By,Vijaya Chandran Ramasami

KUID 698659

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Orthogonal FrequencyDivision Multiplexing

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TABLE OF CONTENTS

ABSTRACT .................................................................................................................................................. 5

OVERVIEW OF THE REPORT ................................................................................................................ 6

1. OFDM SYSTEM MODEL ....................................................................................................................... 7

1.1. INTRODUCTION ..................................................................................................................................... 71.2. OFDM USING INVERSE DFT ................................................................................................................ 71.3. GUARD TIME AND CYCLIC EXTENSION............................................................................................... 101.4. RAISED COSINE WINDOWING ............................................................................................................. 111.5. OFDM GENERATION.......................................................................................................................... 111.6. OFDM SYSTEM DESIGN..................................................................................................................... 12

2. ADVANTAGES OF OFDM ................................................................................................................... 14

2. 1. MULTI-PATH DELAY SPREAD TOLERANCE ........................................................................................ 142.2. EFFECTIVENESS AGAINST CHANNEL DISTORTION............................................................................... 142.3. THROUGHPUT MAXIMIZATION (TRANSMISSION AT CAPACITY) .......................................................... 152.4. ROBUSTNESS AGAINST IMPULSE NOISE .............................................................................................. 152.5. FREQUENCY DIVERSITY...................................................................................................................... 16

3. THE PEAK POWER PROBLEM IN OFDM ...................................................................................... 16

3.1. POWER AMPLIFIER LINEARITY ........................................................................................................... 163.2. CLIPPING ............................................................................................................................................ 173.3. ERROR-CONTROL CODING.................................................................................................................. 183.4. PEAK CANCELLATION......................................................................................................................... 183.5. PAR REDUCTION CODES.................................................................................................................... 183.6. SYMBOL SCRAMBLING TECHNIQUES .................................................................................................. 19

4. SYNCHRONIZATION IN OFDM SYSTEMS.................................................................................... 19

4.1. SYNCHRONIZATION USING CYCLIC EXTENSION.................................................................................. 194.2. SYNCHRONIZATION USING TRAINING SEQUENCES.............................................................................. 214.3. OPTIMAL TIMING IN THE PRESENCE OF MULTI-PATH.......................................................................... 21

5. MULTI-CARRIER CDMA ................................................................................................................... 22

5.1. SYSTEM MODEL ................................................................................................................................. 225.2. ADVANTAGES OF MC-CDMA ............................................................................................................ 23

6. APPLICATIONS OF OFDM ................................................................................................................ 24

6.1. DIGITAL AUDIO BROADCASTING (DAB) ............................................................................................ 246.2. DIGITAL V IDEO BROADCASTING (DVB) ............................................................................................ 256.3. WIRELESS LANS................................................................................................................................ 256.4. OFDMA............................................................................................................................................. 26

CONCLUSION ........................................................................................................................................... 26

REFERENCE: ............................................................................................................................................ 27

3

L IST OF FIGURES

FIGURE 1 : A OFDM MODULATOR .............................................................................................................. 8FIGURE 2 : THREE SUBCARRIERS WITHIN AN OFDM SYMBOL ................................................................... 9FIGURE 3: SPECTRA OF INDIVIDUAL SUB-CARRIERS................................................................................... 9FIGURE 4 : GUARD TIME AND CYCLIC EXTENSION - EFFECT OF M ULTIPATH ......................................... 10FIGURE 5 : OFDM SYTEM BLOCK DIAGRAM ............................................................................................ 12FIGURE 6 : SYNCHRONIZATION USING CYCLIC EXTENSION ...................................................................... 20FIGURE 7 : SYNCHRONIZATION USING TRANING SEQUENCES................................................................... 21FIGURE 8 : A M ULTI-CARRIER CDMA TRANSMITTER............................................................................. 22FIGURE 9 : A M ULTI-CARRIER CDMA RECEVIER.................................................................................... 23

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L IST OF TABLES

TABLE 1 : DIGITAL AUDIO BROADCASTING (OFDM PARAMTERS) .......................................................... 24TABLE 2 : WLAN - OFDM PARAMETERS................................................................................................. 26

5

AbstractMulti-Carrier Modulation is a technique for data-transmission by dividing a high-bit rate

data stream is several parallel low bit-rate data streams and using these low bit-rate data

streams to modulate several carriers. Multi-Carrier Transmission has a lot of useful

properties such as delay-spread tolerance and spectrum efficiency that encourage their

use in untethered broadband communications. OFDM is a multi-carrier modulation

technique with densely spaced sub-carriers, that has gained a lot of popularity among the

broadband community in the last few years. This report is intended to provide a tutorial

level introduction to OFDM Modulation, its advantages and demerits, and some

applications of OFDM.

6

Overview of the ReportThis report is organized as follows:

� The first section of the report presents the OFDM System Model. Details of

generation and demodulation of OFDM are presented, along with system design

issues.�

The second section of the report presents some of the important advantages of

OFDM that suit its use in Broadband communications.�

The third section of the report discusses the Peak Power Problem in OFDM and

some techniques used to overcome the problems of Power Amplifier Non-Linearity.�

The fourth section of the report discusses Synchronization Issues associated with

OFDM and some synchronization methods commonly used in OFDM.�

The fifth section of the report discusses a relatively new technique of combining

OFDM with CDMA called Multi-Car r ier CDMA (MC-CDMA). Transmitter and

Receiver structures for MC-CDMA and some of the advantages offered by MC-

CDMA are discussed.�

The final section of the report presents some of the applications of OFDM for

broadband communications. Applications such as DAB, DVB and WLAN are

considered in some detail.

7

1. OFDM System Model

OFDM is a multi-channel modulation system employing Frequency Division

Multiplexing (FDM) of orthogonal sub-carriers, each modulating a low bit-rate digital

stream.

1.1. Introduction

In older multi-channel systems using FDM, the total available bandwidth is divided into

N non-overlapping frequency sub-channels. Each sub-channel is modulated with a

separate symbol stream and the N sub-channels are frequency multiplexed. Even though

the prevention of spectral overlapping of sub-carriers reduces (or eliminates) Inter-

channel Interference, this leads to an inefficient use of spectrum. The guard bands on

either side of each sub-channel is a waste of precious bandwidth. To overcome the

problem of bandwidth wastage, we can instead use N overlapping (but orthogonal) sub-

carriers, each carrying a baud rate of 1/T and spaced 1/T apart. Because of the frequency

spacing selected, the sub-carriers are all mathematically orthogonal to each other. This

permits the proper demodulation of the symbol streams without the requirement of non-

overlapping spectra. Another way of specifying the sub-carrier orthogonality condition is

to require that each sub-carrier have exactly integer number of cycles in the interval T.

It can be shown that the modulation of these orthogonal sub-carriers can be represented

as an Inverse Fourier Transform. Alternatively, one may use a DFT operation followed

by low-pass filtering to generate the OFDM signal. The details of this method are

explained in the next section.

It must be noted that OFDM can be used either as a modulation or a multiplexing

technique.

1.2. OFDM using Inverse DFT

The use of Discrete Fourier Transform (DFT) in the parallel transmission of data using

Frequency Division Multiplexing was investigated in 1971 by Weinstein and Ebert [1].

Consider a data sequence d0, d2, …, dN-1, where each dn is a complex symbol. (The data

8

sequence could be the output of a complex digital modulator, such as QAM, PSK etc).

Suppose we perform an IDFT on the sequence 2dn (the factor 2 is used purely for scaling

purposes), we get a result of N complex numbers Sm (m = 0,1…,N-1) as:

∑ ∑−

=

−

=

==1

0

1

0

)2exp(2)2exp(2N

n

N

nmnnnm tfjd

N

nmjdS ππ [m = 0,1,..N-1] ------(2.1)

Where,

ss

n mTtNT

nf == and -------(2.2)

Where, Ts represents the symbol interval of the original symbols. Passing the real part of

the symbol sequence represented by equation (2.1) thorough a low-pass filter with each

symbol separated by a duration of Ts seconds, yields the signal,

Figure 1 : A OFDM Modulator

TttT

njdty

N

nn ≤≤

î= ∑

−

=

0for ,)2exp(Re2)(1

0

π -------(2.3)

Where, T is defined as NTs. The signal y(t) represents the baseband version of the OFDM

signal.

Serial ToParallel

Converter

x

x

mtfje 12π

mN tfje 12 −π

+sm

dn

9

Figure 2 : Three Subcarr iers within an OFDM symbol

Figure 3: Spectra of Individual Sub-Carr iers

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

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It is easy to note from (2.3), that�

The length of the OFDM signal is T.�

The spacing between the carriers is equal to 1/T.�

The OFDM symbol-rate is N times the original baud rate.

There are N orthogonal sub-carriers in the system.

The signal defined in equation (2.3) is the basic OFDM symbol.

1.3. Guard Time and Cyclic Extension

One of the main advantages of OFDM is its effectiveness against the multi-path delay

spread frequently encountered in Mobile communication channels. The reduction of the

symbol rate by N times, results in a proportional reduction of the relative multi-path

delay spread, relative to the symbol time. To completely eliminate even the very small

ISI that results, a guard time is introduced for each OFDM symbol. The guard time must

be chosen to be larger than the expected delay spread, such that multi-path components

from one symbol cannot interfere with the next symbol. It the guard time is left empty,

this may lead to inter-car r ier inter ference (ICI ), since the carriers are no longer

orthogonal to each other. To avoid such a cross talk between sub-carriers, the OFDM

symbol is cyclically extended in the guard time. This ensures that the delayed replicas of

the OFDM symbols always have an integer number of cycles within the FFT interval as

long as the multi-path delay spread is less than the guard time.

Figure 4 : Guard Time and Cyclic Extension - Effect of Multipath

Multipath component that does not cause ISI

guard Symbol guard

guard Symbol guard

guard Symbol guard

Multipath component that causes ISI

11

1.4. Raised Cosine Windowing

If the ODFM symbol were generated using equation (2.3), the power spectral density of

this signal would be similar to the one shown in Fig (psd). The sharp-phase transitions

caused by phase modulation results in very large side-lobes in the PSD and the spectrum

falls off rather slowly (according to a sinc function). If the number of sub-carries were

increased, the spectrum roll-off will be sharper in the beginning, but gets worse at

frequencies a little further away from the 3-dB cut-off frequency. To overcome this

problem of slow spectrum roll-off, a windowing may be used to reduce the side-lobe

level. The most commonly used window is the Raised Cosine Window given by [2]:

î

+≤≤+≤≤

≤≤++=

)(1 t )),/(cos5050

,0.1

0 )),/(cos(5.05.0

)(

rsrr

rs

rr

TTT)((t-T..

TtT

TtTt

tw

ββπβ

ββππ

Here Tr is the symbol interval which is chosen to be shorter than the actual OFDM

symbol duration, since the symbols are allowed to partially overlap in the roll-off region

of the raised cosine window. Incorporating the windowing effect, the OFDM symbol can

now be represented as:

TttT

njdtwty

N

nn ≤≤

î= ∑

−

=

0for ,)2exp()(Re2)(1

0

π

It must be noted that filtering can also be used as a substitute for windowing, for tailoring

the spectrum roll-off. But windowing is preferred to filtering because, it can be carefully

controlled. With filtering, one must be careful to avoid rippling effects in the roll-off

region of the OFDM symbol. Rippling causes distortions in the OFDM symbol, which

directly leads to less-delay spread tolerance.

1.5. OFDM Generation

Based on the previous discussions, the method for generating an ODFM symbol is as

follows.

First, the N input complex symbols are padded with zeros to get Ns symbols that are

used to calculate the IFFT. The output of the IFFT is the basic OFDM symbol.

12

� Based on the delay spread of the multi-path channel, a specific guard-time must be

chosen (say Tg). A number of samples corresponding to this guard time must be taken

from the beginning of the OFDM symbol and appended at the end of the symbol.

Likewise, the same number of samples must be taken from the end of the OFDM

symbol and must be inserted at the beginning.�

The OFDM symbol must be multiplied with the raised cosine window to remove the

power of the out-of-band sub-carriers.

The windowed OFDM symbol is then added to the output of the previous OFDM

symbol with a delay of Tr, so that there is an overlap region of rTβ between each

symbol.

Figure (modem) shows the block diagram of an OFDM transmitter and receiver.

Figure 5 : OFDM Sytem Block Diagram

1.6. OFDM System Design

OFDM system design, as in any other system design, involves a lot of tradeoff’s and

conflicting requirements. The following are the most important design parameters of an

ChannelCoding

SymbolMapping

Serial ToParallel

IFFTParallel

To Serial

CylicExtension

RaisedCosineWindow

DAC

RF-TXModule

ChannelDecoder

SymbolDemap

ParallelTo Serial

FFTSerial ToParallel

RemoveCylic

Extension

Timing &Frequenc

SyncADC

RF-RXModule

FrequencyCorrected

Signal

OutputBits

Input Bits

13

OFDM system. The following parameters could be a part of a general OFDM system

specification:�

Bit Rate required for the system.�

Bandwidth available.�

BER requirements. (Power efficiency).�

RMS delay spread of the channel.

Guard TimeGuard time in an OFDM system usually results in an SNR loss in an OFDM system,

since it carries no information. The choice of the guard time is straightforward once the

multi-path delay spread is known. As a rule of thumb, the guard time must be at least 2-4

times the RMS delay spread of the multi-path channel. Further, higher-order modulation

schemes (like 32 or 64 QAM) are more sensitive to ISI and ICI than simple schemes like

QPSK. This factor must also be taken into account while deciding on the guard-time.

Symbol DurationTo minimize the SNR loss due to the guard-time, the symbol duration must be set much

larger than the guard time. But an increase in the symbol time implies a corresponding

increase in the number of sub-carriers and thus an increase in the system complexity. A

practical design choice for the symbol time is to be at least five times the guard time,

which leads to an SNR loss that is reasonable.

Number of Sub-carriersOnce the symbol duration is determined, the number of sub-carriers required can be

calculated by first calculating the sub-carrier spacing which is just the inverse of the

symbol time (less the guard period). The number of sub-carriers is the available

bandwidth divided by the sub-carrier spacing.

Modulation and Coding ChoicesThe first step in deciding on the coding and modulation techniques is determining the

number of bits carried by an OFDM symbol. Then, a suitable combination of modulation

and coding techniques can be selected to fit the input data rate into the OFDM symbols

and, at the same time, satisfying the bit-error rate requirements. The choice of modulation

14

and coding techniques are lot easier now, since each channel is assumed to almost

AWGN and one doesn’ t need to worry about the effects of multi-path delay spread.

2. Advantages of OFDM

OFDM possesses some inherent advantages for Wireless Communications. This section

glances on few of the most important reasons on why OFDM is becoming more popular

in the Wireless Industry today.

2. 1. Multi-path Delay Spread ToleranceAs discussed earlier, the increase in the symbol time of the OFDM symbol by N-

times (N being the number of sub-carriers), leads to a corresponding increase in the

effectiveness of OFDM against the ISI caused due to multi-path delay spread. Further,

using the cyclic extension process and proper design, one can completely eliminate ISI

from the system.

2.2. Effectiveness against Channel DistortionIn addition to delay variations in the channel, the lack of amplitude flatness in

the frequency response of the channel also causes ISI in digital communication systems.

A typical example would be the twister-pair used in telephone lines. These transmission

lines are used to handle voice calls and have a poor frequency response when it comes to

high frequency transmission. In systems that use single-carrier transmission, an equalizer

might be required to mitigate the effect of channel distortion. The complexity of the

equalizer depends upon the severity of the channel distortion and there are usually issues

such as equalizer non-linearities and error propagation etc that cause additional trouble.

In OFDM systems on the other hand, since the bandwidth of each sub-carrier is

very small, the amplitude response over this narrow bandwidth will be basically flat (of

course, one can safely assume that the phase response will be linear over this narrow

bandwidth). Even in the case of extreme amplitude distortion, an equalizer of very

simple structure will be enough to correct the distortion in each sub-carrier.

15

2.3. Throughput Maximization (Transmission at Capacity)The use of sub-carrier modulation improves the flexibility of OFDM to channel

fading and distortion makes it possible for the system to transmit at maximum possible

capacity using a technique called channel loading. Suppose the transmission channel has

a fading notch in a certain frequency range corresponding to a certain sub-carrier. If we

can detect the presence of this notch by using channel estimation schemes and assuming

that the notch doesn’ t vary fast enough compared to the symbol duration of the OFDM

symbol, it can be possible to change (scale down/up) the modulation and coding schemes

for this particular sub-carrier (i.e, increase their robustness against noise), so that capacity

as a whole is maximized over all the sub-carriers. However, this requires the data from

channel-estimation algorithms. In the case of single-carrier systems, nothing can be done

against such fading notches. They must somehow survive the distortion using error-

correction coding or equalizers.

2.4. Robustness against Impulse NoiseImpulse noise is usually a burst of interference caused usually caused in channels such as

the return path HFC (Hybrid-Fiber-Coaxial), twisted-pair and wireless channels affected

by atmospheric phenomena such as lightning etc. It is common for the length of the

interference waveform to exceed the symbol duration of a typical digital communication

system. For example, in a 10 MBPS system, the symbol duration is 0.1 sµ , and a impulse

noise waveform, lasting for a couple of micro-seconds can cause a burst of errors that

cannot be corrected using normal error-correction coding. Usually complicated Reed-

Solomon codes in conjunction with huge interleaves are used to correct this problem.

OFDM systems are inherently robust against impulse noise, since the symbol duration of

an OFDM signal is much larger than that of the corresponding single-carrier system and

thus, it is less likely that impulse noise might cause (even single) symbol errors. Thus,

complicated error-control coding and interleaving schemes for handling burst-type errors

are not really required for OFDM Systems simplifying the transceiver design.

16

2.5. Frequency Diversity.OFDM is the best place to employ Frequency Diversity. In fact, in a combination of

OFDM and CDMA called the MC-CDMA transmission technique (section 5), frequency

diversity is inherently present in the system. (i.e, it is available for free)

Even though, OFDM provides a lot advantages for Wireless Transmission, it has a few

serious disadvantages that must be overcome for this technology to become a success.

The following sections discuses two serious problems associated with OFDM

transmission.

3. The Peak Power Problem in OFDM

One of the most serious problems with OFDM transmission is that, it exhibits a high

peak-to-average ratio. In other words, there is a problem of extreme amplitude

excursions of the transmitted signal. The OFDM signal is basically a sum of N complex

random variables, each of which can be considered as a complex modulated signal at

different frequencies. In some cases, all the signal components can add up in phase and

produce a large output and in some cases, they may cancel each other producing zero

output. Thus the peak-to-average ratio (PAR) of the OFDM system is very large.

The problem of Peak-To-Average Ratio is more serious in the transmitter. In order to

avoid clipping of the transmitted waveform, the power-amplifier at the transmitter front-

end must have a wide linear range to include the peaks in the transmitted waveform.

Building power amplifiers with such wide linear ranges is a costly affair. Further, this

also results in high power consumption. The DAC’s and the ADC’s must also have a

wide range to avoid clipping.

There has been a lot of research put into the study of overcoming the PAR problem in

OFDM [4,5,6,7]. The following sections discuss some of the most common and

important of those techniques as well as other issues.

3.1. Power Amplifier LinearityPractical Power Amplifiers have an input power range over which they have a linear

transfer curve. Usually the linearity of non-ideal power amplifiers is measured using a

17

term called the 1 dB compression point. It is defined as the input power at which the

output power of the amplifier is 1 dB less than the output power obtained with an ideal

amplifier. The figure(power) shows a typical response curve of a non-ideal power

amplifier.

3.2. ClippingOne important feature of the peak-to-average ratio in the OFDM is the fact that the

percentage of symbols have a very large peak-power is less (and the percentage decreases

with an increase in the number of sub-carriers). Thus in this case, the simplest possible

solution to the peak-power problem would be Clipping, i.e., limiting the peak amplitude

to some maximum level. Although simple, this method has a few disadvantages.�

Clipping produces a kind of self-interference that causes some degradation in the

BER performance.�

The non-linear distortion caused due to clipping increases the amount of out-of-band

radiation.

The increase in the out-of-band radiation is basically because of the fact that the clipping

operation is a multiplication of the OFDM symbol with a rectangular function that is 1 if

the amplitude is below a threshold and a smaller value if the amplitude is above the

threshold. This rectangular waveform increases the out-of-band radiation, and as a result,

the spectrum has a roll-off that is inversely proportional to the frequency.

The problem of slow spectrum roll-off can be overcome to some extent, by windowing

the rectangular clipping waveform. Several windows are proposed in literature. Some of

the most common ones are Gaussian, Cosine, Hamming, Kaiser etc. Simulation results

show a slight degradation in BER with clipping. When windowing is applied the BER

performance is still worse, since a large portion of the signal is affected by windowing

than by clipping alone.

The required back-off for the power amplifier can be determined by specifying the

amount of attenuation for the out-of-band spectral components, relative to the in-band

spectral components. It has been shown that windowing offers a 3-dB gain in the required

back-off when compared to clipping alone.

18

3.3. Error-Control CodingOne of the problems with clipping is the degradation in BER. Specifically, the symbols

that have a large PAR ratio are vulnerable to errors. To reduce this effect, forward error

correction (FEC) can be applied across several OFDM symbols. When FEC is applied,

the errors caused due to large PAR in particular symbols can be corrected by the

surrounding symbols.

3.4. Peak CancellationAnother method of removing the peaks in a OFDM signal is to subtract a time-shifted

and scaled reference function such that each subtracted reference function reduces the

peak power of at least one signal sample. It is desirable to choose a signal with

approximately the same bandwidth as the transmitted signal. The most commonly used

peak-canceling function is the sinc function because of its desirable frequency-domain

properties. The sinc function can be time-limited by multiplying by a raised-cosine

window. It can be shown that the peak cancellation technique will result in a lesser out-

of-band interference than the clipping and windowing techniques. A further advantage of

the peak-cancellation technique is the fact that it can be digitally implemented, following

the IFFT in the transmitter.

3.5. PAR Reduction CodesA more elegant solution to the PAR problem is the use of coding techniques. The PAR

can be reduced by using a code that only produces OFDM symbols for which the PAR is

below some desired level. The more the reduction in the PAR, the smaller is the coding

rate. It has been shown that (pg 138) it is possible to construct codes with a code rate of

¾ that provides a maximum PAR of 3 dB. Another interesting result in this direction is

the fact (pg 139) that the correlation properties of complementary sequence can translate

into a relatively small PAP ratio of 3-dB when these codes are used to modulate an

OFDM Symbol. All these results have lead to the usage of Golay-Complementary

sequences for generating these codes. Golay complementary sequences are sequence

pairs for which the sum of auto-correlation function is zero for all delay shifts that are not

equal to zero. A lot of research papers have been published on the usage of Golay Codes

for OFDM transmission, that deal with the efficient generation of these code and the

optimal and sub-optimal decoding and other interesting properties.

19

3.6. Symbol Scrambling TechniquesThe basic idea of these techniques is that, for each OFDM symbol, the input sequence is

scrambled by a certain number of scrambling sequences. The output signal with the

smallest PAR is transmitted. If the PAR for one OFDM symbol has a probability p of

exceeding a certain level without scrambling, the probability that it will exceeding with

scrambling (given a set of k scrambling codes) is pk. Thus scrambling hopes to reduce the

probabilitiy of occurrence of high PARs, rather than reducing the levels of these PARs.

4. Synchronization in OFDM Systems

Another important issue in OFDM transmission is synchronization. There are basically

three issues that must be addressed in synchronization.�

The receiver has to estimate the symbol boundar ies and the optimal timing instants

that minimize the effects of inter-carrier interference (ICI) and inter-symbol

interference (ISI).�

In an OFDM system, the sub-carriers are exactly orthogonal only if the transmitter

and the receiver use exactly the same frequencies. Thus receiver has to estimate and

correct for the carrier frequency offset of the received signal.�

Further, the phase information must be recovered if coherent demodulation is

employed.

Another associated problem with OFDM systems is the effect of phase noise. Phase

noise is present in all practical oscillators and it manifests itself in the form of random

phase modulation of the carrier. Both phase-noise and frequency offset cause significant

amount of ICI in an OFDM receiver. The effect these are worse in OFDM than single

carrier systems. The use of efficient frequency and phase estimation schemes can help

reduce these effects. Some of the common methods used to achieve synchronization in

OFDM systems are:

4.1. Synchronization using Cyclic ExtensionSince a Cyclic extension is added to every OFDM symbol, the first Tg seconds of the

OFDM symbol is identical to the last part. This property can be exploited for both timing

and frequency synchronization using a scheme depicted in figure (1).

20

This scheme correlates Tg seconds of the OFDM symbol with a part that is T seconds

delayed (T – being the symbol time, less the guard period Tg). The output of the

correlator can be written as:

∫ −−−=gT

dTtrtrty0

)()()( τττ

The symbol timing is estimated from the correlation peaks at the output of the correlator.

The characteristics of the correlation peaks (in terms of the correlation side-lobe levels

and the standard deviation of the correlation magnitude) are better if the correlation is

performed over a large number of independent samples. Since the number of independent

samples is proportional to the number of sub-carriers, this cyclic extension correlation

method is efficient only if a large number of sub-carriers are present (more than 100). In

the case of less number of sub-carriers, the side-lobe to peak ratio of the correlator output

will be high and sometimes this might lead to wrong timing.

Once the timing is established using the correlation output, the frequency offset can be

directly estimated. The phase of the correlator output is equal to the phase drift between

samples that are T seconds apart. Hence the frequency offset can be estimated as the

correlation phase divided by Tπ2 .

Figure 6 : Synchronization using Cyclic Extension

The cyclic extension technique is basically used for blind synchronization where it is not

possible to use a training sequence.

Conjugation

Find MaxCorrelation

Estimate Phase

x

T

Integrateover Tg

Frequency Offset

Timing

OFDMSignal

21

4.2. Synchronization using Training SequencesIn cases like packet data transmission in which a training sequence is available, a much

more efficient method of timing recovery is to correlate the received signal with the

known training sequence and to find the peaks in the correlator output. This method is

illustrated in fig (corr).

Here T is the sampling interval and ci are the matched filter coefficients, which are in

turn, the complex conjugates of the known training sequence. From the correlation peaks

in the output signal, both the symbol timing and the frequency offset can be estimated.

Figure 7 : Synchronization using Traning Sequences

4.3. Optimal Timing in the Presence of Multi-pathThe effect of multi-path is the introduction of ICI and ISI in the OFDM symbol. These

effects are significant only if the delay spread of the channel exceeds the guard interval.

ICI is caused mainly because the FFT interval is no longer flat (because the roll-off

regions due the multi-path components interfere with the flat region of the FFT interval).

ISI is caused mainly because of the overlap between the previous OFDM symbol and the

current OFDM symbol in the FFT interval. The solution to this timing problem is to find

the delay window with a width equal to the guard time-that contains the maximum signal

power. The optimal FFT starting time is then equal to the starting delay of the found

delay window, plus the delay that occurs between a matched filter peak output from a

single OFDM pulse and the delay of the last sample from the flat part of the OFDM

signal envelope, minus the length of the FFT interval.

T T T

x x x

+ Find Max

SymbolTiming

22

5. Multi-Carrier CDMARecently a new proposal for a system based on a combination of CDMA and OFDM has

gained increasing attention in the research community. This system is called the Multi-

Carr ier CDMA (MC-CDMA) system and it combines the advantages offered by both

OFDM and CDMA. This section describes the basic architecture and the advantages of

this system:

5.1. System ModelA MC-CDMA transmitter spreads the data signal using a given spreading code in the

frequency domain. In other words, each chip of the signal is transmitted over a separate

sub-carrier. The block diagram of a basic OFDM transmitter is shown in figure (trans).

In the MC-CDMA transmitter, the input data stream is first converted into a parallel

symbol stream (of width P), using a serial to parallel converter. Each data symbol is

spread using a spreading code K. All the data in total ( KP× ), are now transmitted in

parallel using sub-carrier modulation (OFDM).

Figure 8 : A Multi-Carr ier CDMA Transmitter

Serial ToParallel

Spreading

IDFT

Spreading

Datastream

23

In the MC-CDMA receiver, after down-conversion, the K sub-carrier components

corresponding to the received users data is first coherently detected with the DFT and

combined (using various diversity combining strategies) to yield the received data.

Figure 9 : A Multi-Carr ier CDMA Recevier

5.2. Advantages of MC-CDMACombining OFDM with CDMA has a lot of advantages when compared to using DS-

CDMA alone. Some of them are discussed in this section:�

The transmitted symbol duration is much larger than the chip duration of DS-CDMA,

this makes the job of synchronization much easier.�

Provided there is an adequate guard interval provided, the multi-path correction in the

form of RAKE combining is not necessary.�

The OFDM-CDMA system provides inherent frequency diversity, since a single

symbol is spread over a wide range of frequencies that may fade independently and a

diversity combiner can be used to improve the fading performance of the system.�

Finally, it must be noted that all these advantages are in addition, to what is already

offered by CDMA.

FFT

Weighting(Diversity)

Parallel ToSerial

ReceivedSignal

Despreading

Weighting(Diversity)

Despreading

SymbolStream

24

6. Applications of OFDMA lot of applications that use OFDM technology have spawned over the last few years. In

this section, one such application will be described in detail, while a introduction to the

other applications will be provided.

6.1. Digital Audio Broadcasting (DAB)DAB is an European standard for digital broadcasting that is intended to replace the

current analog technologies such as AM and FM. It was standardized by the European

Telecommunications Institute (ETSI) in 1995 [8]. DAB has got four transmission modes

with different parameters as shown in the table below:

Mode –I Mode –I I Model I I I Mode IV

# of sub-carriers 1536 384 192 768

Sub-carrier

Spacing

1 kHz 4 kHz 8 kHz 2 kHz

Symbol Time 1.246 ms 311.5 us 155.8 us 623 us

Guard Time 246 us 61.5 us 30.8 us 123 us

Carrier Frequency < 375 MHz < 1.5 GHz <3 GHz < 1.5 GHz

Transmitter

Separation

< 96 km < 24 km < 12 km < 48 km

Table 1 : Digital Audio Broadcasting (OFDM Paramters)

The DAB transmitted data consists of number of audio signals sampled at a rate of 48

kHz with a 22-bit resolution. This audio signal is then compressed at rates ranging from

32 to 384 kbps, depending upon the desired signal quality. The resulting digital data is

then divided into frames of 24 ms. DAB uses differential QPSK modulation for the

sub-carriers. A null-symbol (or a silence period that is slightly greater than the OFDM

symbol length) is used to indicate the start of the frame. A reference OFDM symbol is

then sent to serve as a starting point for the differential decoding of the QPSK sub-

carriers. Differential Modulation avoids the use of complicated phase-recovery schemes.

DAB uses a rate ¼ convolutional code with a constraint length of 7 for error-correction.

The coding rate can also be increased using puncturing. Interleaving is used to separate

25

the coded bits in the frequency domain as much as possible, which avoids large error

bursts in the case of deep fades affecting a group of sub-carriers.

DAB is designed to be a single frequency network, in which the user receives same

signals from several different transmitters. This greatly enhance spectral efficiency. Even

though there is a delay in the reception of signals from different transmitters, this

situation can be considered as a multi-path situation and can be easily handled by

selecting the guard interval properly. Further, this can be considered a form of transmit

diversity, that the DAB receiver can take advantage of.

6.2. Digital Video Broadcasting (DVB)Digital Video Broadcasting (DVB) is a standard for broadcasting Digital Television over

satellites, cables and thorough terrestrial (wireless) transmission. DVB was standardized

by the ETSI in 1997 [9]. The following are some important parameters of DVB:�

DVB has two modes of operation: the 2k mode with 1705 sub-carriers and the 8k

modes with 6817 sub-carriers.�

DVB uses QPSK, 16-QAM or 64-QAM sub-carrier modulation.�

DVB uses a Reed-Solomon outer code (204,188,t=8) and a inner convolutional code

with generator polynomials (177,133 octal) combined with two layers of interleaving

for error-control.�

Pilot Sub-carriers are used to obtain reference amplitudes and phases for coherent

demodulation. Two-dimensional channel estimation is performed using the pilot sub-

carriers, which aids in the reception of the OFDM signal.

6.3. Wireless LANsWireless LANs are one of the most important applications of OFDM. A lot of standards

have been proposed for Wireless LANs during the past decade, most of then based on

spread-spectrum schemes. In July 1998, IEEE Wireless LAN standardization group IEEE

802.11 standardized a scheme based on OFDM operating in the 5-GHz band. It is

interesting to note that this standard is one of the first packet-based one to use OFDM.

The parameters of this WLAN standard are given in table (1)

26

Data Rate 6,9,12,18,24,36,48,54 Mbps

Modulation BPSK, QPSK, 16-QAM, 64 QAM

Coding Rate 1/2, 2/3,3/4

# of Sub-Carr iers 52

# of pilots 4

OFDM Symbol Duration 4 us

Guard Interval 800 ns

Sub-Carr ier Spacing 312.5 kHz

3 dB bandwidth 16.56 MHz

Channel Spacing 20 MHz

Table 2 : WLAN - OFDM Parameters

One of the main reasons for using OFDM for Wireless LANs is relatively small amount

of delay spread encountered in such applications. In the case of indoor environments, the

delay spread is still much less and the efficiency of OFDM in such environments is very

high. In outdoor-environments however, directional antennas need to be employed if the

same guard interval were used (to reduce the effect of delay spread).

6.4. OFDMAFinally, it is also possible to use OFDM for multiple-access too. This technique is called

OFDMA and is implemented by providing each user with a small number of sub-carriers.

Even though this technique is similar to FDMA, it avoids the use of large guard bands

that are used to prevent adjacent channel interference.

ConclusionOFDM has several interesting properties that suit its use over Wireless channels and

hence many Wireless standards have started to use OFDM for modulation and multiple

access. The various methods of generation and demodulation of OFDM and specific

issues such as linearity and synchronization were analyzed. Application of OFDM such

MC-CDMA, DAB, DVB , WLAN etc, were also discussed in detail.

27

Reference:

1. Weinstein.S. B, Ebert P.M, “Data Transmission by Frequency Division Multiplexing

using the Discrete Fourier Transform”, IEEE Transactions on Communications, Vol-

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2. Richard Van Nee, Ramjee Prasad, “OFDM for Wireless Multimedia

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