SEER 03 Tehnica de Modulatie OFDM Eng

7/27/2019 SEER 03 Tehnica de Modulatie OFDM Eng

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2. ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING

Cuprins2. Orthogonal Frequency Division Multiplexing ............................................................... 12.1 Introduction .............................................................................................................. 22.1 OFDM basic principles ............................................................................................ 42.2 Guard time ............................................................................................................... 62.3 An OFDM System Block Diagram .......................................................................... 84.4 Timing and Frequency Synchronization ................................................................ 11

2.4.1 Timing Synchronization.................................................................................. 122.4.2 Frequency Synchronization ............................................................................ 14

2.4.3 Synchronization Methods ............................................................................... 15

2.5 The Peak-to-Average Power Ratio ........................................................................ 182.5.1 Signal distortion techniques ....................................................................... 202.5.2 The Coding Techniques .................................................................................. 242.5.3 The Scrambling Techniques ........................................................................... 24

2.6 OFDMA ................................................................................................................ 252.7 Conclusions: OFDM Pros and Cons ...................................................................... 25n =144/125 ................................................................................................................... 28

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


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2.1 IntroductionOrthogonal frequency division multiplexing (OFDM) is a multicarrier modulation

technique. The multicarrier modulation techniques have proven to be very efficient in

mitigating with the negative effects of highly dispersive channels.

Lets consider the case of high data rate -R0 - communications systems (bandwith

-B0 , symbol time - T0 ). The designers must avoid both the ISI due to the delay spread

and the necessity of using complex equalization processors involved by the selective

fading.

The Multicarrier Modulation Techniques propose to replace the solution of a high

data rate single modulated carrier with the parallel transmission of a large number, say

N, of low data rate modulated subcarriers. To preserve the data rate the rate of each

subcarrier is aR0/N(bandwidth -B0/N, and symbol time - T=NT0 ).

By using an appropriate value ofN, we can make symbol time (T=NT0) larger than

the channel delay spread and ISI produced by the multipath propagation could be

significantly reduced (figure 2.1.a). At the same time the bandwith of each subchannel

can be made narrow enough (B0/N


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The simplest way to implement the orthogonality is to distribute the subcarriers

along the bandwidthB0 in such a way that the individual bandwidths do not overlap.

In this case the transmitter and the receiver could have the block diagrams given in

figure 2.2.

The main drawbacks of this solution consist in:

the inefficient usage of the frequency spectrum,the complexity of the equipment that grows linearly withN, andthe complexity of the Low Pass Filters used in the receivers.OFDM overcomes these drawbacks by using subchannels with overlapping

bandwidths and DFT to process the OFDM signal both at the transmitter and at the

receiver.

We have to remark that in its turn DFT lend itself on efficient implementation

such as FFT.

These aspects and other innovative options made OFDM an efficient technology

from the point of view: of the implementation, of the efficient management of

intersymbol interference (ISI) in highly dispersive channels and of the efficient usage of

the frequency bandwidth.

Consequently OFDM technique was preferred for many modern high-data-rate

communications systems: WiFi, WiMAX, DVB, DAB, xDSL, etc.

This chapter aims to facilitate a practical understanding of key OFDM concepts

such as: FFT processing of the signal, guard interval generation, frequency equalization,

synchronization, peak-to-average power ratio, etc.

a.

x(t)

+S/P

Conv.

Data in

R0 bps

X

cos 2f1 t

X

cos 2f2t

X

cos 2fNt

r(t)

Data out

R0 bpsP/S

Conv

.

LPFX

cos 2f1t

X

cos 2f2t

LPF

X

cos 2fNt

LPF

b.

Figure 2.2 Basic block diagrams of: a. multicarrier transmitter, b. multicarrier receiver


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Some considerations about OFDM implementation in the case of WiMAX

technology will be also given.

2.1 OFDM basic principlesThe specific feature of OFDM as a multicarrier modulation technique is that it uses

subcarriers with overlapping bandwidths and DFT computational technique in order to

generate and to demodulate the subcarriers.

It can be demonstrated that, in this case, the subcarriers are orthogonal if they are

spaced at 1/Tin the frequency domain.

Let D=[d0, d1, d2, d3, .. dN,]be the N length data vector obtained as output for a

serial to parallel data converter. Every data symbol modulates a distinct subcarrier. Two

successive subcarriers are separated in the frequency domain by an offset 1/T.

Consequently a common expression of theNsubcarriers OFDM symbol beginning at ts

is:

Ttttt

TtttttT

ifjd

tsss

ss

N

Ni

scNi s

0

)))(5.0

(2exp(Re)(

12

2

2/

(2.1)

wherefc stands for the central frequency of the RF bandwidth.

A similar equation can be derived in the base band:

Ttttt

TtttttT

ijd

tsss

ss

N

Ni

sNi s

0

))(2exp(Re)(

12

2

2/

(2.2)

In figure 2.3.a, the first four subcarriers of an OFDM symbol corresponding to a

data vector D=[1,-1,1,1, .], are sketched. If the frequency offset between two

successive subcarriers is equal to 1/Tall the subcarriers will have an integer number of

cycles during symbol time T. It can be shown that this is the key for the orthogonality.

Indeed lets analyse the output of the coherent demodulator:


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2/

12

2

2/

12

2

2/

))(2exp(

))(2exp())(2exp(

Ni

N

Ni

Tt

t

sNi

N

Ni

sNi

Tt

t

s

TddtttT

ki

jd

dtttT

ijdtt

T

kj

s

s

s

s

s

s

(2.3)

We can remark that, due to the integer number of cycles per symbol time, the only

subcarrier that contributes to the output signal amplitude is the one processed by the

considered branch of the demodulator.

To explore the behaviour of the OFDM components in the frequency domain lets

remark that every subcarrier is modulated with a Tseconds long rectangular function sothat the spectrum of each subcarrier will be governed by the sinc(x) function defined as

x

x

sinxsinc

(2.4)

withsinc(0)=1, and zero crossings occurring at x=fT=1, 2, 3. .

It follows that, in the frequency domain, the amplitude spectrum of every

subcarrier is sinc alike and has the main lob width equal to 2/THz and zero crossings

that occur at multiples of 1/THz.

In figure 2.3.b the spectrum of six successive subcarriers is given. If we consider

that the demodulation represents an ideal sampling process in the frequency domain, in

the centre of every subcarrier spectrum, it is clear that no interference between

subcarriers will result (all the spectrums are zero except the sampled one).`

Figure 2.3 The components of an OFDM symbol

a. Time domain

t

T

b. Frequency domain

f1 f2 f3 f4 f5 f6 f7-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Frequency

1/T


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To investigate the possibilities of efficiently generating the OFDM symbols lets

consider the vector d having the N data symbols serial to parallel converted as

components.

Every data symbol phase/amplitude modulates a subcarrier. A BPSK modulation

results in the peculiar case of binary data symbols (figure 2.3).

This observation suggested the possibility to consider that the data vector

represents the IDFT of a signal consisting of theNsubcarriers [4].

Denoting by F theNxN DFT matrix one can write:

s = F-1

D (2.5)

In (2.5) s is a vector having as components the samples of the OFDM signal. At

the receiver the data vector can be recovered by direct DFT of the received OFDM

symbol.

By identifying the IDFT/DFT as a solution to generate and to demodulate the

OFDM symbol the necessary equipment becomes very simple and efficient by

comparison with the solution mentioned before in the general case of Multicarrier

Modulation.

More than that, the DFT lends itself on a highly efficient implementation known

as FFT so that OFDM technique benefits from a very convenient implementation even if

Nbecomes very large.

2.2 Guard timeMost of the high-data-rate communications systems using OFDM work in multipath,

selective fading environment. The OFDM symbol will be spread in time so that ISI

between symbols occurs. ISI can be kept to the level of two subsequent symbols by

using an enough large value ofN.

In order to keep the spread signal to the level of one symbol only a guard time, Tg,between OFDM symbols (figure 2.4) was introduced. By choosing the value Tg larger

than the delay spread each symbol will interfere only with itself.

There are two approaches to create the guard time interval:

zero signal guard interval,cyclic prefix guard interval (figure 2.4).


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The first solution is very simple: between two successive OFDM symbols a

interval ofTg is left unused, that is a zero signal is transmitted during this interval. In

the case of the second solution the samples from an interval Tg from the end of the

OFDM symbol are taken and pasted in the guard interval. The most widely used solution

is the second one.

Lets make a short comparison between the two solutions to explain the reasons of

this choice.

The first solution is more power efficient than the second one having in mind that

to transmit the cyclic prefix we have to spend some power from the total power of the

transmitter resulting in a power penalty and a data rate penalty.

In other words the use of the cyclic prefix entails power loss:

dBNN

NdB

TT

TlossPower

gg

)log(10)log(10

(2.6)

Of course the power loss implies a SNR loss that must be limited.

At the same time in the presence of the multipath propagation the first solution

cant maintain the orthogonality between the subcarriers. This effect can be observed in

figure 2.5 where we considered a two path propagation environment and, in order to

make the picture more clear, we retained only two subcarriers.

In the case of zero signal guard interval, the delayed signal exhibits no more an

integer number of cycles during the FFT interval so that intercarrier interferences (ICI)

will occur (figure 2.5.a).

This is not the case if a cyclic prefix is transmitted (figure 2.5 b) as long as the

delay is not larger than the guard time interval. Consequently, in order to have a channel

T

a.

t

t

T Tg

b.

Figure 2.4 The two approaches to create the guard time interval : a. zero signal, b. cyclic

refix


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without ICI, the guard time has to be chosen larger than the radio channel maximum

delay spread.

Short Commentary 1. In many cases the standards specify not one but more

values for the guard time interval in order to cope with specific radio propagation

environment. E.g. in the IEEE 802.16 standards the guard interval is specified by a

parameter G called guard fraction. The guard time interval is Tg=GT. As it can be seen

in table 2.1 and 2.2 annexed to this section, G can be selected from the next values {1/4,

1/8, 1/16, 1/32} according to the propagation environment.

2.3 An OFDM System Block DiagramAt this moment there are many other issues to discuss before understanding fully how on

OFDM system works.

Although it would be helpful to review the already presented steps by means of

the block diagram given in figure 2.6. It is an opportunity to mention some collateral but

quite important aspects related to OFDM signal processing.

Figure 2.5 The effect of multipath propagation on OFDM symbols in the case of zero signal guard

intervals

Tg

t

t

b.

a.

T


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The first step in the OFDM signal processing is to split the wideband binary data

stream of data rateR0 inNstreams ofR0/Nrate.

A QAM modulator can be used to convert the binary data stream to an m-ary data

stream. This way the spectral efficiency of the system or, alternatively, the quality of the

transmission can be controlled.

The binary data stream or the output stream of the QAM modulator is S/P

converted. It results an Nsize vector, denoted by X, which is the input of the N-point

IFFT processor.

The output of the IDFT processor is:

x = F-1

X (2.7)

The components of the vector x represents the N samples of the basic OFDM

symbol which is a sum of the samples of theNsubcarriers.

In the case of the binary stream the subcarriers are BPSK modulated while in the

case of an m-ary stream they could be QPSK, 16QAM, 64QAM, etc. modulated.

Short Commentary 2.Having in mind the features of DFT transform it can be

observed that if we use all the N subcarriers to transmit data no oversampling is present

and the undesired components cant be easily removed after the DFT processor at the

receiver. Consequently a fraction of the N subcarriers will be forced to zero (null

subcarriers) to create an adequate frequency guard interval. For example in the case of

IEEE 802.16d N=NFFT=256 and only Nu=200 subcarriers carry useful data, the other

55 are null subcarriers and one is the DC component (this is also unused).

In order to avoid the ISI that appears in multipath propagation environment a

guard interval generated as a cyclic prefix is appended after the IFFT operation.

Baseband Communication Channel

ADCDiscard

CP

S/P

converter

N

FFT

processor FEQ

Recovered

dataQAM

demod.

QAM

modulatorBinary

data

S/P

converter

N

IFFT

processor

Adding

CPP/S

converter DAC

Figure 2.6 A Block diagram of an OFDM communication system


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To do that one copies the last Ng samples of the computed samples and pastes

them in front of the first sample. Consequently, the transmitted OFDM symbol which

contains both the IFFT samples and the cyclic prefix will incorporateN+ Ngsamples.

Short Commentary 3. Sometimes the spectral density of the OFDM signal

obtained by concatenating the symbol generated as it was described by now does not fit

the requirements from the point of view of the out-of-band radiated power. Having in

mind that the OFDM symbol has sharp transitions the slope of spectrum decays slowly

according to sinc function. The spectrum can go down more rapidly if individual

symbols are processed by means of an adequate time window. The most frequently used

window is the raised cosine. Such a solution is recommended by the standard IEEE

802.16d.

In order to obtain the signal to be transmitted through the wideband

communication channel the samples are P/S converted with a sampling rate fs=1/Ts.

Sampling frequency is chosen in correlation with the bandwith of the system.

For example the standard IEEE 802.16d specifies a parameter n (that in some

cases is 8/7) and the sampling frequency is given by:

8000)8000

( 0nB

floorfs

(2.8)

The serial OFDM symbol is D/A converted and then transmitted by means of the

base band channel. The received signal is the sum of the response of the communication

channel to the transmitted signal and additive noise.

The received signal is sampled with the same rate that was used in the P/S

converter at the transmitter side and then A/D converted.

The Ng samples of the CP are discarded and the remaining N samples are S/P

converted to be used as input vectory of theN-point FFT processor.

In the terms of the digital communication channel the vector y can be expressed

as:

where: h stands for the FIR (finite impulse response) of the communication channel;

- for the circular convolution; n - for the vector corresponding to the additive noise.

*= h x + n 2.9


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The components of the output vector of the FFT processor:

Y = F y (2.10)

are the recovered subcarriers complex amplitudes.

If we assume ideal conditions the component Yi corresponding to the subcarrier i

has the form:

iiii NXHY (2.11)

The QAM demodulator will be able to make a correct decision if the influence of

the channel is removed (equalization).

This equalization is done by the FEQ block by dividing the every component of

the FFT output vector by the complex channel gain evaluated at the each subcarrier

frequencyHi:

iiii HNXX / (2.12)

After the QAM demodulator an estimated of the input data stream is obtained. We

have to point out that in the above given description we considered that the transmitter

and receiver are perfectly synchronized and that the receiver knew the channel transfer

function necessary for the equalization.

A real system must extract information for synchronization and equalization

from the incoming signal.Some of the procedures used to obtain the necessary information and the Peak to

Average Power Ratio (PAPR) issue will be discussed in the next sections.

4.4 Timing and Frequency SynchronizationOne of the biggest problems of the OFDM modulation technique is the synchronization.

To ensure ISI-free (intersymbol) detection, precise timing information (regarding where

the symbol boundary lies) is needed to guarantee that the samples for FFT processing

are extracted from an uncorrupted portion of the received OFDM symbol. This is

referred to as timing synchronization.

To ensure subcarrier orthogonality and hence ICI-free (intercarrier) detection, the

frequency offset that exists between the transmitter and receiver carrier frequencies must

be estimated and compensated. This is referred to asfrequency synchronization.

Compared to single-carrier systems, the OFDM timing-synchronization

requirements are somewhat relaxed owing to the presence of the cyclic prefix.


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On the other hand, the frequency synchronization requirements are significantly

more stringent, since the orthogonality of the subcarriers is reliant on their being

individually discernible in the frequency domain.

Figure 2.7, shows an OFDM symbol in time domain (a) and in frequency domain (b).

The issue of timing and frequency synchronization can be appreciated by inspecting

these two figures. If the timing window is slid to the left where the cyclic prefix is

added, only a phase change will be introduced to each of the subcarriers.

In the frequency domain, if the carrier frequency synchronization is perfect, thereceiver samples at the peak of each subcarrier, where the desired subcarrier amplitude

is maximized, and the intercarrier interference (ICI) are zero.

However, if the carrier frequency is misaligned, that is if we sample with an offset

d, some of the desired energy is lost and, more significantly, intercarrier interference

(ICI) is introduced.

A deeper analysis of the timing and frequency synchronization issues and some

methods to implement synchronization will be given in the following three subsections.

2.4.1 Timing SynchronizationThe effect of timing errors in symbol synchronization is somewhat relaxed in OFDM

since, as we mentioned above, the OFDM symbol naturally accommodates a reasonable

degree of synchronization error due to the cyclic prefix presence.

Looking at the figure 2.7.a it is clear that perfect synchronization is achieved if the

FFT processor uses theNtime-domain samples after the cyclic prefix. In this case even

Figure 2.7 The OFDM symbol timing and frequency synchronization

a. Time

t

TT

b. Frequency

f1 f2 f3 f4 f5 f6 f7-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Frequency

1/T

d


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if the cyclic prefix length Tgis equivalent to the length of the channel impulse response

, successive OFDM symbols can be decoded ISI free.

Of course is quite difficult to achieve perfect synchronization, consequently a

timing offset t occurs. Lets emphasize that, in this context, t 0 corresponds to sampling later

than at the ideal instant.

In the absence of the multipath any timing offset, t 0 and in the case that the timing synchronization margin is

exceeded, the intersymbol interference occurs and it cant be removed during the signal

processing.

Lets see how it works in the case t> 0. It can be observed (figure 2.8) that we

lose some of the desired energy, corresponding to the first samples that are received only

as delayed replicas. At the same time it incorporates energy from the subsequent symbol

guard time interval.

If the condition for ISI free reception is not fulfilled a degradation of the SNR will

occur. The SNR degradation can be approximated by [1, 7]:

T TG

Timin s nc.

Figure 2.8 Timing synchronization margin.


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2

2)(

sTN

ttSNR

(2.13)

where Tsstands for the sampling period.

By looking at this expression it results the following conclusions result:

o SNR decreases quadratically with the timing offset.o Longer OFDM symbols are increasingly immune from timing offset; that

is, more subcarriers are more convenient from this point of view.

Since in general t


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SNRdNTCdNTCNE

NESNR s

sos

os 2

02

0

)(1))(/(

/

(2.15)

where: Es stands for the average symbol energy,

N0 - the white gaussian noise power spectral density;C0 - a constant that dpends on various assumptions.

Short Commentary 4. If the same parameters are estimated for subcarriers placed by

the end of the band the results given by these expressions are a little pessimistic.

From the expression (2.22) it results the next conclusions:

o SNR decreases quadratically with the frequency offset;o SNR decreases quadratically with the number of subcarriers;o the loss in SNR is proportional to the SNR itself;o in order to keep the loss negligible - say, less than 0.1 dB, the relative frequency

offset needs to be about 1 percent to 2 percent of the subcarrier spacing;

2.4.3 Synchronization MethodsThe synchronization methods can be categorized as follows:

blind - cyclic prefix based;training symbol based.In the case of blind methods the receiver has no special information and it must do

the best it can to extract the necessary information from the structure of the received

signal. It will use the redundancy involved by the cyclic prefix.

Lets remember that in order to create the cyclic prefix we copied the last Ng

samples of the FFT output vector (a part that is Tg seconds long) and pasted them in

front of the first sample, so that each OFDM symbol has two identical parts as it is

shown in figure 2.9.

T Cyclicprefix

Figure 2.9 The use of the cycling prefix for time synchronization

Identical parts

TG

FFT time

interval

TG


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By calculating the correlation of the received signal with its delayed and

conjugated replica we can obtain the necessary information about the OFDM symbol

boundaries. A block diagram of the synchronization method based on the cyclic prefix is

given in figure 2.10.

Making a synthesis of the analysis given in [2] lets retain the next feature of the

cyclic prefix based synchronization method:

o The output signal of the correlator has peaks at the end of every guard interval,that is, at the beginning of the FFT analysis window for each symbol.

o Between main peaks a series of undesired sidelobs exist.o Because of the statistical nature of the OFDM signal, the correlator output is not

strictly periodic, but it shows some fluctuations especially when the number of

the subcarriers is small. In fact it was pointed out that main peaks are clear and

the sidelobes a small, by comparison to the main peaks, when the number of the

subcarriers is large, preferably larger than 100.

It is not necessary to place the analysis window for every OFDM symbol. Only the

relative position is relevant and it must be updated from time to time. Thus, we may

average over several OFDM symbols to obtain a more regular symbol synchronization

signal. This averaging also reduces the impairments due to noise.

In a mobile radio environment, the output signal of the correlator is smeared out

because of the impulse response of the channel. Consequently it is a nontrivial task to

find the optimal position of the Fourier analysis window. This may be aided by using the

results of the channel estimation.

To attain a distinct correlation peak and reasonable SNR the method needs averaging

over a large number of symbols (usually larger than 10);

Figure 2.10 Synchronization method based on the cyclic prefix

Find themaximum of

the correlation

Estimate the

phase of the

maximum

Timing

Synchronization

Frequency

Synchronization

ConjugateDelay

T

r(t)

X

gT

dtTtrtr0

)()(


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We can conclude that the cyclic prefix synchronization method is particularly

suited in circuit-switched connection where no special symbols are available.

This is not the case of packet transmission where the synchronization time must be

as short as possible, preferably a few OFDM symbols only. In this case the

synchronization method needs special symbols to be transmittedtraining symbols.

The receiver knows the data content of the training symbols and the entire

received signal will be used for synchronization purposes. Figure 2.11 shows a block

diagram of the matched filter that can be used to correlate the received signal with the

known OFDM training symbol.

In figure 2.11 Ts stands for the sampling period and ci for the matched filter

coefficients, which are the equal to the conjugated training symbol samples.The trainingsymbol consists of more, let say n, identical OFDM symbols without a guard time.

Alternatively we can consider that there is one symbol only with a guard interval

equal to n-1 FFT intervals. It is shown that such a structure gives the best possible cyclic

correlation properties in terms of the level of the undesired sidelobs.

Representing the correlation obtained in the case of n =5 it was shown that the

level of the undesired sidelobs is at least 20 dB lower than the main correlation peak [2].

The output signal of the matched filter during the first and the last symbol

intervals should be skipped having in mind that they are influenced by the initial zero

signal existing in the matched filter or by the signal coming after the training symbol

respectively.

The values in between could be used to derive the necessary synchronization

information. With an adequate structure of the training symbols the synchronization

process could give the information needed for frequency synchronization too.

An accurate estimate for the frequency offset and for the Doppler spectrum can be

obtained from the measurements at a certain number of subcarrier positions.

T

X

Ts

X

Ts

Xc1c0 cN-1

Find

maximun Timing

Synchronization

r(t)

Figure 2.11 The block diagram of a synchronization circuit based on a a training OFDM symbol


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Many technologies such as DVB-T, wireless LAN (IEEE 802.11a), WiMAX etc.

use certain subcarriers (continuous pilots) boosted by a certain factor and carrying

known data.

For example Wireless LAN systems require a very fast frequency synchronization

at the beginning of every burst. For this purpose, a special OFDM symbol at the

beginning of the burst has been defined. In this OFDM symbol, only 12 subcarriers are

modulated to serve as a frequency reference.

The downlink synchronization differs from the uplink one in WiMAX systems.

For the downlink the preamble consists of two known OFDM symbols. For the uplink

the periodic ranging is used to synchronize.

Since WiMAX is an OFDM-based system with many competing users, each user

implements the synchronization at the mobile. This requires the base station to

communicate the frequency offset to the MS

Short Commentary 5.The subcarriers used for frequency synchronization are called

conti nuous pil otsto distinguish them from the pilots used for channel estimation which

a called scattered pilots. At certain positions in time and frequency the modulation

symbols are replaced by known pilot symbols. At these positions the channel will be

measured.

Short Commentary 6.Note that we use few, let say Npsubcarriers, as pilot carriers. So

that user data is transmitted by means of Nd=N-Nn-Npsubcarriersonly.

2.5 The Peak-to-Average Power RatioOFDM signals have a high peak-to-average ratio (PAPR) because in the time domain, a

multicarrier signal is the sum of many narrowband signals. At some time instances, this

sum is large and at other times is small, which means that the peak value of the signal is

substantially larger than the average value.

Note that the peak power is defined as the power of a sine wave having the

amplitude equal to the peak value of the OFDM symbol.


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Let consider the peculiar case of an N BPSK modulated subcarriers OFDM

symbol. If all the carriers have the same phase a PAPR equal toN(figure 2.12) results.

A high PAP reduces the efficiency of the RF power amplifier, and implies high

resolution ADC/DAC.

When transmitted through a nonlinear device, such as a high-power amplifier

(HPA) or a Digital-to-Analog converter (DAC), a high peak signal, generates out-of-

band energy and in-band distortion (constellation tilting and scattering). These

degradations may affect the system performance.

The nonlinear behaviour of a power amplifier can be characterized by amplitude

modulation/amplitude modulation (AM/AM) and amplitude modulation/phase

modulation (AM/PM) responses. In the case of a solid-state power amplifier the AM/PM

conversion is small enough to be neglected. Figure 2.13 shows a typical AM/AM

response for a power amplifier.

If the amplifier works out of the linear region out-of-band radiation and in-band

signal distortion is generated. To specify the limits of the linear region the requirements

from the point view of the acceptable levels of these effects must be specified.

In the case of an OFDM signal the power amplifier must work in the linear region

for all the dynamic range. In this case the power amplifier is under utilized and a backoff

(input or output) is imposed.

Fi ure 2.12 The envelo e value of a BPSK modulated OFDM s mbol

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8

Envelope

value

t/T


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The output backoff is defined, here, as the ratio of the output power and the

limitation output power with a sinusoidal input signal. The amount of backoff is usually

greater than or equal to the PAPR of the signal. So that, if the PAPR is large we must

use more expensive power amplifiers than those required by the average power.

At the same time, in the case of mobile devices, this effect will limit the battery

life. In conclusion it is desirable to have the average and peak values as close as possible

in order to maximize the efficiency of the power amplifier.

To reduce the peak power of the OFDM symbols several techniques have been

proposed. They can be divided in three categories:

signal distortion techniques;coding techniques;scrambling techniques.

2.5.1 Signal distortion techniquesIf all the carriers have the same phase a PAPR equal to N (figure 2.12) results Signal

distortion techniques reduce the peak amplitudes by nonlinearly distorting the OFDM

signal around the peaks.

As examples of these techniques we can mention: clipping, peak windowing, peak

cancellation.

Figure 2.13 A typical AM/AM conversion of a power amplifier

Vout

Vin

Linear region

Output Backoff

Average Peak

Nonlinear region


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The simplest distortion technique is clipping. Although very simple to implement

the use of this technique is limited because there are a few associated problems. The

distortion of the amplitude of the OFDM signal generates:

a kind of self interference that degrades the BER;an increased level of out-of-band radiation.The second effect can be simply explained by viewing the clipping as a

multiplication of the OFDM signal by a rectangular window function that is 1 if the

signal is under a given threshold and smaller than 1 else. The spectrum of the processed

signal is the convolution of the OFDM signal spectrum with the spectrum of the window

function. The out-of-band behaviour is determined by the wider spectrum of the two,

which is the one of the rectangular window function.

The processing of the signal by means of an window function can be considered

not only an way to have a deeper view on the clipping technique but a technique by

itself: peak windowing. The case of rectangular window brings few more aspects by

comparison with the clipping technique. First of all it is a new way of implementation.

Second we can optimise the number of affected OFDM samples.

Figure 2.14 Clipping and windowing


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To minimize the out of band radiation the window should be as large as possible in

time that is as narrowband as possible in the frequency domain. On the other hand the

window should not be too long because an increased number of affected samples

increases the BER.

From the point of view of the out-of-band radiation it is more interesting to use

nonrectangular windows: cosine, Kaiser, Hamming, etc.

Short Commentary 6. An important disadvantage of the distortion techniques is that

symbols with great PAR suffer more degradation so that they are more vulnerable to

errors. A solution to reduce this effect is to apply Forward Error Correction across

several OFDM symbols. This procedure will reduce the error probability enough for

real time circuit switched traffic but not enough for packet transmission. In this case all

the retransmissions will have the same large error probability. To solve this problem

standard scrambling techniques using a different seed for every retransmission could be

applied. This way the PAR can be changed from one retransmission to another.

The peak cancellation technique tries to avoid the undesirable effect of out-of-

band radiation introduced by the preceding two techniques. To do this it uses a linear

cancellation technique based on the subtraction of a time-shifted and scaled reference

function from the OFDM signal instead of the nonlinear peak removing procedure.

By subtracting a right shifted and scaled reference function the peak power of at

least one signal sample of the signal is reduced. At the same time by selecting an

appropriate reference function with approximately the same bandwidth as the OFDM

signal we can be sure that the process does not cause any out-of-band interference.

A suitable reference signal is the sinc function. To limit in time the sinc function it

is processed with a cosine window. A windowed sinc function is represented in figure

2.14 and a block diagram of a transmitter using the cancellation technique is given in

figure 2.15.


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-8 -6 -4 -2 0 2 4 6 8-0.4-0.2

00.20.40.60.8

1

Vref

Relative time in Nyquist SamplesFigure 2.14 A windowed reference function

Peak cancellation can be done digitally after the generation of the OFDM symbol. It

involves a peak amplitude detector, a comparator to check if the peak exceeds some

threshold and a scaling of the peak and surrounding samples. It is also possible to do the

Figure 2.16 An OFDM symbol with a large PAR and the reference signal to be subtracted

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

Envelope

value

Cancellation

signal envelopeSymbol envelope

Time in symbol intervals

Figure 2.15 A block diagram of an OFDM transmitter with peak cancellation.

Coded

data

S/P

converterIFFT

processing

Adding

CP DACPeak

cancellation

RF

front

end

P/S

convertet


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peak cancellation immediately after the IFFT processor. An OFDM symbol and the

delayed and scaled reference signal to be subtracted are sketched in figure 2.16.

2.5.2 The Coding TechniquesIt was demonstrated that only a small fraction of all possible OFDM symbols has a large

PAR. This suggests that the PAR can be reduced by means of coding method that selects

OFDM symbols having the PAR below a given level.

To implement a coding PAPR reduction technique we must identify solutions for

coding and decoding the corresponding codes. It was remarked that many of the codes

with low PAPR are Golay complementary sequences [10].

Golay complementary sequences are sequence pairs for which the sum of

autocorrelation functions is zero for all delay shifts unequal to zero.

On this basis it was demonstrated in [8] that the correlation properties of the

complementary sequences convert in a small PAR of approximately 3dB when they are

used to modulate OFDM symbols.

A solution to reduce PAPR by using Golay complementary codes was

implemented in a modem for the MAGIC WAND project [9].

2.5.3 The Scrambling TechniquesThe main idea of the scrambling techniques is that for each OFDM symbol, the input

sequence is scrambled by a certain number of scrambling sequences. We shall select for

transmission transmit the signal having the smallest PAPR.

This class of techniques could be viewed as a special case of PAPR reduction

codes. If the scrambling sequences are uncorrelated the resulting OFDM symbols and

the associated PAPR are uncorrelated.

Consequently if the PAPR of a given OFDM symbol has the probability p to

exceed a certain level without scrambling, the probability is reduced to pk, by using k

PAPR will be under a certain level; it decreases the probability that symbols with large

PAPR occur.

The scrambling techniques were first proposed in [10,11] in two approaches:

selected mappingandpartial transmit sequences.

The difference between the two approaches is that the first applies independent

scrambling rotations to all subcarriers, while the latter only to group of subcarriers.


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2.6 OFDMAO concluzie general la aspectele prezentate cu privire la OFDM: OFDM este o tehnic

de modulaie foarte eficient n rezolvarea problemelor specifice canalelor radio:

utilizarea eficient a benzii de frecven, de propagarea multicale i de fading-ul

selectiv n frecven.

Intr-un sistem OFDM, resursele pot fi valorificate n domeniul timp prin

simbolurile OFDM iar n domeniul frecven prin subpurttoare. Resursele de timp i

frecven pot fi organizate n subcanale pentru a fi alocate unui numr oarecare de

utilizatori individuali.

Aceasta este ideea de baz pentru OFDMA (Orthogonal Frequency Division

Multiple Access).

Figura 2.6.1 Folosirea OFDM ca tehnologie de acces multiplu

OFDMA este o schem de acces multiplu/multiplexare care furnizeaz

multiplexarea fluxului de date ctre utilizatori multipli n subcanale pe calea

descendent i accesul multiplu al utilizatorilor pe subcanale pe calea ascendent.

Una dintre tehnologiile care folosesc tehnica OFDM/OFDMA este WIMAX mobil

(avnd la baz standardul IEEE 802.16e). Mai concret, modul cum se definescsubcanalele folosite n acest scop va fi descris n capitolul referitor la tehnologia

WIMAX.

2.7 Conclusions: OFDM Pros and Cons

OFDM enjoys several advantages over other solutions for high-speed transmission:

o Reduced computational complexity: OFDM can be easily implemented usingFFT/IFFT, and the processing requirements grow only slightly faster thanlinearly with data rate or bandwidth. The computational complexity of OFDM


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can be shown to be , whereB is the bandwidth and Tm is the delay spread. This

complexity is much lower than that of a standard equalizer-based system, which

has a complexity.

oGraceful degradation of performance under excess delay: The performanceof an OFDM system degrades gracefully as the delay spread exceeds the value

designed for. Greater coding and low constellation sizes can be used to provide

fallback rates that are significantly more robust against delay spread. In other

words, OFDM is well suited for adaptive modulation and coding, which allows

the system to make the best of the available channel conditions. This contrasts

with the abrupt degradation owing to error propagation that single-carrier

systems experience as the delay spread exceeds the value for which the equalizer

is designed.

o Exploitation of frequency diversity: OFDM facilitates coding and interleavingacross subcarriers in the frequency domain, which can provide robustness against

burst errors caused by portions of the transmitted spectrum undergoing deep

fades. In fact, WiMAX defines subcarrier permutations that allow systems to

exploit this.

o Use as a multiaccess scheme: OFDM can be used as a multiaccess scheme,where different tones are partitioned among multiple users. This scheme is

referred to as OFDMA and is exploited in mobile WiMAX. This scheme also

offers the ability to provide fine granularity in channel allocation. In relativelyslow time-varying channels, it is possible to significantly enhance the capacity by

adapting the data rate per subscriber according to the signal-to-noise ratio of that

particular subcarrier.

o Robust against narrowband interference: OFDM is relatively robust againstnarrowband interference, since such interference affects only a fraction of the

subcarriers.

o Suitable for coherent demodulation: It is relatively easy to do pilot-basedchannel estimation in OFDM systems, which renders them suitable for coherent

demodulation schemes that are more power efficient.

Despite these advantages, OFDM techniques also face several challenges:

o The problem associated with OFDM signals having a high peak-to-averageratio that causes nonlinearities and clipping distortion. This can lead to power

inefficiencies that need to be countered.


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o OFDM signals are very susceptible to phase noise and frequency dispersion,and the design must mitigate these imperfections. This also makes it critical to

have accurate frequency synchronization.


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Annex 1. Examples of OFDM transmission parameters according to WiMAX

standards

Table A 2.1. Parameters of the OFDM transmission for the downlink FUSK according

to IEEE 802.16d

Symbol Description Relation Possible values Example

B0=BW Nominal

Bandwidth of the

channel

* The channel

bandwidth may

be selected as amultiple of:

1.25 MHz

1.5 MHz;

1.75 MHz;

2 MHz;

2.75MHz.

For the numerical

example we shall

use B0=BW=5MHz

n Sampling factor: a

parameter used to

determine the

sampling time, Ts.

* n is correlated

with BW:n=144/125

n=86/75;

n=8/7;

n=57/50

n=316/275

For other

situations n=8/7;

n =144/125

N=NFFT Number of

subcarriers and the

size of the DFT

transform

* 256, 1024, 2048 N=256

G Guard fraction * 1/8; 1/16; 1/32 G=1/8

Nu=Nused Number of used

subcarrier

* 200

Nn Number of null

subcarriers

Nn= N - Nu 56 Guard subcarriers +

DC subcarrier

Nd Number of data

subcarriers

* 192

Np Number of pilot

subcarriers

Np=N-NnNd 8

fs Sampling

frequency

floor(nBW/8000)8000 fs=5.760 MHz ForBW=5MHz

Ts Sampling time 1/ fs 173.61ns

T Useful symbol time NFFT Ts 44,4441 s

f Subcarrier spacing fs /NFFT 22.5 Hz

Tg Guard interval time G T Tg= 5.555 s For G=1/8

Ng The Cyclic Prefix

number of samples

G

N Ng= 32 ForG = 1/8


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Table A 2.2. Parameters of the OFDM transmission according to IEEE 802.16e

for downlink FUSK

Symbol Description Relation Possible values Comments

B0=BW Nominal

Bandwidth of the

channel

* The channel

bandwidth may beselected as a

multiple of:

1.25 MHz

1.5 MHz;

1.75 MHz;

2 MHz;

2.75MHz.

For the numerical

example we shall

use BW=10 MHz

n Sampling factor: a

parameter used to

determine the

sampling time, Ts.

* n is correlated withBW:

for the c) case

(BW=k1.75)

n=8/7;for the a,b,d,e cases

n=28/25

- For other

situations n=8/7;

n=28/25

N=NFFT Number of

subcarriers and the

size of the DFT

transform

* 128; 512; 1024; 2048 N=NFFT=1024

G Guard fraction * ; 1/8; 1/16; 1/32 G=1/16

Nu=Nused Number of used

subcarrier

* Nu=Nused=865 Including pilots

and DC subcarrier

Nn Number of null

subcarriers

Nn= N - Nu 159

Nd Number of data

subcarriers

* 768

Np Number of pilot

subcarriers

Np=N-NnNd 96

fs Sampling frequency floor(nBW/8000)8000 fs=11.2 MHz ForBW=10MHz

Ts Sampling time 1/ fs Ts =89.2857ns

T Useful symbol time N Ts T=91,42857 s

f Subcarrier spacing fs /NFFT f= 109,375 kHz

Tg Guard interval time G T Tg= 5.71428s ForG = 1/16

Ng The Cyclic Prefix

number of samples

G N Ng= 64 ForG = 1/16


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Bibliography

1. Andrews J.G., A. Ghosh, R. Muhamed, Fundamentals of WiMAX :understanding broadband wireless networking, Prentice Hall, 2007.

2. Van Nee R., R. Prasad, OFDM for Wireless Multimedia Communications,Artech House, 2000.

3. H. Schulze, C.Lders,Theory and Applications of OFDM and CDMA; WidebandWireless Communications, John Willey&Sons, 2005

4. Weinstein S., P. Ebert, Data transmission by frequency-division multiplexingusing the discrete Fourier transform. IEEE Transactions on Communications,

19(5):628634, October 1971.

5. IEEE. 802.16d, Part 16: Air interface for fixed broadband wireless accesssystems, June 2004.

6. IEEE 802.16e, Standard for Local and metropolitan area networks, part 16: AirInterface for Fixed and Mobile Broadband Wireless Access Systems Amendment

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