SEER 03 Tehnica de Modulatie OFDM Eng
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Transcript of 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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