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Orthogonal Frequency Division

Multiplexing/Modulation:

OFDM

CADWCSCADWCS

Spring 2010Spring 2010

Introduction to OFDMIntroduction to OFDM

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

carriers instead of a single wide-band carrier totransport information

AdvantagesVery easy and efficient in dealing with multi-pathRobust against narrow-band interference

DisadvantagesSensitive to frequency offset and phase noisePeak-to-average problem reduces the power

efficiency of RF amplifier at the transmitter

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

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Multicarrier ModulationMulticarrier Modulation

Orthogonal Frequency Division Multiplexing

Based on the fast Fourier transform

Standardized for DAB, DVB-T, IEEE 802.11a, 802.16a,HyperLAN II

Considered for fourth-generation mobile communicationsystems

subchannel

frequency

ma

gnitude

carrier

channel

Multipath Propagation

Simple Model

Multipath Propagation

Simple Model

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

| 0 | | 1 | | 2 |1 2

0

1

2

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Equivalent PropagationChannelEquivalent PropagationChannel

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

multipathchannel

convolution

Effective channel at receiver

Propagation channel

Transmit / receive filters

hc(t) typically random& changes with time

Must estimate and re-estimate channel

Impact of Multipath: Delay

Spread & ISI

Impact of Multipath: Delay

Spread & ISI

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

0

0.2

0.4

0.6

0.8

1

t/Ts

2Ts 4Ts

Ts

-6 -4 -2 0 2 4 6 8

-0.5

0

0.5

1

t/Ts

-6 -4 -2 0 2 4 6 8

-0.2

0

0.2

0.4

0.6

0.8

t/Ts

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

Requires equalization to remove resulting ISI

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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 Sampling period Tsdetermines effect of delay spread

40 us20 kmMacro cell15 us5 kmMicro cell

300 ns0.1 kmPico cell

Max Delay SpreadCell size

TV broadcast60600 nsDABAudio90160 nsDVB-TWLAN650 ns802.11a

ApplicationChannel tapsSampling Period

Multicarrier ModulationMulticarrier Modulation

Divide broadband channel into narrowband subchannels

No ISI in subchannelsif constant gain in every subchannel and ifideal sampling

subchannel

frequency

magnitu

de

carrier

channel

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Monocarrier vs. Multicarrier modulation

To improve the spectral efficiency:

To use orthogonal carriers (allowing overlapping)

Eliminate band guards between carriers

Selective Fading

Very short pulses

ISI is compartively long

Equalizers are very long

Poor spectral efficiencybecause of band guards

Drawbacks

It is easy to exploit

Frequency diversity

Flat Fading per carrier

N long pulses

ISI is comparatively short

N short Equalizers needed

Poor spectral efficiencybecause of band guards

Advantages

Furthermore

It allows to deploy

2D coding techniques

Dynamic signalling

N carriers

B

Pulse length ~ N/B

Similar toFDM technique

Data are shared among several carriersand simultaneously transmitted

B

Pulse length ~1/B

Data are transmited over onlyone carrier

Channel

Guard bands

Channelization

Orthogonal Frequency Division Modulation

Data coded in frequency domain

N carriers

B

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

f

Transmit

Symbol: 8 periods of f 0

Symbol: 4 periods of f0

Symbol: 2 periods of f 0

+

Receivetime

B

Decode each frequencybin separately

Channel frequencyresponse

f

f

Time-domain signal Frequency-domain signal

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OFDM uses multiple carriers

to modulate the data

N carriers

B

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).

Intercarrier Separation =

1/(symbol duration)

No intercarrier guard bands

Controlled overlapping of bands

Maximum spectral efficiency (Nyquist rate)

Very sensitive to freq. synchronization

Easy implementation using IFFTs

Features

Data

Carrier

T=1/f0Time

f0B

Frequency

One OFDM symbol

Time-frequency grid

OFDM Modulation and Demodulation

using FFTsb0b1b2...

.bN-1

Data coded infrequency domain:one symbol at a time

IFFT

Inverse fastFourier transform

Data in time domain:one symbol at a time

d0d1d2d3....dN-1

time

f

P/S

Parallel to

serial converterTransmit time-domainsamples of one symbol

d0, d1, d2, ., dN-1

Receive time-domainsamples of one symbol

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

Serial toparallel converter

d0d1d2....dN-1

time

FFT

Fast Fouriertransform

b0b1b2

.

.

.

.bN-1

f

Decode each

frequency binindependently

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Frequency Domain EqualizationFrequency Domain Equalization

For the kth carrier:xk= Hksk+ vk

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

Hk-1

ssk

Noise enhancement factor

k

|Hk|2

|Hk-1|2

k

good

bad

Effect of the cyclic prefix

CP

Passing

the

channelh(n)

i(t)

j(t)

h(n)=(1)n/n n=0,,23

j(t)

i(t)

i(t)

To combat the time dispersion: including special time guards in the symbol transitions

CP

TTc

copyFurthemore it converts Linear conv. = Cyclic conv.

(Method: overlap-save)

CP functions:It acomodates the decaying transient of the previous symbolIt avoids the initial transient reachs the current symbol

Including the Cyclic Prefix

Symbol: 8 periods of fi

Symbol: 4 periods of fi

Initial transientremains within

the CP

Final transientremains within

the CP

The inclusion of a CPmaintains the orthogonality

Passing

the

channelh(n)

Initial transient Decaying transient

Channel:

Symbol: 8 periods of f i

Symbol: 4 periods of fi

Without the Cyclic Prefix

Loss of orthogonality

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P/SQAM

decoder

invertchannel=

frequencydomain

equalizer

S/P

quadrature

amplitude

modulation(QAM)

encoder

N-IFFT

add

cyclicprefix

P/S

D/A +

transmitfilter

N-FFT S/Premovecyclic

prefix

TRANSMITTER

RECEIVER

Nsubchannels Ncomplex samples

Ncomplex samplesNsubchannels

Receivefilter

+

A/D

multipath channel

An OFDM ModemAn OFDM Modem

Bits

00110

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

Channel changes very slowly ~ 1 s Subchannel gains known at transmitter Bit-loading (sending more bits on goodchannels) increases throughput

OFDM Channel may change quickly ~ 10 ms Not enough time to convey gains to transmitter Forward error correction mitigates problems on bad channels

frequency

magnitu

de

DMT: Send more data here

OFDM: Try to code so bad subchannels can be ignored

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Key difference with DMT

Bandpass transmission allows for complex waveforms

Transmit: y(t) = Re{(I(t)+j Q(t)) exp(j2p fct)}= I(t) cos(2 fct) Q(t) sin(2 fct)

DMT vs. OFDMDMT vs. OFDM

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

Adds redundancy to data stream

Examples: convolutional codes, block codes

Mitigates the effects of bad channels

Reduces overall throughput according to the coding rate k/n

Automatic repeat request (ARQ) Adds error detecting ability to data stream Examples: 16-bit cyclic redundancy code Used to detect errors in an OFDM symbol

Bad packets are retransmitted (hopefully the channel changes)

Usually used with FEC

Minus: Ineffective in broadcast systems

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Typical Coded OFDMEncoderTypical Coded OFDMEncoder

FEC

BitwiseInterleaving

SymbolMapping

Reed-Solomon and/or convolutional code

Intersperse coded and uncoded bits

Data bits Parity bits

Rate 1/2

Map bits to symbols

Typical Coded OFDM

Decoder

Typical Coded OFDM

Decoder

Frequency-domain

equalization

Symbol

Demapping

Deinterleaving

Decoding

Symbol demapping Produce soft estimate of each bit

Improves decoding

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Frequency diversity using coding

Random errors: primarily introduced by thermal and circuit noise.

Channel-selected errors: introduced by magnitude distortion inchannel frequency response.

Data bits

Bad carriers

T=1/f0Time

f0

B

Frequency

Time-frequency grid

Frequency response

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

f

Ideal Channel EstimationIdeal Channel Estimation Wireless channels change frequently ~ 10 ms

Require frequent channel estimation Many systems use pilot tones known symbols

Given sk, for k = k1, k2, k3, solve xk = l=0L hl e

-j2 k l/N sk for hl Find Hk = l=0

L hl e-j2 k l / N (significant computation)

More pilot tones

Better noise resilience Lower throughput (pilots are notinformative)

frequency

magnitude Pilot tones

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Channel Estimation ViaInterpolationChannel Estimation ViaInterpolation

More efficient approach is interpolation Algorithm

For each pilot ki find Hki = xki/ ski Interpolate unknown values using interpolation filter

Hm = m,1 Hk1 + m,2 Hk2 + Comments

Longer interpolation filter: more computation, timing sensitivity

Typical 1dB loss in performance in practical implementation

frequency

ma

gnitude

OFDM and MIMO SystemsOFDM and MIMO Systems Multiple-input multiple-output (MIMO) systems

Use multiple transmit and multiple receive antennasCreates a matrixchannel

Equivalent system for kth tonexk = Hk sk + vk

Vector inputs and outputs

OFDM Modulator

OFDM Modulator

Joint

Demodulator

H(t)

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Why OFDM in Broadcast?Why OFDM in Broadcast?

Enables Single Frequency Network (SFN) Multiple transmit antennas geographically separated

Enables same radio/TV channel frequency throughout a country

Creates artificially large delay spread OFDM has no problems

20km

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

1

Why OFDM for High-Speed

Internet Access?

Why OFDM for High-Speed

Internet Access? High-speed data transmission

Large bandwidths -> high rate, many computations

Small sampling periods -> delay spread becomes a seriousimpairment

Requires much lowerBER than voice systems

OFDM pros

Takes advantage of multipath through simple equalization

OFDM cons Synchronization requirements are much more strict

Requires more complex algorithms for time / frequencysynch

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

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OFDM Systems and ApplicationsOFDM Systems and Applications

Orthogonal Frequency Division Multiplexing (OFDM)

Digital modulation scheme

Wireless counterpart to discrete multitone transmission Used in a variety of applications

o Broadcast

o High-speed internet access

Standard Meaning Carrier Freq. Rate (Mbps) ApplicationsDAB Digital Audio Broadcasting FM radio 0.008-0.384 Audio broadcasting

DVB-T Digital Video Broadcasting UHF 3.7-32 Digital TV broadcasting

DVB-H Digital Video Broadcasting UHF 13.7 Digital broadcasting to

handheld

IEEE 802.11a Wireless LAN / WiFi 5.2 GHz 6 - 54 Wireless Internet

IEEE 802.11g Wireless LAN / WiFi 2.4 GHz 6 54 Wireless Internet

IEEE 802.11n Wireless LAN (High Speed) 2.4 GHz - ?? 6 100 Wireless Internet

IEEE 802.16 Broadband Wireless Access 2.1 GHz &

others

0.5 20 Fixed / Mobile Wireless

Internet

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