2014-1 OFDM

OFDM SystemsOFDM Systems

20142014

11

EE--mail : mail : [email protected]@ssu.ac.kr

: 02: 02--820820--06320632

CIPLabCommunication &Information Processing

2

Wireless Channel ImpairmentsWireless Channel Impairments

Path loss

Shadowing

Multi-path fading

Flat fading

Doppler spread

Delay spread

Others (interference, background noise, etc.)


3

Path LossPath Loss

Different, often complicated models are used for different environments

A simple model for path loss

: Local mean received signal power

: Transmit power

: Distance between transmitter and receiver

: Path loss exponent

in free space

in typical urban environments

L

dK

PPL

t

r 1

rP

tPd

242


4

ShadowingShadowing

Large-scale fading

Received signal is shadowed by large obstructions such as hills and buildings

This results in variations in the local mean received signal power

: Log-normal with

Implications

Non-uniform coverage

Increases the required transmit power

]dB[]dB[]dB[ srr GPP ),(~ 20 ss NG dB][104 s


5

MultiMulti--Path Fading (1)Path Fading (1)

Channel impulse response

: Random amplitude of the i-th path

: Random phase of the i-th path

: Delay of the i-th path

i

ij

i tteth i )()(

iiit


6

MultiMulti--Path Fading (2)Path Fading (2)

Effect of multi-path fading : Constructive or destructive interference of arriving rays

Deep Fades


7

Delay spread is small compared to the symbol period

The received signal envelope, r follows a Rayleigh or Rician distribution

Implications

Increases the required transmit power

Causes bursts of errors

]dB[log20]dB[]dB[]dB[ 10 rGPP srr

Flat Fading (1)Flat Fading (1)


8

Flat Fading (2)Flat Fading (2)

Variation of the received power due to combined effect of path loss, shadowing and fading


9

Doppler SpreadDoppler Spread

Measure of spectral broadening caused by the channel time variation due to movement of mobile terminal

Maximum Doppler spread

: Mobile speed (m/s)

: Wavelength (m)

: Carrier frequency (Hz)

: Speed of light (= 3x108 m/s)

Implication : Signal amplitude and phase decorrelate aftera time period ~ (coherence time)

Df

cff cD

cf

c

Df/1


10

Delay Spread (1)Delay Spread (1)

Time domain interpretation

2Re

c

e

i

v

e

d

P

o

w

e

r

Delay

Two-ray model = rms delay spread

Channel Input

0 T

1 1

0 T

2T

2T

Channel Output

T

small

T

large

0 T2T

Inter-Symbol Interference (ISI)


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Small : Negligible ISI

Large : Significant ISI which causes irreducible error floorT/

T

periodsymbolspreaddelayrms

Bit error rate (BER) limitations by ISI

T/


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The delay spread imposes a limit on the maximum bit rate

For example, for QPSK

Maximum bit rateMobile (Rural) 25 usec 8 kbps

Mobile (Urban) 2.5 usec 80 kbps

Micro-cell 500 nsec 400 kbps

Large building 100 nsec 2 Mbps


13


Frequency domain interpretation

Coherence BW

is small (Coherence BW >> signal BW)Flat fading (Frequency nonselective fading)

is large (Coherence BW


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MedianDelay Spread [ns]

Maximum Delay Spread [ns]

Remarks

25 50 Office building




354080

120

8090

120180

Office buildingShopping centerAirportFactory

50120

129300

WarehouseFactory

Delay Spread (Delay Spread (55))

Measured delay spread in 800 MHz ~ 1.5 GHz


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MedianDelay spread [ns]

Maximum Delay Spread [ns]

Remarks

40 120Large building(New York Stock Exchange)



60106

200270

Shopping centerLaboratory

19 30 Office building : Single room only

2030

105

6575

170

Office buildingCafeteriaShopping center



Measured delay spread in 1.8 GHz ~ 2.4 GHz



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MedianDelay Spread [ns]

Maximum Delay Spread [ns] Remarks

40 120Large building(e.g. Stock Exchange)

503510

605535

Office buildingMeeting room (5m5m) with metal wallsSingle room with stone walls


406525

12012565

Indoor sports arenaFactoryOffice building



Measured delay spread in 4 GHz ~ 6 GHz


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Interleaving (1)Interleaving (1)

Channels with memory

Exhibits mutually dependent (or time correlated) signaltransmission impairments

Statistical dependence among successive symbolsBurst errors

Examples : Multi-path fading channel

Most block or convolutional codes are designed to combat random independent errors

Interleaving (or time diversity) is required


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Interleaving

Interleaver shuffles the code symbols over a span of several block length (for block codes) or several constraint length(for convolutional codes)

Required span is determined by burst error duration

Deinterleaver recovers shuffled code symbols into original order

ChannelEncoder Interleaver Modulator

BinaryData

ToChannel

ChannelDecoder DeInterleaver Demodulator

BinaryData

FromChannel

BurstErrors

RandomErrors


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Block interleaving

Convolutional interleaving


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Block Interleaving (1)Block Interleaving (1)

Principles

Block interleaver accepts the coded symbols in blocks from the channel encoder, and permutes the symbols

Uses the same array in both interleaver and deinterleaver

Fills the array in column-by-column manner, and feeds the symbols into the modulator in row-by-row fashion

NM

WriteIn

Read Out


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Block Interleaving (2)Block Interleaving (2)

Properties of block interleaving

Any burst of less than contiguous channel symbol errors results in isolated errors at the deinterleaver output that are separated from each by at least symbols

Any burst of errors , results in output from the deinterleaver of no more than symbol errors. Each output burst is separated from the other bursts by no less than symbols

A periodic sequence of signal errors spaced symbols apart results in a single burst of errors of length at the deinterleaver output

Interleaver/deinterleaver end-to-end delay is approximately symbol times. More precisely, since only memory needs to be filled before transmission can begin (why?), the minimum end-to-end delay is symbol times

Memory requirement is symbols for each location. However, symbols is generally implemented at each location (why?)

N

M

bN )( 1b b

bM N

M

11 )(NMNM2)( 222 MMN

NMNM2


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MultiMulti--Carrier Modulation Schemes (1)Carrier Modulation Schemes (1)

Multi-carrier modulation

Transmission bandwidth is divided into many narrow sub- channels which are transmitted in parallel

Encoder Filter

Encoder Filter

Encoder Filter

......

R/N bps

R/N bps

R/N bps

RF1:NS/P

R bps

T sec

NT sec

)2exp( 0tfj

)2exp( 1tfj

)2exp( 1tfj N

Transmitter


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0f 1Nf

. . .1f 2f

f

MultiMulti--Carrier Modulation Schemes (2)Carrier Modulation Schemes (2)

Decoder

DecoderBPF

Decoder

...

R/N bps

R/N bps

R/N bps

RF N:1P/S

R bps

...

BPF

BPF

)2exp( 0tfj

)2exp( 1tfj

)2exp( 1tfj N

Receiver

Spectrum of a multi-carrier system

Disadvantages

Filter bank at receiver

Spectrally inefficient


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OFDM Basics (1)OFDM Basics (1)

Why OFDM for broadband transmission?

A multi-carrier modulation system

High data rate data Multiple low rate sub-channels

Each sub-channel becomes flat fading channel

Robust to frequency selective fading

Efficient bandwidth utilization by allowing overlapped sub-channels

Digital implementation using fast Fourier transform (FFT)


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Basic OFDM transmitter

Encoder1:NS/P

RFR bps.....

.nX

0X

1X

1NX R/N bps

)2exp( 0tfj

)2exp( 1tfj

)2exp( 1tfj N

T' sec

T = NT' sec


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How to separate the sub-channels in the receiver?

1X

2X

1NX

0X

RF N:1P/S

Decoder

..

)2exp( 0tfj

.

)2exp( 1tfj

)2exp( 2tfj

)2exp( 1tfj N Basic OFDM receiver


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Sub-channel separation

Integrates over , then by orthogonality of the subcarriers

OFDM signal spectrum

01 1withmf f m f f NT T

T NT mm XX

. . .0f 1f 2f 1Nf

f

f


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OFDM Signals (1)OFDM Signals (1)

Passband, real-valued, continuous-time description

: i-th complex QAM (or PSK)-modulated symbol

: Number of subcarriers

: Symbol duration (after S/P)

: Main carrier frequency

1

0( ) Re exp( 2 ( ) ) , 0

N

i ci

is t d j f t t TT

idNT

cf


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Baseband, complex-valued, continuous-time description

1

0( ) exp( 2 ), 0

N

ii

is t d j t t TT

T

Example of four subcarriers in an OFDM signal interval


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Assuming all subcarriers have the same amplitude and phase

Each subcarrier has exactly integer number of cycles in the interval

Number of cycles between adjacent subcarriers differs by exactly one Orthogonality

Correlator output for the k-th subcarrier

01

00

1

00

exp( 2 ) ( )

exp( 2 ) exp( 2 )

exp( 2 )

T

NT

ii

N T

ii

k

kj t s t dtT

k ij t d j t dtT T

i kd j t dtT

d T

T


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Maximum value of one subcarrier spectrum corresponds to zero crossings of all the others

Inter-Carrier Interference (ICI)-free

Spectrum of individual subcarriers


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Base-band, complex-valued, discrete-time description

Sampling at each

IDFT (Inverse Discrete Fourier Transform) of QAM (or PSK) symbols, followed by P/S

Efficient IFFT implementation

1

0( ) exp( 2 ), 0

N

ii

is t d j t t TT

Tt n nTN

1

0exp( 2 ) , 0, , 1

N

n ii

ins d j n NN

N


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Guard Time and Cyclic Prefix (1)Guard Time and Cyclic Prefix (1)

Guard time (or guard interval)

Large OFDM symbol duration Robust to delay spread and ISI

ISI can be completely eliminated by introducing guard time larger than the expected delay spread for each OFDM symbol

Guard time could consist of no signals at all ICI occurs because orthogonality between subcarriers no longer holds

Part of subcarrier #2 causingICI on subcarrier #1

Subcarrier #1

Delayed subcarrier #2

Guard time ( ) FFT integration time = 1/carrier spacing ( )

OFDM symbol time ( )

Channeldelay

sT

gT TEffect of multi-path

with zero-signal in theguard time


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Effect of delay spread and guard time



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How to avoid ISI and ICI simultaneously?Cyclic prefix

Delayed replicas of OFDM symbol always have an integer number of cycles within FFT interval

Guard time / Cyclic prefix( )

FFT integration time = 1/carrier spacing ( )

OFDM symbol time ( )sT

gTT OFDM symbol with

cyclic prefix


36


First arriving path Reflection OFDM symbol time

Guard time FFT integration timePhase transitions

Reflection delay

Example of an OFDM symbol in a two-ray multi-path channel


37


With cyclic prefix,1

0exp( 2 ), 0, , 1

N

n ii

ins d j n NN

, , , 1n N n gs s n

gg

TN

T

s gT T T

1 1

s

fT T

s

N NRT T

Copy

t

TsT

gT


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Guard Time and Cyclic Prefix (6)Guard Time and Cyclic Prefix (6)2

sT

f

1fT

2 2 1( 1)(1 )OFDM s s g s

NB N f N fT T T

gg

s

TT

Guard interval factor

11

OFDM

g

BR


39


16N

64N

256N


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Windowing (1)Windowing (1)

Windowing

Usually sharp phase or amplitude transitions caused by modulation are observed at OFDM symbol boundaries

OFDM signal consists of unfiltered QAM subcarriers

As results, out-of-band spectrum of each OFDM subcarrier decreases slowly according to sinc function

Adjacent channel interference (ACI)

Windowing : Makes amplitude go smoothly to zero at symbol boundaries Spectrum goes down more


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Raised cosine window

: Roll-off factor

: OFDM symbol duration in the case ofno window

0.5 0.5 cos( /( )), 0

( ) 1.0 ,

0.5 0.5 cos(( ) /( )) , (1 )

s s

s s

s s s s

t T t T

w t T t T

t T T T t T

0 0.5 1-0.5-1

-60

-80

-40

-20

0

20

Normalized Frequency

P

o

w

e

r

S

p

e

c

t

r

a

l

D

e

n

s

i

t

y

(

d

B

)

Typical OFDM spectrum

)10( gs TTT


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sT

s gT T T

prefixT TpostfixT

(1 ) sTg prefix postfixT T T

OFDM signal with cyclic extensions and windowing

Effect of windowing on OFDM spectrum

Increasedroll-off factor


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Windowing decreases delay spread tolerance

ICI and ISI are introduced because of amplitude modulation of delayed OFDM symbol

Orthogonality property is destroyed

Effective guard time is decreased by

T

Multipath delay

sT


44

OFDM System Design (1)OFDM System Design (1)

OFDM system requirements

Available bandwidth

Required bit rate

Tolerable delay spread

Doppler spread

OFDM system design parameters

Number of subcarriers ( )

Guard time ( )

Symbol duration ( )

subcarrier spacing ( )

Modulation type per subcarrier

Type of FEC code

NgT

Tf


45


Typical OFDM system configuration

IFFT (TX)

FFT (RX)

P/S

Add CyclicExtension

andWindowing

S/PRemoveCyclic

Extension

DACRF TX

Timing andFrequencySynchro-nization

ADCRF RX

FECEncoding Interleaving

QAMMapping

PilotInsertion S/P

FECDecoding

De-interleaving

QAMDemapping P/S Equalization

BinaryInputData

BinaryOutputData

Symbol Timing

ToChannel

FromChannel


46


Guard time : Determined by channel delay spread

Symbol duration (FFT interval)

To reduce SNR loss due to guard time, it is desirable to have symbol duration much larger than guard time

However, large symbol duration causes more subcarriers with tight spacing Complex implementation, sensitivity to phase/frequency errors, and large PAPR (Peak-to-Average Power Ratio)

gT

Guard time = 2 - 4 times of rms delay spread

T

gT


47


For less than 1-dB SNR loss due to delay spread

OFDM total symbol duration :

subcarrier spacing :

Symbol duration T = 4 - 5 times guard time

( 1)1dB 4g g

g

T T k Tk

T kT

gs TTT Tf /1


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Design example

Guard time :

FFT interval :

OFDM symbol duration :

subcarrier spacing :

Require bit rate :

Bit rate : 20 Mbps Tolerable delay spread : 200 nsBandwidth : < 15 MHz

Desired system specification

ns800spreaddelay4 gTs45 gTT

s8.4 gs TTTkHz250/1 Tf

20 Mbps 96bits / 4.8 s


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QPSK (2 bits/symbol) + rate-3/4 FEC coding

1.5 bits/symbol/carrier

64 subcarriers

64250 kHz = 16 MHz > Target BW 15 MHz

Can not meet the BW specification

16-QAM (4 bits/symbol) + rate-1/2 FEC coding

2 bits/symbol/carrier

48 subcarriers

48250 kHz = 12 MHz < Target BW 15 MHz

A proper modulation scheme

OFDM SystemsWireless Channel ImpairmentsPath LossShadowingMulti-Path Fading (1)Multi-Path Fading (2)Flat Fading (1)Flat Fading (2)Doppler SpreadDelay Spread (1)Delay Spread (2)Delay Spread (3)Delay Spread (4) 14 15 16Interleaving (1)Interleaving (2)Interleaving (3)Block Interleaving (1)Block Interleaving (2)Multi-Carrier Modulation Schemes (1)Multi-Carrier Modulation Schemes (2)OFDM Basics (1)OFDM Basics (2)OFDM Basics (3)OFDM Basics (4)OFDM Signals (1)OFDM Signals (2)OFDM Signals (3)OFDM Signals (4)OFDM Signals (5)Guard Time and Cyclic Prefix (1)Guard Time and Cyclic Prefix (2)Guard Time and Cyclic Prefix (3)Guard Time and Cyclic Prefix (4)Guard Time and Cyclic Prefix (5)Guard Time and Cyclic Prefix (6)Guard Time and Cyclic Prefix (7)Windowing (1)Windowing (2)Windowing (3)Windowing (4)OFDM System Design (1)OFDM System Design (2)OFDM System Design (3)OFDM System Design (4)OFDM System Design (5)OFDM System Design (6)

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2014-1 OFDM