Slides - Ofdm Tutorial 2008_mm

7/29/2019 Slides - Ofdm Tutorial 2008_mm

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Orthogonal Frequency Division

Multiplexing/Modulation:

OFDM

Marina Mondin

[email protected]

Politecnico di Torino, Dip. di Elettronica

1

Multipath Propagation

Simple Model

Multipath Propagation

Simple Model

| 0 | | 1 | | 2 |1 2

0

1

2c = kk - k

where k = 0, , K-1k : path gain (complex)0 = 0 normalize relative delay of first pathk =k - 0 difference in time-of-flight 2


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Equivalent PropagationChannelEquivalent PropagationChannel

convolution

heff(t) =gtr(t) *hc(t) * grx(t)transmit filters receive filters

multipathchannel

Effective channel at receiver

Propagation channel

Transmit / receive filters

hc(t) typically random & changes with time

Must estimate and re-estimate channel3

Impact of Multipath: Delay

Spread & ISI

Impact of Multipath: Delay

Spread & ISI

0.5

1

-6 -4 -2 0 2 4 6-0.2

0

0.2

0.4

0.6

0.8

1

t/T

2Ts 4Ts-6 -4 -2 0 2 4 6 8

-0.5

0

t/Ts

0.2

0.4

0.6

0.8

s

Ts -6 -4 -2 0 2 4 6 8-0.2

0

t/Ts

Max delay spread =effective number of symbol periods occupied by channel

Requires equalization to remove resulting ISI4


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Effective Delay SpreadEffective Delay Spread

Delay spread depends on difference in path lengths Effective delay spread: function of the maximum difference s

Cell size Max Delay Spread

Pico cell 0.1 km 300 nsMicro cell 5 km 15 usMacro cell 20 km 40 us

Sampling Period Channel taps Application

802.11a 50 ns 6 WLANDVB-T 160 ns 90 AudioDAB 600 ns 60 TV broadcast

5

Concept of MulticarrierConcept of Multicarrier

ModulationModulationDivide broadband channel into narrowband

subchannels

o n su c anne s cons an ga n n everysubchannel and if ideal sampling

Considered for fourth-generation mobile communicationsystems

e

channel

subchannel

frequency

magnitu

carrier

6


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OFDM: Basic conceptsOFDM: Basic concepts

OFDM (Orthogonal Frequency Division Multiplexing)z Multicarrier transmissionz Single data-stream transmitted over lower rate subcarriers

Main feature of OFDM

S/P

converterserial bit stream,

Rb,ser N parallel bit sub-streams,

Rb,par= Rb,ser/N

001000

10

interferences

Adopted for various wireless standardsz IEEE 802.11a, IEEE 802.16a, DAB, DVB (+DSL), HyperLAN II

7

MonocarrierMonocarrier vs. Multicarriervs. Multicarrier modulationmodulation

N carriers

Similar to

Channel

Guard bands

ChannelizationGuard bands

Selective Fading

Very short pulses

Drawbacks

It is easy to exploit

Fre uenc diversit

Flat Fading per carrier

N lon ulses

Advantages

Furthermore

B

Pulse length ~N/B

Data are shared among several carriersand simultaneously transmitted

B

Pulse length ~1/B

Data are transmited over only one carrier

To improve the spectral efficiency:

To use orthogonal carriers (allowing overlapping)

Eliminate band guards between carriers

ISI is compartively long

Equalizers are very long

Poor spectral efficiencybecause of band guards

ISI is comparatively short

N short Equalizers needed

Poor spectral efficiencybecause of band guards

It allows to deploy

2D coding techniques

Dynamic signalling

8


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OFDM is a special case of FDM (Frequency DivisionMultiplexing), which uses overlapping subchannels in

OFDM: a special MulticarrierOFDM: a special MulticarrierModulationModulation

or er o cope w e ne c ency o e conven onanonoverlappingmulticarrier technique (FDM)

FDM

Saving of

bandwidth OFDM

Frequency subchannels

9

OFDM: a special Multicarrier

Modulation

OFDM: a special Multicarrier

Modulation

To realize the overlapping multicarrier technique,it is necessary to avoid crosstalk betweensu c annesz i.e. the subchannels are received without Inter-

Channel (Inter-Carrier) Interference (ICI).z subchannel subcarrier

Orthogonality between the different modulatedsubcarriers is needed

spacing

10


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N carriers

Transmit

Symbol: 2 periods of f0

The OFDM signal (1)The OFDM signal (1)

Data coded in frequency domain

B

Transformation to time domain:each frequency is a sine wavein time, all added up.

f



Channel frequencyresponse

f

Receive time

B

Decode each frequencybin separately

f

Time-domain signal Frequency-domain signal 11

TheThe OFDMOFDM signalsignal (2)(2)

N carriers

Data

ncy

Time-frequency grid

B

Intercarrier Separation = No intercarrier guard bands

Controlled overlapping of bands

Features

Carrier

T=1/f0Time

f0B

Frequ

One OFDM symbol

Modulation technique

A user utilizes all carriers to transmit its data as coded quantity at each

frequency carrier, which can be quadrature-amplitude modulated (QAM).

Maximum spectral efficiency (Nyquist rate)

Very sensitive to freq. synchronization

Easy implementation using IFFTs

12


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OFDM: signal generationOFDM: signal generation

Ndata parallel frequency sub-carriersz Ndata, number of subcarriers carrying information symbols

Bits on each subcarrier are then ma ed onto di italconstellation symbols dk (complex), belonging to M-PSK or M-QAM constellationsz index k indicates the subcarrier

Number of data bits necessary to generate one symbolon each subcarrier:Nbit =log2(M)*Ndata

Np, number of pilot subcarriersz where pilot symbols are transmitted

Nz, number of zero subcarriersz where zero symbols are transmitted, as a guard band

Total number of subcarriers,NFFT= Ndata+Np+Nz (odd) fc, central carrier frequency

13

Signal generation (2)Signal generation (2) OFDM symbol (complex envelope), s(t)

z TFFT, OFDM symbol durationz k/TFFT, k-th subcarrier frequency

Each subcarrier has an integer number of cycles in theintervalTFFT

The number of cycles inTFFT between adjacent subcarriersdiffers by one

14


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OFDM subcarriersOFDM subcarriers

15

Ortogonality among subcarriersOrtogonality among subcarriers

Orthogonality among subcarriers is guaranteed

OFDM symbol in the frequency domain

z extremely flat in-band spectrumz fast out-of-band decay (as faster as the number of

subcarriers increases)

16


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Spectra of the individualsubcarriersSpectra of the individualsubcarriers

17

OFDM Symbol spectrumOFDM Symbol spectrum

18


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The IFFT operation (1)The IFFT operation (1)

Observe the OFDM symbol

it can be seen as the IDFT (Inverse Discrete FourierTransform) of a discrete frequency spectrumS[fk],withz frequency samples S[fk] = dkz frequency sampling step 1/TFFT

-,

z a very efficient implementation is achieved by the(Inverse) Fast Fourier Transform (IFFT) algorithm

19

The IFFT operation (2)The IFFT operation (2)

in this figure: xi = dk

20


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OFDMOFDM ModulationModulation andand DemodulationDemodulation

usingusing FFTsFFTs

b0b1b2.

IFFT

Inverse fast

d0d1d2d3

P/S

Parallel to

d0, d1, d2, ., dN-1

.

.

.bN-1

Data coded infrequency domain:one symbol at a time

Data in time domain:one symbol at a time

.

.

.

.dN-1

time

f

sera convererTransmit time-domainsamples of one symbol

Decodeeach

Receive time-domainsamples of one symbol

d0, d1, ., dN-1S/P

Serial toparallel converter

d1d2

.

.

.

.dN-1

time

FFT

Fast Fourier

transform

b1b2

.

.

.

.bN-1

f

frequency binindependently

21

An OFDM MoDemAn OFDM MoDem

quadrature

N subchannels N complex samples

S/Pamplitudemodulation

(QAM)encoder

N-IFFTadd

cyclicprefix

P/SD/A +

transmitfilter

TRANSMITTER

RECEIVERmultipath channel

Bits

P/SQAM

decoder

invertchannel

=frequencydomain

equalizer

N-FFT S/Premovecyclicprefix

N complex samplesN subchannels

Receivefilter

+A/D

22


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Guard TimeGuard Time

An OFDM transmission consists in a sequence of symbols scp(t), thatlast T seconds (T>TFFT) and are spaced T seconds apart, i.e.,

Due to the presence of a delay spread in the channelimpulse response, a Guard Time (GT) is introducedforeach OFDM symbol, to eliminate ISI almost

i scp,i -

Each symbol scp,i(t-iT) carriesNbit information bits

z a guard time is a time interval TG [s] between two successivesymbols, during which no transmissions take place

The GT must be chosen larger than the expecteddelay spread of the propagation channel

23

Cyclic prefixCyclic prefix In OFDM, the guard time is used to transmit a

cyclic prefixThe OFDM symbol is cyclically extended in the GT,

to prevent ICI (Inte -Channel Interference)

cp samples in the GT

24


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Cyclic prefix (2)Cyclic prefix (2)

Orthogonality between subcarriers is preservedz integer number of cycles within an integration period

z no phase discontinuities are generated

Multipath signals with delays smaller than TG,cannot cause ICI

25

Loss of orthogonality

(due to frequency offset)k(t) = exp(jk2t/T) y k+m(t) = exp j2(k+ m)t/T( )

k+m

(t) = exp j2(k+ m+ ) /T( ) con 1/ 2

Transmission pulses

Reception pulse with offset &

with

Im() = exp jk2t /T( )exp j(k + m+)2t /T( )dt0T

=T 1 exp(j2)( )

j2(m+ )

Im() =T sin

m+ I

m

2 ()m

T( )2 1m2m=1

N1

T( )2 2314

for N>>1 (N > 5 Is enough)

Interference between

channels k and k+m

Summing up m

2 4 6 8 10 12 14 16-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10Total ICI due to loss of orthogonality

Carrier position within the band (N=16)

ICIin

dB

=0.05

=0.02 =0.01 =0.005

=0.002 =0.001

Practical limit assumed r.v.Gaussian =

0-0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4

Frequency offset:

Interference:Im()/TendB

m=1

m=3m=5m=7

-70

-60

-50

-40

-30

-20

-10

0

Asymetric

26


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Loss of orthogonality (in time)

Xi = c0 k (t)l*(t )dt

T /2

T /2 +

+ c1 k(t)l* (t )dtT / 2+T / 2

Let us assumea misadjustment 2 consecutivesymbols

EXi

2

T2

= 4

T

21

2+ 0

1

2= 2

T

2 ICI 20log 2

T

,


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Spectrum Shaping: WindowingSpectrum Shaping: Windowing

In order to reduceout-of-band

,windowing is appliedto the individualOFDM symbols scp,i[n]

A commonly usedwindow type is theRaised-Cosine

window, with symbolintervalT=TFFT+TGand roll-off

29

Windowing

Effect of the roll-off

Windowing

Effect of the roll-offLarge roll-off factors improve the spectral

behavior in terms of out-of-band emissions lowered side-lobes

Windowing decreases the overall delay-spread tolerance by a factor In practice, the effective GTTG is reduced by the

amountT

30


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quadrature

N subchannels N complex samples

An OFDM ModemAn OFDM Modem

S/Pamplitudemodulation

(QAM)encoder

N-IFFTadd

cyclicprefix

P/SD/A +

transmitfilter

TRANSMITTER

RECEIVERmultipath channel

Bits

00110

P/SQAM

decoder

invertchannel=

frequencydomain

equalizer

N-FFT S/Premovecyclicprefix

N complex samplesN subchannels

Receivefilter

+A/D

31

Ideal Channel EstimationIdeal Channel Estimation Wireless channels change frequently ~ 10 ms Require frequent channel estimation Many systems use pilot tones known symbols

z Given sk, for k = k1, k2, k3, solve xk =l=0L hl e-j2 k l/N sk for hlz Find Hk =l=0L hl e-j2 k l / N (significant computation)

More pilot tonesz Better noise resiliencez Lower throughput (pilots are not informative)

frequency

magnitude Pilot tones

32


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Frequency Domain EqualizationFrequency Domain Equalization

For the kth carrier:xk = Hk sk + vk

where Hk = n hk(nTs) exp(j2 k n/ N) and n = 0, ,. N-1 Frequency domain equalizer xk

Hk-1

xk ssk= ssk + vvk Hk-1

= sk + vk

-

k

|Hk|2

|Hk-1|2

k

good

bad

k = k k-

33

Frequency Domain Equalization with

constant amplitude modulations (QPSK)

Frequency Domain Equalization with

constant amplitude modulations (QPSK)

For the kth carrier:xk = Hk sk + vk

Frequency domain equalizer xkssk= ssk + vvk abs(Hk)Hk

-1

= sk + vkabs(Hk)Hk-1

No noise enhancement factor k2 =k

2

same noise variance

in all subchannels

Has a rotated pdf,

but since Gaussian

pdf has circular

symmetry, noise

variance is unchanged34


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Channel Estimation ViaInterpolationChannel Estimation ViaInterpolation

More efficient approach is interpolation Algorithm

z For each pilot ki find Hki = xki / skiz Interpolate unknown values using interpolation filterz Hm =m,1 Hk1 +m,2 Hk2 +

Commentsz Longer interpolation filter: more computation, timing sensitivityzTypical 1dB loss in performance in practical implementation

e

frequency

ma

gnitu

35

DMT vs. OFDMDMT vs. OFDM DMT (Discrete Multitone Transmission)

z Channel changes very slowly ~1 sz Subchannel gains known at transmitter

- OFDM (wireless)

z Channel may change quickly ~10 msz Not enough time to convey gains to transmitterz Forward error correction mitigates problems on bad channels

e

DMT: Send more data here

OFDM: Try to code so bad subchannels can be ignored

frequency

magnitu

36


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DMT vs. OFDMDMT vs. OFDM

Key difference with DMT

Bandpass transmission allows for complex waveforms

ransm : y = e + exp p c= I(t) cos(2 fc t) Q(t) sin(2 fc t)

37

Coded OFDM (COFDM)Coded OFDM (COFDM) Error correction is necessary in OFDM systems Forward error correction (FEC)

z Adds redundancy to data streamz Examples: convolutional codes, block codesz Mitigates the effects of bad channelsz Reduces overall throughput according to the coding rate k/n

Automatic repeat request (ARQ)z Adds error detecting ability to data stream

-z Used to detect errors in an OFDM symbolz Bad packets are retransmitted (hopefully the channel changes)z Usually used with FECz Minus: Ineffective in broadcast systems

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FrequencyFrequency diversitydiversity usingusing codingcoding

Random errors: primarily introduced by thermal and circuit noise.

Channel-selected errors: introduced by magnitude distortion in.

Data bits

Bad carriersf0

B

Frequency

Time-frequency grid

T=1/f0Time

Frequency response

Errors are no longer random. InterleavingInterleaving is often used to scramblethe data bits so that standard error correcting codes can be applied.

39

Typical Coded OFDM

Encoder

Typical Coded OFDM

Encoder

FECReed-Solomon and/or convolutional code

BitwiseInterleaving

Symbol

Intersperse coded and uncoded bits

Data bits Parity bits

Rate 1/2

Map bits to symbols

40


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Typical Coded OFDMDecoderTypical Coded OFDMDecoder

Frequency-domain

Symbol demappingz Produce soft estimate of each bitz

SymbolDemapping

Deinterleaving

Decoding

41

OFDM in BroadcastOFDM in Broadcast Enables Single Frequency Network (SFN)

z Multiple transmit antennas geographically separatedz Enables same radio/TV channel frequency throughout a countryz Creates artificially large delay spread OFDM has no problems

20km

1

0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

42


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OFDM for High-SpeedInternet AccessOFDM for High-SpeedInternet Access

High-speed data transmissionz Large bandwidths -> high rate, many computations

--impairment

z Requires much lowerBER than voice systems OFDM pros

zTakes advantage of multipath through simple equalization OFDM cons

z Synchronization requirements are much more strict

synch

z Peak-to-average power ratio Approximately 10 log N (in dB) Large signal peaks require higher power amplifiers Amplifier cost grows nonlinearly with required power

43

OFDM Systems and ApplicationsOFDM Systems and ApplicationsStandard Meaning Carrier Freq. Rate (Mbps) Applications

DAB Digital Audio Broadcasting FM radio 0.008-0.384 Audio broadcastingDVB-T Digital Video Broadcasting UHF 3.7-32 Digital TV broadcastingDVB-H Di ital VideoBroadcastin UHF 13.7 Di ital broadca tin to

Ortho onal Fre uenc Division Multi lexin OFDM

handheld

IEEE 802.11a Wireless LAN / WiFi 5.2 GHz 6 - 54 Wireless InternetIEEE 802.11g Wireless LAN / WiFi 2.4 GHz 6 54 Wireless InternetIEEE 802.11n Wireless LAN (High Speed) 2.4 GHz - ?? 6 100 Wireless InternetIEEE 802.16 Broadband Wireless Access 2.1 GHz &

others0.5 20 Fixed / Mobile Wireless

InternetIEEE 802.20 Mobile Broad. Wireless Access 3.5 GHz ~1 Mobile Internet / Voice?

Digital modulation scheme

Wireless counterpart to discrete multitone transmission

Used in a variety of applications

o Broadcast

o High-speed internet access44


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Example: IEEE 802.11aExample: IEEE 802.11a

IEEE 802.11 employs adaptive modulationz Code rate & modulation depends on distance from base stationz Overall data rate varies from 6 Mbps to 54 Mbps

Reference: IEEE Std 802.11a-1999 45

IEEE 802.11a Wireless LANIEEE 802.11a Wireless LAN System parametersz FFT size: 64

u u zzNumber of pilots 4 (data tones = 52-4 = 48 tones)zBandwidth: 20MHzzSubcarrier spacing : f= 20 MHz / 64 = 312.5 kHzzOFDM symbol duration: TFFT = 1/f= 3.2uszCyclic prefix duration: TGI = 0.8us

=s gna

TFFTTGI

CP s y m b o l i

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802.11a System Specification802.11a System Specification

GI2 T1 GI OFDM Symbol GI OFDM SymbolT2t1t2 t3 t4 t5 t6 t7 t8 t9t10

Short training sequence:AGC and frequency offset

Long training sequence:Channel estimation

Sampling (chip) rate: 20MHz Chip duration: 50ns Number of FFT points: 64 FFT symbol period: 3.2s Cyclic prefix period: 16 chips or 0.8s

zTypical maximum indoor delay spread < 400ns:

z FFT symbol length / OFDM frame length = 4/5

Modulation schemez QPSK: 2bits/samplez 16QAM: 4bits/samplez 64QAM: 6bits/sample

Coding: rate convolutional code with constraint length 747

IEEE 802.11a pilot structureIEEE 802.11a pilot structure

48


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IEEE 802.11a Spectrum Mask

Power Spectral Density

-20 dB

-28 dB

-40 dB

Frequency (MHz)

f carrier9 11 20 30-9-11-20-30

Requires extremely linear power amplifier design.

49

OFDM: Quick SummaryOFDM: Quick Summary

Basic ideazUsing a large number of parallel narrow-band sub-

carrers ns ea o a s nge w e- an carrer otransport information

AdvantageszVery easy and efficient in dealing with multi-pathzRobust against narrow-band interference

DisadvantageszSensitive to fre uenc offsetand hase noise

z Peak-to-average problem reduces the powerefficiency of RF amplifier at the transmitter

Adopted for various wireless standards 802.11a, 802.16a, DAB, DVB (+DSL)

50

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