UNIVERSITY OF NAIROBI    

                  

                                             FINAL YEAR PROJECT REPORT 

                                                                            PROJECT No: 88 

                                           CARRIER  SYNCHRONIZATION  IN  ORTHOGONAL FREQUENCY 

DIVISION MULTIPLEXING 

                                                                                       By: 

                                                                  MAGIGE   JONES   MAGIGE 

                                                                     REG.  NO. F17/2133/04 

  SUPERVISOR:  DR. V. K. ODUOL 

     EXAMINER:  DR. G.S.O ODHIAMBO 

                                                                                MAY   2009  

                A  PROJECT SUBMITTED IN PARTIAL FULFILLMENT FOR THE REQUIREMENT OF 

  THE AWARD OF BACHELOR OF SCIENCE DEGREE IN ELECTRICAL AND ELECTRONIC ENGINEERING 

                                   DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING 

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Abstract   

Orthogonal frequency division multiplexing (OFDM) is a special case of multicarrier transmission where a 

single data stream is transmitted over a number of lower rate subcarriers. 

In this project, transmitter and receiver was simulated complete with synchronization, to evaluate the 

performance of the OFDM system in a frequency selective channel  .The carrier recovery scheme 

employed in synchronization was the decision‐directed carrier recovery method. A simple Phase Locked 

Loop was looked at as it forms the basis of the decision‐directed carrier recovery method.This method of 

carrier recovery uses a decision device known as a slicer in the carrier recovery loop. 

 

A MATLAB program was written complete with a sub‐program for the synchronization, to investigate 

Orthogonal Frequency Division Multiplexing (OFDM) communication systems. 

The simulations obtained were plots of each step involved during the OFDM  modulation and 

demodulation processes, a corresponding plot in all the plots involved reflecting the varying power per 

Hertz (Power Spectral density) was also obtained using the periodogram method, i.e. The Welchs Power 

Spectoral Density estimate method. It showed varying energy distribution in each spectrum 

The implemented system uses 4‐Quadrature Amplitude Modulation (4‐QAM) on each subcarrier which 

were also depicted in the signal constellation (4‐QAM Constellation), which clearly reflects the 

undistorted passband signal. The system is not equipped with any higher level of error control, such as 

retransmissions. 

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ACKNOWLEDGEMENTS 

I would like to thank project supervisor,Dr V.K Oduol for the suggestions, ideas and for his constructive 

comments in keeping me on track while working on the project and writing this report. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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TABLE OF CONTENTS               PAGE NO 

Abstract …………………………………………………………………………………………………………i 

Acknowledgement……………………………………………………………………………………..…ii 

Dedication………………………………………………………………………………………………………v 

1.0 Introduction…………………………………………………………………………….…………1 

1.1 Background ……………………………………………………………………………………….…….1 

1.2 Overview …………………………………………………………………….………………….……….2 

1.3 Problem specification………………………………………………………………………………3 

1.4 Report outline……………………………………………………………….……...…………………4 

2.0 Principles and theory of OFDM…………………………………………….……..….….5 

2.1 Multicarrier……………………………………………………………………………………………..5 

2.2 Orthonogality……………...............................................................................6 

2.3 Idealized system model…………………………………………………..………………………8  

2.4 Transmitter………………………………………………..……………………………………………8 

2.5 Receiver…………………………………………………………………………………………..……….9 

2.6 DFT and IDFT………………………………………………………………………….…….…………..9 

2.7 FFT and IFFT………………………………………………………………………….…….…….……10. 

2.8 Mathematical description of OFDM……………………………………………..….…….11  

2.9 Propagation characteristics of mobile radio channels…………………  ………. 12 

2.10 Attenuation …………………………………………………………………………………….…….12 

2.11 Multipath effects…………………………………………………………………………….…….13 

2.11.1 Raleigh fading…………………………………………………………….…………13 

2.11.2 Frequency selective fading……………………………………….…………..13  

2.12 Delay spread………………………………………………………………………………………….14 

2.13 Intersymbol interference………………………………………………………..…………….14. 

2.14 Guard interval and cyclic prefix for elimination of ISI…………………….….….15 

2.15 Interleaving………………………………………………………………………………..….………15. 

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2.16 Adaptive transmission…………………………………………………………………………16 

2.17 Advantages of OFDM …………………….......................................................16. 

2.18 Disadvantages of OFDM…………………………………………………………………..….17 

3.0 Synchronization……………………………………………………………………….……….18 

3.1 Carrier recovery ………………………………………………………………………….…………18 

3.1.1 Concepts of a simple phase locked loop (PLL)………………..………19. 

3.1.2 Costas loop……………………………………………………………………..………21 

3.1.3 Decision directed carrier recovery loops……………………..…………22 

4.0 System design /simulation…………………………………………………….………….24 

4.1 System model…………………………………………………………………………….……….….24 

4.2 QAM modulation symbol sequence………………………………………….……….……24 

4.2.1 Symbol sequence…………………………………………..……….….25.  

4.2.2 Pulse shaping filter………………………………………….….……..25 

4.2.3 Carrier modulation………………………………………….…….……25 

4.3 FFT implementation ………………………………………………………..……………….……27 

4.4 OFDM reception…………………………………………………………………….…………..……35 

5.0 Analysis……………………………………………………………………………….…….………40 

5.1System performance and limitations……………………………………….…40 

5.2 Conclusions and recommendations…...........................................41 

5.3 Future work...................................................................................41 

References………………………………………………………………………………………….…..….. 42 

Appendices …………………………………………………………………………….……………..………44.. 

A‐ MATLAB CODE…………………………………………………………………… ……………44 B‐ Dictionary ………………………………………………  ……………………………...……….54 

 

 

 

 

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                                                        DEDICATION 

 

                              To my mother, my father and family. may 

                                    God bless you for  all your support 

 

 

 

 

 

 

 

 

 

 

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1.0 Introduction

1.1 Background

There is an increasing demand for high data rate services in modern society. One way to meet this

demand is to expand the existing infrastructure e.g. by connecting all users of bandwidth

consuming applications to fiber optic network. However this solution is not financially viable.

Developing alternative techniques that make use of exist

ing infrastructure is therefore an interesting option for broadband providers.

Orthorgonal Frequency Division multiplexing (OFDM) is a method that allows transmission of

high data rates over extremely hostile channels at a comparable low complexity. OFDM has

developed into a popular scheme for wideband digital communication whether wireless or over

copper wire used in application as digital television and audio broadcasting, wireless networking

and broadband internet access.

OFDM can be seen as either a modulation techniques or multiplexing technique. The primary

advantage of OFDM over single carrier scheme is its ability to cope with severe channel conditions

for examples, attenuation of high frequencies in a long copper wire, narrowband interference and

frequency selective fading due to multipath without complex equalization filters. Channel

equalization is simplified because OFDM may be viewed as using many slowly–modulated

narrowband signals rather than one rapidly-modulated wideband signal. The low symbol rate

makes the use of a guard interval between symbols affordable, making it possible to handle time-

spreading and eliminates intersymbol interference (ISI). This mechanism also facilitates the

design of single frequency networks, where serial adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

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combined constructively, rather than interfering as would occur in a traditional single carrier

system.

1.2 Overview

For testing and evaluating the performance of an OFDM system a MATLAB simulation code was

written. Figure 1.1 shows a simplified flow chart of the code.

Transmitter

In

AWGN Multipath

Figure 1.1: OFDM Simulation Flowchart

Serial to parallel

IFFT Parallel to serial

Modulator

CHANNEL

Demodulator Serial to parallel

FFT Parallel to serial

Out

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The transmitter first converts the input data from a serial stream to parallel sets. Each set of data

contains one symbol, Si, for each subcarrier. An inverse fast Fourier transform converts the

frequency domain datasets into samples of the corresponding time domain representation of this

data. Specifically, the IFFT is useful for OFDM because it generates samples of a waveform with

frequency components satisfying orthogonality conditions. Then, the parallel to serial block

creates the OFDM signal by sequentially outputting the time domain samples.

The channel simulation allows examination of common wireless channel characteristics such as

noise and multipath propagation effects. By generating random data to the transmitted signal,

simple noise is simulated. Multipath simulation involves adding attenuated and delayed copies of

the transmitted signal to the original. This simulates the problem in wireless communication when

the signal propagates on many paths. For example, a receiver may see a signal via direct path as

well as a path that bounces off a building.

The receiver performs the inverse of a transmitter. First the OFDM data are split from a serial

stream to parallel sets. The Fast Fourier transform (FFT) converts the time domain samples back

into a frequency domain representation. The magnitudes of the frequency components correspond

to the original data. Finally, the parallel to serial block converts this parallel data into a serial

stream to recover the original input data.

1.3 Problem Specification

The objects of this project are as follows:

Design a digital OFDM communication system complete with synchronization

Make the system capable of copying with time varying fading channel

Use of computer simulations that displays the channel response in real time on a user interface.

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1.4 Report Outline

The second chapter of this report describes the principles and theory of OFDM. It discusses the

building blocks, the mathematical description, channel characteristics and how OFDM overcomes

the effects of hostile channel. Chapter three enumerates on the importance of synchronization and

how it has been achieved in this project. Chapter four covers the system design, explaining in

detail the specific implementation issues. Chapter five discusses the analysis, conclusion and

suggestions are made for future work. Finally the end is the reference list followed by the

appendixes.

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2.0 PRINCIPLES AND THEORY OF OFDM

2.1 A multi-carrier system

OFDM is so called a multi-carrier system. The principle of a multi-carrier system is to divide the

available bandwidth into sub channels as depicted in fig 1.1 below and to transmit the information

in parallel on those sub channels.

Frequency frequency response response

Fig: 2.1

In a classical parallel data system, the total signal frequency band is divided into N non

overlapping frequencies sub channels. Each subchannel is modulated with a separate symbol and

the N subchannels are frequency modulated. It seems good to avoid spectral overlap of channels to

eliminate interchannel interference (ICI). However this leads to inefficient use of the available

spectrum.

2.2 Orthogonality

In OFDM, the sub carriers frequencies are chosen so that the subcarriers are orthogonal to each

other, meaning that cross talk between the sub channels is eliminated and inter carrier guard bands

are not required. This greatly simplifies the design of both the transmitter and the receiver unlike

conventional FDM; a separate filter for each sub channel is not required

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The orthogonality requires that the sub carrier spacing is ∆f = k/(TU) hertz where Tu seconds is the

useful symbol duration and K is a positive integer, typically equal to 1 therefore with N

subcarriers, the total passband bandwidth will be B ≈ N·∆f (Hz).

The orthogonality also allows high spectral efficiency with a total symbol rate near the nyquist

rate. Almost the whole available frequency band can be utilized.this is illustrated

In the fig below

Fig2.2Concept of OFDM signal: Orthogonal multicarrier method versus convectional multicarrier

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Figure 2.2 above illustrates the difference between the convectional nonoverlapping multicarrier

technique and the overlapping multicarrier modulation technique. As shown in figure by using the

overlapping multicarrier modulation technique, we save almost 50% of the available bandwidth

.To realize the overlapping multicarrier modulation however; we need to reduce crosstalk between

subcarriers, which means that we want orthogonality between the different modulated carriers.

OFDM requires very accurate frequency synchronization between the receiver and the transmitter;

with frequency deviation the subcarriers will no longer be orthogonal causing intercarrier

interference (ICI) i.e. crosstalk between the subcarriers.

2.3 Idealized system model

2.4Transmitter

Fig 2.2: transmitter

S(n) is a serial stream of binary digits. By inverse multiplexing (demultiplexing ) these are first

demultiplexed into N parallel streams and each one mapped to a symbol stream using some

modulation constellation preferably (QAM, PSK etc)

An inverse fast Fourier Transform (IFFT) is computed on each set of symbol giving a set of

complex time domain samples. The real and imaginary component are then converted to the

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analogue domain using digital to analogue converters (DACs).These samples are then quadrature

mixed to passband. The analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively. These signals are then summed to give the transmission signal

s(t).Specifically the IFFT is useful for OFDM because if generates samples of a waveform with

frequency components satisfying orthogonality conditions

2.5 receiver

Fig2.3: receiver

The receiver picks up the signal r(t), which is then quadrature mixed down to baseband using

cosine and sine waves at the carrier frequency. The baseband signals are then sampled and

digitized using analogue to digital converters(ADCs).A forward fast Fourier transform is used to

convert back to the frequency domain. This brings about N parallel streams each of which is

converted to a binary stream using an appropriate detector. These streams are then combined into

a serial stream S(n) which is an estimate of the original binary stream at the transmitter.

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2.6 DFT AND IDFT

A discrete Fourier transform is a kind of Fourier transform that requires an input function that is

discrete. It transforms a discrete time domain input into frequency domain. Such inputs are often

created by sampling a continuous function. The IDFT performs the inverse of the DFT

The sequence of N complex numbers Xo………….Xn-1 is transformed into the sequence of N

complex numbers Xo….... ….Xn-1 by the DFT according to the formula

The inverse discrete Fourier transform (IDFT) is given by

where Xk represent the amplitude and phase of the different sinusoidal components of the input

signal xn

The DFT computes the Xk from the xn while the IDFT shows how to compute the xn as a sum of

sinusoidal components with frequency K/N cycles per sample

2.7 FFT AND IFFT

The Fast Fourier Transform (FFT) is an efficient algorithm to compute the DFT and its inverse.

DFT decomposes a sequence of values into components of different frequencies. But computing it

directly from the definition is often too slow to be

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practical. An FFT is a way to compute the same result more quickly. The IFFT performs the

inverse of FFT.

2.8 Mathematical description of OFDM

If N sub carriers are used, and each sub carrier is modulated using M alternative symbols, the

OFDM symbol alphabet consists of MN combined symbols.

The low pass equivalent OFDM signal is expressed as:

Where (Xk) are the data symbols, N is the number of subcarriers and T is the OFDM symbol time.

The sub carrier spacing of ¼ makes them orthogonal over each symbol period. This property is

expressed as

Where(*) denotes the complex conjugate operation and( δ) is the Kronecker delta.

To avoid intersymbol interference in multipath fading channels, a guard interval of length Tg is

inserted prior to the OFDM block. During this interval a cyclic prefix is transmitted such that the

signal in the interval equals the signal in the interval . The

OFDM signal with cyclic prefix is thus:

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2.9 Propagation characteristics of mobile channels

In an ideal radio channel, the received signal would consist of only a single direct path signal,

which would be a perfect reconstruction of the transmitted signal. However in a real channel, the

signal is modified during transmission in the channel. The received signal consists of a

combination of attenuated, reflected, refracted and diffracted replicas of the transmitted signal. On

top of all these, the channel adds noise to the signal and can cause a shift in the carriers frequencies

if the transmitter or receiver is moving (Doppler effect) understanding of these effects on the

signal is important because the performance of a radio system is dependent on the radio channel

characteristics

2.10 Attenuation

Attenuation is the drop in the signal power when transmitting from one point to another. It can be

caused by the transmission path length, obstruction in the signal path, and multipath effects. Any

objects which obstruct the line of sight signal from the transmitter to the receiver can cause

attenuation

Shadowing of the signal can occur whenever there is an obstruction between the transmitter and

receiver. It is generally caused by buildings and hills and is the most important environmental

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attenuation factor. Shadowing is most severe in heavily built up areas due to the shadowing from

buildings. However, hills can cause a large problem due to the large shadow they produce. Radio

signals diffract off the boundaries of obstructions thus preventing total shadowing of the signal

behind hills and buildings. However, the amount of diffraction is dependent on the radio frequency

used with low frequency diffracting more than high frequency signals. Thus high frequency signals

especially ultra high frequencies and microwave signals require line of sight for adequate signal

strength. To overcome the problem of shadowing, transmitters are usually elevated as high as

possible to minimize the number of obstructions

2.11 Multipath Effects

2.11.1 Raleigh fading

In a radio link the RF signal from transmitter may be reflected from objects such hills, buildings or

vehicles. This gives rise to multiple transmission paths at the receiver. The relative phase of

multiple reflected signals can cause constructive or destructive interference at the receiver. This is

experienced over very short distance thus is termed fast fading.

2.11.2 Frequency selective fading

In any radio transmission, the channel spectral response is not flat. It has dips or fades in the

response due to reflections causing cancellation of certain frequencies at the receiver. Reflections

off nearby objects e.g ground, buildings, trees, etc can lead to multi path signals of similar signal

power as the direct signal. This can result in deep nulls in the received signal power due to

destructive interference.

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For narrow bandwidth transmissions if the null in the frequency response occurs at the

transmission frequency then the entire signal can be lost. This can be partly overcome in two ways.

By transmitting a wide bandwidth signal or spread spectrum, as CDMA, any dips in the spectrum

only results in a small loss of signal power, rather than complete loss. Another method is to split

the transmission up into many small bandwidth carriers as is done in COFDM /OFDM

transmission. the original signal is spread over a wide bandwidth thus any nulls in the spectrum

are unlikely to occur at all of the carrier frequencies this will result in only some of the carriers

being lost rather than the earlier signal

2.12 Delay spread

The received radio signal from a transmitter consists of typically a direct signal plus reflections of

objects such as buildings, and other structures. The reflected signals arrive at a later time than the

direct signal because of the extra path length, giving rise to a slightly different arrival time of the

transmitted pulse thus spreading the received energy. Delay spread is the time spread between the

arrival of the first and last multipath signal seen by the receiver.

In a digital system, the delay spread can lead to intersymbol interference. This is due to the delayed

multipath signal overlapping with the following symbols. This can cause significant errors in high

bit rate systems

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2.13 Intersymbol interference (ISI)

When digital data (of whatever origin) is transmitted over a band limited channel, dispersion in the

channel gives rise to a troublesome form of interference called intersymbol interference(ISI) .ISI

refers to interference caused by the time response of the channel spilling over from one symbol

into another. This has the effect of introducing deviation (errors) between the data sequence

reconstructed at the receiver output and the original data sequence applied to the transmitter input,

therefore unless corrective measures are taken ISI may impose a limit on the attainable rate of

data transmission that is far below the physical capability of the channel

2.14 Guard Interval and cyclic prefix for Elimination of InterSymbol Interference

One key principles of OFDM is since low symbol rate modulated schemes (i.e where the symbols

are relatively long compared to the channel time characteristics ) suffer less from inter symbol

interference caused by multipath, it is advantageous to transmit a large number of low rate

streams in parallel instead of a single high rate stream. Since the duration of each symbol is long it

is feasible to insert a guard interval between the OFDM symbols thus eliminating intersymbol

interference

The cyclic prefix is the end of the OFDM symbol copied into the guard interval. It is transmitted

during the guard interval. The guard interval is transmitted followed by the OFDM symbol

2.15 Interleaving

Frequency (sub carrier) interleaving increases resistance to frequency selective channel conditions

such as fading. for example when a part of the channel bandwidth is faded, frequency interleaving

ensures that the bit errors that would result from those sub carriers in the faded part of the

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bandwidth are spread out in the bit stream, rather than being concentrated. Similarly, time

interleaving ensures that bits that are originally close together in the bit stream are transmitted for

apart in time, thus mitigating against severe fading as would happen when traveling at high speed

However frequency interleaving offers little help for narrowband channels that suffer from flat

fading. Time interleaving is of little benefit in slowly fading channels such as for stationary

reception

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit

stream that is presented to the error correction decoder because when such decoders are presented

with a high concentration of errors, the decoder is unable to correct all the bit errors and a burst of

uncorrected errors occurs.

2.16 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return channel. Based on this information we can perform a task to counter

the condition in the channel. e.g if a particular range of frequencies suffers from interference or

attenuation, the carriers within that range can be disabled or made to run slower by applying more

robust modulation.

2.17 Advantages of OFDM

Can easily adapt to severe channel conditions without complex equalization

Robust against narrow band co-channel interference

Robust against intersymbol interference (1S1) and fading caused by multipath propagation

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High spectral efficiency

Efficient implementation using FFT

Low sensitivity to time synchronization errors

Tuned sub channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks.

2.18 Disadvantages of OFDM

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak to average power ratio (PAPR) requiring linear transmitter’s circuitry, which suffers

from poor power efficiency.

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3.0 SYCHRONIZATION

Before an OFDM receiver can demodulate the subcarriers, it has to perform at least two

synchronization tasks. The first one is to find out where the symbol boundaries are and what the

optimal timing instants are to minimize the effects of intercarrier interference (ICI) and

intersymbol interference (ISI).This is called timing or symbol recovery.

The second task is to estimate and correct the carrier frequency offset of the receiver signal to

avoid ICI. This is what is called carrier recovery.

For coherent receiver, the carrier phase has to be synchronized, too. Further, a coherent QAM

receiver needs to detect the amplitudes and phases of all subcarriers to define the decision

boundaries for the QAM constellation of each subcarrier. Usually the OFDM received signal has a

frequency offset, which immediately results in ICI, this means that the subcarriers are not perfectly

orthogonal, producing phase noise.

3.1 Carrier recovery

Carrier recovery typically entails two subsequent steps. The first step is estimation of carrier

synchronization parameters. These parameters are the carrier frequency offset and the carrier phase

offset.

The carrier frequency offset is mainly caused by two mechanisms;

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The frequency instability in either the transmitter or receiver oscillator and the doppler effect when

the receiver is in motion relative to the transmitter

The carrier phase offset is the result of three major components, the phase instability in oscillators,

the phase due to transmission delay and thermal noise (such as AWGN)

The second stage of carrier recovery is the correction of the received carrier signal according to the

estimates made

One of the most easiest and effective methods of carrier recovery is by using a phase locked loop

(PLL). The carrier recovery loop is a specific use of a PLL.

It needs a training signal and also matches carrier frequency and phase.

3.1.1 Concepts of a simple phase locked loop (PLL)

A PLL is a closed loop frequency controlled system in which functioning is based on the phase

sensitive detection of phase difference between the input and output signals of a controlled

oscillator. The term ‘phase locking’ means the task of aligning the output phase of the oscillator

voltage with the phase of the reference voltage

Phase locking is achieved by changing the frequency of the oscillator momentarily.

A unique property of a PLL is that during the phase locked condition the frequency of the input

and the output signals are the same. Therefore a PLL is an oscillator whose frequency is locked

into some frequency component of an input signal, which is done with a feedback control loop.

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Phase detector

Components of a PLL are; a phase detector, a voltage controlled oscillator and a low pass filter.

Figure 3.1 below shows the blocks that constitute a simple PLL

r(t) e(t) e’(t)

x(t)

Fig3.1: A simple Phase Locked Loop

The phase detector (PD); generates an error signal that drives the PLL. It measures the difference

between phase of local Oscillator and the input carrier. The error should be proportional to the

phase difference between the signals r(t) and x(t)

The loop filter; filters the phase error signal e(t) in order to provide a better signal to the VCO .

The error signal generated by the PD is actually a noisy estimate of the phase error, i.e the error

signal consist of an error term and a noise term. The loop filter

therefore processes e(t) in order to generate a useful error while suppressing the effect of the noise

as much as possible

LPF Loop filter

VCO

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3.1.2 Costas loop

Training sequence i.e before the actual transmission of data, the transmitter sends a standard

sequence of symbols that are known a prior by both the transmitter and receiver

If a long enough training sequence is available, the receiver can lock onto the carrier during the

training period. After the training period, the receiver has a good estimate of carrier phase

If the SNR is high, the probability of error is very small and therefore the decisions made by the

receiver are most likely to be correct. These “correctly decided symbol” are fed to the PLL to

continue to track the carrier phase

The costas loop performs both phase-coherent suppressed carrier reconstruction and synchronous

data detection within the loop.

r(t)

e(t)

Fig3.2: costas loop

LPF

Loop Filter

VCO

LPF

π/2 shifter

21

The upper loop is referred to as the quadrature or tracking loop and functions as a typical PLL,

providing a data- corrupted error signal. The lower in phase or decisioning loop provides data

extraction at the output of the lower mixer and corrects the data corruption.The corrected error

signal is applied through the loop filter to the VCO, which yields a phase estimate ( the data signal

is removed by multiplication before the loop filter.)

3.1.3 Decision-directed carrier recovery loops

The carrier recovery loop here uses a decision–directed phase detector. Many blocks in a receiver

use decision-directed algorithms. The algorithm processes the current received

symbol and makes a decision as to what it thinks the corresponding transmitted symbol was. The

decision is typically made using a decision device known as a slicer.

The slicer makes a decision by quantizing the received sample to the nearest constellation point

and that quantized symbol is used as an estimate of the actual transmitted symbol. Noise and other

impairments can cause the slicer to make incorrect decisions. Most decision-directed algorithms

can tolerate a few decision errors, but when several, errors occur in a short period of time, the

algorithm will often diverge

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Received

Signal x(t)

Locally generated Signal y(t) Phase error e(t) Fig 3.3: Architecture of a decision-directed carrier recovery loop

Decision Device

Phase Detector

Loop Filter

VCO

Symbol decisions

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4.0 SYSTEM DESIGN/SIMULATION

In the previous chapter, the theory of an OFDM system is treated. This chapter covers the design

aspects of the system. It explains the different building blocks of the system, how the different

system parameters are chosen and the corresponding outputs of the MATLAB simulations.

4.1 System Model

This section discusses the different building blocks of the system. The main emphasis is put on

functionality of the OFDM transceiver.

The OFDM system was modeled using MATLAB to allow various parameters of the system to be

varied and tested. The aim of doing the simulations was to measure the performance of OFDM

under different channel conditions, and to allow for different OFDM configurations to be tested.

4.2 QAM Modulation

To increase the data rate, the system uses 4-Quadrature amplitude modulation (4–QAM) on each

subcarrier, mapping one bit into one complex –valued symbol. The square signal constellation is

used, however, a comparison is made of the normal QAM signal and the discussed OFDM where

QAM is used to generate OFDM symbols. In the previous chapters, we have considered

transmission from the passband signaling point of view, since only a few practical communications

channels bear transmission of the baseband signals. Most physical transmission media are

incapable of transmitting frequencies at d.c or near d.c. In this section we consider complex

modulated (QAM) pass band signals.

The principles of a passband QAM transmitter is shown below:

24

ejwct

Bits

Complex Complex

Baseband Passband

Signal Signal

Fig 4.1: A passband 1/Q transmitter

4.2.1 Symbol Sequence

The first step in this section is the generation of a random 4-QAM symbol sequence. The QAM

alphabet is generated first, and after that symbol sequence by “random indexing”. QAM signals

consists of symbol elements

4.2.2 Pulse Shaping Filter

Before frequency translation, the symbol sequence is transformed into a baseband waveform using

the shaping filter. In this case we use the standard raised cosine filter with roll off factor 0.35 and

over sampling factor 16 (that is 16 samples per symbol).

4.2.3 Carrier Modulation

The role of carrier modulation is frequency translation. Modulating a complex baseband signal

with a complex exponential yields a complex-valued analytic passband signal. Since physical

media only accepts real valued signals, only the real part of the signal is transmitted (which indeed

contains all the information of the original complex baseband signal).

Coder QAM Complex symbols

R.E {.} Transmit Filter

Real Passband Signal

25

26

4.3 FFT Implementation

The first task to consider is that the OFDM spectrum is centered on fc. One way to achieve the

centering is the use of a 2N-IFFT and T/2 as the elementary period. The OFDM symbol duration is

specified considering a 2, 048-IFFT (N= 2,048); therefore we shall use a 4,096-IFFT.

A block diagram of the generation of one OFDM symbol is shown in the figure below where we

have indicated the values used in the MATLAB code. The next task to consider is the simulation

period. T is defined as the elementary period for a baseband signal, but since we are simulating a

passband signal, we have to relate it to a time–period, I/Rs, that considers at least twice the carrier

frequency. For simplicity we use the integer relation, Rs = 40/T. This relation gives a carrier

frequency close to 90MHz, which is the range for a VHF channel. We can proceed to describe

each of the steps specified in the figure below.

A B C D E s(t)

Fig 4.5: OFDM Symbol generation simulation

QAM Symbols

Serial to parallel

4,096 IFFT

Parallel to serial

tf T/2

Fp =1/T LPF

27

28

In figure 4.6 and figure 4.7, we can observe the results after the IFFT operation and. We can also

notice that carrier is the discrete time baseband signal. We could use this signal in baseband

discrete time domain simulations, but we must recall that the main OFDM drawbacks occur in the

continuous time domain; therefore we must provide a simulation tool for the latter. The first step to

produce a continuous time signal is to apply a transmit filter, tf, to the complex signal carriers. The

impulse response, or pulse shape, of tf, is shown in figure 4.8 below

The output of this transmit filter is shown in figure 4.9 in the time domain and in figure 4.10 in the

frequency domain. The frequency response of figure 4.10 is periodic as required of the frequency

response of a discrete time system, and the bandwidth of the spectrum shown in the figure is given

by Rs.

The reconstruction or digital to analog filter response is shown in figure 4.11. It is a Butterworth

filter of order 13 and cut–off frequency of approximately 1/T. The output of the filter is also shown

in figure 4.12 and figure 4.13.

29

30

31

32

The next step is to perform the quadrature multiplex double-sided band amplitude modulation of

the reconstruction output. In this modulation, an in-phase signal m1(t) and a quadrature signal

MQ(t) are modulated using the formula:

S(t) = m1(t) cos (2∏ fct) + mQ (t) sin (2∏fct)

33

34

4.4 OFDM Reception

As mentioned before, the design of an OFDM receiver is open; i.e. there are only transmission

standards. With an open receiver design, most of the research and innovations are done in the

receiver, for example the frequency sensitivity drawback is mainly a transmission channel

prediction issue, something that is done at the receiver; therefore, a basic receiver structure is

presented in this report. A basic receiver that just follows the inverse of the transmission process

is shown in figure 4.16 below:

G H I J

F

K

fc fig 4.16: OFDM reception simulation

Orthogonal frequency division multiplexing (OFDM) is very sensitive to timing and frequency

offsets. Even in the ideal simulation environment, we have to consider the delay produced by the

filtering operation. For our simulation, the delay caused by the reconstruction filter and the

demodulation filters is such that it is enough to impede the reception, and it is the cause of the

slight differences we can see between the transmitted and the received signals (figure 4.7 versus

figure 4.22). The result of this simulation are shown below.

Demodulation filter

Serial to parallel

4,096 FFT

Parallel To serial

QAM Slicer

r (t)

35

36

37

38

39

5.0 ANALYSIS CONCLUSION AND RECOMMENDATIONS

This chapter describes the analysis of the simulations in regard to performance and limitations of

the system.

5.1 System performance and limitations

In figure 4.6 and figure 4.7 an inverse fast Fourier transform converts the frequency domain

datasets into samples of the corresponding time domain representation of this data.

Specifically, the IFFT is useful for OFDM because it generates samples of a waveform with

frequency components satisfying orthogonality conditions. Here the signal carrier uses T/2 as its

time period. We can also notice that carriers is the discrete baseband signal. We could have used

the signal in the baseband discrete-time domain simulations, but this was limited by the fact that

OFDM drawbacks occur in the continuous time domain, this necessitated the simulation tool for

the latter.

Figure 4.8 indicates a transmitter pulse. In actual practice, the pulses will modulate a carrier for

transmission over relatively long distances. The outputs are shown in figure 4.9 and figure 4.10 in

time and frequency domain respectively. The frequency response of figure 4.10 is periodic as

required of the frequency response of a discrete time system, and the bandwidth of the spectrum

shown in this figure is given by Rs.

The reconstruction or digital to analog filter response is shown in figure 4.11. It is a Butterworth of

order 13 and cut-off frequency of approximately 1/T. The need for this filter is to give an analogue

baseband signal ready for up conversion. The reason for choosing this kind of filter rather than,

say, Chebyshev filter is that, for a given order, the Chebyshev filter has greater variation in the

passband than the Butterworth design, but falls off at a faster rate outside the passband. The output

of the filter is also shown in figure 4.12 which gives the shape of the carriers discrete signal and

figure 4.13 the corresponding FFT for the baseband with its estimates power spectral density.

Figure 4.15 shows the complete modulated signal (envelope) which carriers the information to the

receiver.

The OFDM receiver is open; that is, there are only transmission standards. With an open receiver,

most of the research and innovations are done in the receiver. For instance, the frequency

sensitivity drawback is mainly a transmission channel prediction issue, something that is done at

the receiver.

40

OFDM is very sensitive to timing and frequency offsets. Even in this ideal simulation

environment, we have considered the delay produced by the filtering operation. For our simulation,

the delay caused by the reconstruction and demodulation filters is about 64/Rs. This delay is

enough to impede the reception and it is the cause of the slight differences we can note between

the transmitted and the received signals (figure 4.7 versus figure 4.22 for example). With the delay

taken care of, the rest of the reception process gives what was transmitted. The result of the

reception simulation is shown between figures 4.17 and 4.24.

5.2 Conclusion and recommendations

We can find many advantages in OFDM, but there are still many complex problems to solve.

According to the simulations, OFDM appears to be a good modulation technique that offers a

superior performance in systems where multipath channel posses a threat. Some factors were not

tested here like peak power chipping, start time error and the effect of frequency stability errors.

The codification used for the system could be improved.

The use of channel estimation is a very interesting function to be added to the receiver to make the

system more resistant to fading and Doppler effects, overall, if it is going to be used aboard

vehicles in a highway.

5.3 Future Work

This chapter lists suggested future work.

DSP – based OFDM modem for full duplex communication between two PCs over frequency

selective channel. Other suggested areas are for emphasis in future would include:

• Algorithm refinement. Most of the algorithms used, e.g. the Welch’s power spectral density

(PSD) estimating method was not chosen because they have better performance compared to

others. There was simply not enough time for a comparison. A thorough evaluation of different

algorithms should be prioritized area in future work.

• User interphase development. The user interface could be implemented so that more

parameters can be adjusted and more results, e.g. bit error rate, displayed.

41

References

1) J.J. Van de Beek, “Synchrkonization and channel Estimation in OFDM Systems”, PhD

Divisional of Signal Processing, Lulea University of Technology, 1998.

2) Chang R. W. “Synthesis of Band Limited Orthogonal Signals for Multichannel Data

Transmission”, Bell Syst. Tech. J., Vol 45, pp. 1775 – 1796, Dec. 1996

3) Salzberg, B. R., “Performance of an efficient parallel data transmission system”, IEEE Trans.

Comm., Vol. COM – 15, pp. 805 – 813, Dec. 1967

4) Gullilermo Acosta., “Orthogonal Frequency Division Multiplexing based on the European

standard, 2001.

5) U.S Patent No. 3, 488,4555 “Orthogonal Frequency Division Multiplexing,” filed November

14, 1966, issued Jan. 6, 1970.

6) Wireless LAN Medium Access Control (MAC) AND Physical Layer (PHY) Specification, IEEE

Standard, supplement to standard 802 part 11: Wireless LAN, New York, NY, 1999.

7) Luis Intini., “Orthogonal Frequency Division Multiplexing for wireless networks”, University

of California, December 2000.

8) Tipler P., “Physical for Scientists and Engineers, 3rd Edition, worth publishers”, pp. 464 –

468, 1991.

9) Rappaport,T.S., “Wireless Communications Principle and Practice, IEEE Press, New York,

Prentice Hall, pp 169-177, 1996.

10) Van Nee, R., Prasad R., “OFDM for wireless Multimedia Communications”, Artech

House,Boston, pp 80-81, 2000.

42

11) Schmidl, T.M, and Cox, D.C., “Robust Frequency and timing Synchronization on OFDM”,

IEEE Trans. On Comm., Vol. 45, No 12. pp. 1613-1621, Dec. 1997.

12) Classen, F, Meyer, H, “Frequency synchronization algorithms for OFDM systems suitable for

communications over frequency selective fading channels”, Proceedings of IEEE Vehicular

Technology Conference (VTC), IEEE, 1994. pp. 1655-9.

13) Proakis, J. G., “Digital Communications”, Prentice Hall, 3rd edition, 1995.

14) Tufvesson, F, Maseng, T, “Pilot assisted channel estimation for OFDM in mobile cellular

systems”, IEEE 47 th Vehicular Technology conference Technology in Motion, Phoenix, AZ,

USA, 4-7 May 1997,Vol.3 pp. 1639-43, 1997.

43

APPENDIX

A.Matlab Code

Generation of Random Quadrature Amplitude Modulation(QAM) MATLAB code

Symbol Sequence

M=2;

temp_M=-(M-1):2:(M-1);

for i=1:M

for k=1:M

QAM(i,k)=temp_M(i)+j*temp_M(k);

end

end

QAM=QAM(:).';

index=randint(1,2000,[1 M^2]);

sym=QAM(index);

Pulse shaping filter

over=16;

Pulse=rcosine(1,over;normal;0.35);

[trash,pos]=max(pulse);

sig=kron(sym,[1 zero(1,over-1)]);

sig=filter(pulse,1,sig);

sig=sig(pos:end);

Figure(1);plot(eal(sig(1:800)));grid;

w_c=0.4;

44

r=2*real(sig.*exp(j*w_c*pi*(0:length(sig)-1)));

figure(2);plot(r(1:800));grid;

W=linspace(-pi,pi,1024);

R=freqz(r(1000:2023),1,W);

R=R./max(abs(R));

figure(3);subplot9211);

plot(W/pi,abs(R));

grid;

y=r.*exp(-j*w_c*pi*(0:length(sig)-1)));

Y=freqz(y(1000:2023),1,W);

Y=Y./max(abs(Y));

figure (3);subplot(212);

plot(W/pi,abs(Y));grid;

f=remez(50,[0 0.2 0.3 1],[1 1 0 0]);

F=freqz(f,1,W);

hold on;

plot(W/pi,abs(F),’r’,LineWidth’,2);

hold off;

y=filter(f,1,y);

y=y(26:end);

Y=freqz(y(1000:2023),1,W);

Y=y./max(abs(Y));

figure (3);

subplot(212);

plt(W/pi,abs(Y));

grid;

Axis([-1 1 0 1.1]);

Plot(y(1+over:over:end),’*’;MarkerSize’,8);

45

Axis([-2 2 -2 2]);grid;

End;

Orthogonal Frequency Division Multiplexing

OFDM Transmission

%OFDM parameters

Tu=224e-6;

T=Tu/2048;G=1;

Delta=G*Tu;

Ts=delta+Tu;

Kmax=1705;

K min=10;

FS=4096;

q=10;

fc=q*1/T;

Rs==4*fc;

T=o:1/Rs:;Tu;

%Data generation

M=Kmax+1;

Rand(‘state’,0);

A=-1+2*round(rand(M,1)).’+*(-1+2*round(rand(M,1))).;

A=length(a);

Information=zeros(FS,1);

Information(1:(A/2))=[a(1:(A/2)).’];

Information((FS_((A/2)_1)):FS)=[a(((A/2)+1);

Carriers=FS*ifft(info,FS);

46

Tt=0:T/2:Tu;

Figure(1);

Subplot(211);

Stem(tt(1:20),real(carriers(1:20)));

Subplot(212);

Stem(tt(1:20),imag(carriers(1:20)));

Figure(2);

F=(2/T)*(1:(FS))/(FS);

Subplot(211);

Plot(f,abs(fft(carriers,FS))/FS);

Subplot(212);

Pwelch(carriers,[],[],[],2/T);

%D/A simulation

L=length(carriers);

Chips=[carriers.’;zeros((2*q)-1,L)];

P=1/Rs:1/Rs;T/2;

g=ones(length(p),1);

figure(3);

stem(p,g);

dummy=conv(g,chips(:));

u=[dummy(1:length(t))];

figure(4);

subplot(211);

plot(t(1:400),real(u(1:400)));

subplot(2120;

plot(t(1:400),real(u(1:400)));

figure(5);

ff=Rs*(1(q*FS))/(q*FS);

47

subplot(212);

pwelsh(u,[],[],[],Rs);

%reconstruction filter

[b,a]=butter(13,1/20);

[H,F]=FREQZ(b,a,FS,Rs);

Figure(6);

Plot(F,20*log10(abs(H)));

Baseband=filter(b,a,u);

Figure(7);

Subplot(211);

Plot(t(80:480);real(baseband(80:480)));

Subplot(212);

Plot(t(80:480),imag(baseand(80:480)));

Figure(8);

Subplot(211);

Plot(ff,abs(fft(baseband,q*FS))/FS);

Subplot(212);

Pwelch(baseband,[],[],[],Rs;

&upconverter

S_tilde=(uoft.’)*exp(1i*2*pi*fc*t);

S=real(s_tilde);

Figure(9);

Plot(t(80:480),s(80:480));

Figure(10);

Subplot(211);

48

%plot(ff,abs(fft(((real(baseband).’).*cos(2*pi*fc*t)),q*FS))FS);

%plot(ff,abs(fft(((imag(baseband).’)*sin(28pi*fc*t),q*FS))FS);

Plot(ff,abs(fft(s,q*FS0)/FS);

Subplot(212);

%information(((real(baseband).’).*cos(2*pi*fc*t)),[],[],[],Rs);

%information(((imag(baseband).’).*sin(2*pi*fc*t)),[],[],[],Rs);

Pwelch(s,[],[],[],Rs);

%OFDM Reception

Tu=224e_6;

T=Tu/2048;

G=0

Delta=G*Tu;

Ts=delta+Tu;

Kmax=1705;

Kmin=0;

FS=4096;

q=10;

fc=q*1/T;

Rs=4*fc;

t=0:1Rs:Tu;

tt=0:T/2:Tu;

%Data generator

sM=2;

[x,y]=meshgrid((-sM+1):2:(Sm-1),(-Sm+1):2:(Sm-1));

49

Alphabet=x(:)+li*y(:);

N=Kmax+1;

Rand(‘state’,0);

a=-1+2* round (rand(N,1));+*(-1+2*round(rand(N,1)));

A=length(a);

Information=zeros(FS,1);

Information(1(A/2))=[a(1(A/2)).’];

Information((FS-((A/2)-1))FS)=[a(((A/2+1):A);];

Carriers=FS.*ifft(info,FS);

%Upconversion of baseband signal

L=length(carriers);

Chips=[carrier.’;zeros((2*q)-1,L)];

P=1/Rs:1/Rs:T/2;

g=ones(length(p),1);

Dummy= conv(g,chips(:));

U=[dummy;zeros(46,1)];

[b,aa]=butter(13,1/20);

Baseband=filter(b,aa,u);

Delay=64;

S_tilde=(baseband(delay+1:length(t))).’).*exp(li*2*pi*fc*t);

S=real(s_tilde);

%OFDM RECEPTION

%Downconversion

r_tilde=exp(-li*2*pi*fc*t).*s,%(F)

Figure(11);

Subplot(211);

Plot(t,real(r_tilde));

50

Axis([0e_7 12e-7-60 60]);

Grid on;

Figure(11);

Subplot(212);

Plot(t,imag(r_tilde));

Axis([0e-7 12e-7 -100 150]);

grid on;

figure(12);

ff=(Rs)*(1;(q*(FS))/(q*FS);

subplot(211);

plot(ff,abs(fft(r_tilde,q*FS))/FS);

plot(t,imag(r_tilde));

grid on;

figure(12);

subplot(212);

pwelch(r_tilde,[],[],[],Rs);

%Carrier suppression

[B,AA]=butter(3,1/2);

r_information=2*filter(B,AA,r_tilde);

Figure(13);

Subplots(211);

Plot(t,real(r_information));

Axis([0 12e-7 -60 60]);

Grid on;

Figure(13);

Subplot(212);

Plot(t,imag(r_information));

Axis([0 12e-7 -100 150]);

Grid on;

51

Figure(14);

F=(2/T)*(1:(FS))/(FS);

Subplot(211);

Grid on;

Subplot(212);

Pwelch(r_information,[],[],[],Rs);

%Sampling

r_data=real(r_information(1:(2*q):length(t)))....

+1i*imag(r_information(1:(2*q):length(t)));

Figure(15);

Subplot(211);

Stem(tt(1:20),real(r_data(1:20))));

Axis[o 12e-7 -60 60]);

Grid on;

Figure(15);

Subplot(212)

Stem(tt(1:20),imag(r_data(1:20))));

Axis[0 12e-7 -100 150]);

Grid on;

Figure(16);

F=(2/T)*(1:(FS))/(FS);

Subplot(211);

Plot(f,abs(fft(r_data,FS))/FS);

Grid on;

Subplot(212);

Pwelch(r_data,[],[],[],2/T);

%FFT

52

Information_2N=(1/FS).*fft(r_data,FS);%(1)

Information_h=[information_2N(1:A/2) information_2N((FS-((A/2-1)):FS)];

%slicing

For k=1:N;

A_hat(k)=alphabet((information_h(k)-alphabet)= =min(information_h(k)-alphabet));%(J)

End;

Figure(17)

Plot(information_h((1:A)).’.K’);

Title(‘received comnstellation’)

Axis square;

Axis equal;

Figure(18)

Plot(a_hat((1:A)),’or’);

Title(‘4-QAM constellation’)

Axis square;

Axis equal;

Grid on;

Axis([-1.5 1.5 -1.5 1.5]);

end

53

B. Dictionary

Appendix below is the dictionary of occurring abbreviations and acronyms.

AWGN Additive White Guassian Noise

CP Cyclic Prefix

BER Bit Error Rate

DSP Digital Signal Processor

DFT Discrete Fourier Transform

FFT Fast Fourier Transform

IDFT Inverse Discrete Fourier Transform

IFFT Inverse Fast Fourier Transform

ICI Interchannel Interference

ISI Intersymbol Interference

OFDM Orthogonal Frequency Division Multiplexing

QAM Quadrature Amplitude Modulation

SNR Signal to Noise Ratio