Similarly, the performance of the OFDM in

multipath fading channel was seen to deteriorate at higher velocity, longer delay spread and

higher multipath gain.

4.2 Recommendations

The simulation analyzes and helps to find suitable modulation schemes for different channel

conditions. And thus this research can be further extended to develop and analyze a system with

adaptive modulation. Similarly, channel coding can be added to this model to add error

protection in the system, and in future this model can be expanded to include the components of

the MAC layer and a complete end to end WiMAX system could be built based on this model.

30

Bibliography

IEEE Computer Society and the IEEE Microwave Theory and Techniques Society , IEEE

Standard for Local and metropolitan area networks, Part 16: Air Interface for Broadband

Wireless Access Systems

John Wiley & Sons, WiMAX: Technology for Broadband Wireless Access Loutfi Nuaymi ©

2007, Ltd. ISBN: 0-470-02808-4

Chritian Bauer (Stuttguart), Introduction to WiMAX,

Jeffrey G. Andrews, Ph.D.Arunabha Ghosh, Ph.D.AT&T Labs Inc,Rias Muhamed.AT&T Labs

Inc., Fundamentals of WiMAX

M.A. Mohamed, F.W. Zaki, R.H. Mosbeh, Simulation of WiMAX Physical Layer: IEEE 802.16e

Univ.Prof. Dipl.-Ing. Dr.techn. Markus Rupp, Dipl.-Ing. Christian Mehlführer, Implementation

of a WiMAX simulator in Simulink

Roberto Cristi, Wireless Communications with Matlab and Simulink: IEEE802.16 (WiMax)

Physical Layer

Won Gi Jeon, Student Member, IEEE, Kyung Hi Chang, Senior Member, IEEE, and Yong Soo

Cho, Member, IEEE, An Equalization Technique for Orthogonal Frequency-Division,

Multiplexing Systems in Time-Variant Multipath Channels

31

Appendix

OFDM simulator block diagram

In order to have a general view of the WiMAX simulator described through the thesis, a

complete block diagram of the Simulink model file is given in this appendix.

Simulation on AWGN channel

32

Simulation on Rayleigh and AWGN channel

Simulation on Rayleigh channel

33

CODES FOR SIMULATION AND ANALYSIS

Initialization Code:

clear

BW=input('Required channel bandwidth in MHz(max 20 MHz)=');

disp('choose cyclic prefix to overcome delays spreads')

disp(',1/4 for longest delay spread ,1/8 for long delay spreads ,')

disp('1/16 for short delays spreads ,1/32 for very small delay spread channels')

G=input('= ');

if ((G~=1/4)&(G~=1/8)&(G~=1/16)&(G~=1/32))

error('You have choosen a guard period thats not valid in the IEEE 802.16')

end

inputsize=192;

Nfft=256;

fs=floor((2)*BW*1e6); %sampling freqency

freqspacing= fs/Nfft; %freqency spacing

Tb= 1/freqspacing; %usfel symbol time

Tg= G*Tb ;%Guard time

Ts=Tb+Tg ;%symbol time

samplingttime= Tb/Nfft;

CPsel=[(256-G*256+1):256 1:256];

CPremove=[(256*G+1):(256+G*256)];

SNR=input('Enter the channel SNR in dB=');

34

if SNR<0

error('not a valid SNR value')

end

a= input('Choose the modulation scheme :1=BPSK, 2=QPSK, 3=16 QAM, 4=64QAM ');

if (a==1) %BPSK

m=2;

Ry=[+1 -1];

Iy=[0 0];

qamconst=complex(Ry,Iy);

qamconst=qamconst(:);

bitspersymbol=1;

disp('Modulation scheme of BPSK is chosen');

elseif (a==2) %QPSK

m=4;

Ry=ones(2,1)*[+1 -1];

Iy=([+1 -1]')*ones(1,2);

qamconst=complex(Ry,Iy);

qamconst=qamconst(:)/sqrt(2);

bitspersymbol=2;

disp('Modulation scheme of QPSK is chosen');

35

elseif (a==3) %16-QAM

m=16;

Ry=ones(4,1)*[+1 +3 -1 -3];

Iy=([+1 +3 -3 -1]')*ones(1,4);

qamconst=complex(Ry,Iy);

qamconst=qamconst(:)/sqrt(10);

bitspersymbol=4;

disp('Modulation scheme of 16-QAM is chosen');

elseif (a==4) %64-QAM

m=64;

Ry=ones(8,1)*[+3 +1 +5 +7 -3 -1 -5 -7 ];

Iy=([+3 +1 +5 +7 -3 -1 -5 -7 ]')*ones(1,8);

qamconst=complex(Ry,Iy);

qamconst=qamconst(:)/sqrt(42);

bitspersymbol=6;

disp('Modulation scheme of 64-QAM is chosen');

end

Plotting code:

Effect of doppler shift on BER in QPSK

fd=[.1 1 10 15 20 30 40 50 60 70 80 90 100];

36

ber=[0 0 .054 .104 .162 .2198 .2646 .3015 .3326 .3566 .3769 .391 .398]

%ber_0=[1.6e-6 1.6e-6 .025 .049 .071];

plot(fd,ber,'b*-')

grid on

xlabel('Doppler Shift ')

ylabel('Bit error rate')

title('Effect of doppler shift on BER in QPSK')

hold all

%plot(fd,ber_0,'r+-')

legend('QPSK','DQPSK', 3)

Bit error rate for QPSK for different values of doppler shift

clc

SNR=[0 3 6 9 12 15 18 21 24 27 30];

ber=[ 0.2156 0.1330 0.0580 0.0132 0.0008 0.00001 0 0 0 0 0];

ber_0=[0.2341 0.1654 0.1117 0.0574 0.0179 0.0032 0.0002 0.00001 0 0 0];

ber_1=[0.3141 0.1929 0.1104 0.0795 0.0469 0.0249 0.0115 0.0049 0.0018 0.0004

0.00005];

ber_2=[ 0.3212 0.2612 0.1947 0.1325 0.0854 0.0532 0.0333 0.0187 0.0077 0.0020

0.0002];

ber_3=[ 0.3386 0.2863 0.2257 0.1644 0.1116 0.0686 0.0364 0.0191 0.0079 0.0022

0.0002];

ber_4=[0.3499 0.2981 0.2370 0.1757 0.1221 0.0792 0.0466 0.0236 0.0095 0.0031

0.0005];

semilogy(SNR,ber,'b*-');

grid on

xlabel('SNR ')

37

ylabel('Bit error rate')

title('Bit error rate for QPSK for different values of doppler shift')

hold all

semilogy(SNR,ber_0,'r+-');

semilogy(SNR,ber_1,'bo-')

semilogy(SNR,ber_2,'gx-')

semilogy(SNR,ber_3,'k*-')

semilogy(SNR,ber_4,'cs-')

legend('0.001Hz','1Hz','5Hz','10Hz','20Hz','100Hz', 3)

Bit error rate for QPSK for different delay spread

SNR=[0 3 6 9 12 15 18 21 24 27 30];

ber=[0.2551 0.1788 0.1018 0.0422 0.0112 0.0016 0.0001 0.0000 0 0 0]

ber_0=[ 0.3596 0.3114 0.2548 0.1944 0.1371 0.0908 0.0597 0.0417 0.0322 0.0273

0.0249];

semilogy(SNR,ber,'b*-')

grid on

xlabel('SNR ')

ylabel('Bit error rate')

title('Bit error rate for QPSK for different delay spread')

hold all

semilogy(SNR,ber_0,'r+-')

legend('1.7e-6 delay','2e-5 delay', 3)

Bit error rate for QPSK for different multipath gains

SNR=[0 3 6 9 12 15 18 21 24 27 30];

38

ber=[0.2551 0.1788 0.1018 0.0422 0.0112 0.0016 0.0001 0.0000 0 0 0];

ber_0=[0.2202 0.1398 0.0663 0.0195 0.0026 0.0001 0.00000 0 0 0 0];

ber_1=[0.2101 0.1291 0.0575 0.0149 0.0015 0.00001 0.0000 0 0 0 0];

ber_2=[ 0.2090 0.1279 0.0566 0.0144 0.0014 0.00001 0.0000 0 0 0 0];

semilogy(SNR,ber,'b*-');

grid on

xlabel('SNR ')

ylabel('Bit error rate')

title('Bit error rate for QPSK for different multipath gains')

hold all

semilogy(SNR,ber_0,'r+-');

semilogy(SNR,ber_1,'bo-')

semilogy(SNR,ber_2,'gx-')

legend('-3dB','-10dB','-20dB','-30dB', 3)