1

OFDM – Orthogonal FrequencyDivision Multiplexing

Dr. Jean ArmstrongDepartment of Electronic Engineering

La Trobe University

2

Overview

! Introduction! applications! multicarrier systems

! Why use OFDM?! multipath transmission

! How OFDM works! Applications of OFDM! Problems with OFDM! Research in OFDM

3

Applications of OFDM! Digital Television

! European and Australian standard

! Wireless Local Area Networks (LANs)! Hiperlan 2

! ADSL (asymmetric digital subscriber loop)! High speed data transmitted along existing

telephone lines

! Future mobile telephony?

4

Multicarrier systems

! Single carrier system! signal representing each bit

uses all of the availablespectrum

! Multicarrier system! available spectrum divided

into many narrow bands! data is divided into parallel

data streams eachtransmitted on a separatebandfrequency

!

NW

frequency W

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What is OFDM?

! OFDM is a multicarrier system! uses discrete Fourier

Transform/Fast FourierTransform (DFT/FFT)

! sin(x)/x spectra for subcarriers

! Available bandwidth is dividedinto very many narrow bands! ~2000-8000 for digital TV! ~48 for Hiperlan 2

! Data is transmitted in parallelon these bands

Frequency

W/N

frequency

!

NW

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Why is OFDM so popular fornew broadband systems?

! Most broadband systems are subject tomultipath transmission

! Conventional solution to multipath is anequalizer in the receiver! high data rates - equalizers too complicated

! With OFDM there is a simple way of dealingwith multipath! relatively simple DSP algorithms

7

What is Multipath?

! More than onetransmission pathbetween transmitterand receiver

! Received signal is thesum of many versionsof the transmittedsignal with varyingdelay and attenuation

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Effect of Multipath onReceived Baseband Signal

! Received signal at any time depends on anumber of transmitted bits! Intersymbol Interference (ISI)

! Need equalizer to recover data

Signal on Path 1

Signal on Path 2

Signal on Path 3

Received

Signal

1 2 3 4 5

Received signal depends on bits 2 - 4

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ISI gets worse as data rateincreases

! ISI covers more symbol periods! Equalizer becomes too complicated

Signal on Path 1

Signal on Path 2

Signal on Path 3

Received

Signal

1 2 3 4 5

Received signal depends on bits 1 - 4

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How does OFDM solve themultipath problem?

! Data is transmitted in parallel! longer symbol period! e.g. for N parallel streams, symbol period is N

times as long

! Cyclic prefix! trick to avoid residual ISI

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How are signals transmitted inparallel without interference?

! Each subcarrier has adifferent frequency

! Frequencies chosen sothat an integral numberof cycles in a symbolperiod

! Signals aremathematicallyorthogonal

First three subcarriers

Symbol period

0

2 2sin sin 0,

T kt ltdt k l

T T

π π− = ≠∫

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How is data carried on thesubcarriers?

! Data is carried byvarying the phase oramplitude of eachsubcarrier

! QPSK, 4-QAM, 16-QAM,64-QAM

Two possible subcarrier values

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Baseband OFDM system

High speed data (complex)

Serial

to Parallel

IFFT

Parallel to Serial

D/A

Conver-ter

Low-Pass Filter-

ing

Received high speed data

Parallel to

Serial

Serial to

Parallel

FFT

A/D Conver

-ter

Low-Pass Filter-

ing

Transmitter

Receiver

Discrete frequency domainEach input controls signal at one frequency

Discrete Time DomainSamples of modulatedand multiplexed signals

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How are OFDM signals generated?! Parallel data streams are

used as inputs to an IFFT! IFFT output is sum of

signal samples! IFFT does modulation and

multiplexing in one step! Filtering and D/A of

samples results inbaseband signal

Signal values at the outputof the IFFT are the sum

of many samples of many sinusoids - looks random

Typical IFFT Output Samples

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Modulation! Varying the complex

numbers at the IFFTinput results inmodulation of thesubcarriers

16-QAM8-PSK

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Signals at Input and Output ofTransmitter IFFT

High speed data (complex)

Serial

to Parallel

IFFT

Parallel to Serial

D/A

Conver-ter

Low-Pass Filter-

ing

Transmitter

Complex valuerepresenting datais input to IFFT

IFFT outputgives samplesof modulatedmultiplexed

signal

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OFDM in a multipath environment- effect on one subcarrier

! Received signal inone symbol periodis not a sinusoid

! Causes intercarrierinterference (ICI)

First symbol Second symbol

Signal on Path 1

Signal on Path 2

delay ICI

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Cyclic Prefix

! Each symbol is cyclically extended! Some loss in efficiency as cyclic prefix carries

no new information

Cyclic Prefix Symbol without prefix

Signal transmitted onone subcarrier for

one symbol

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Effect of multipath on symbolwith cyclic prefix

! If multipath delay is less than the cyclic prefix! no intersymbol or intercarrier interference! amplitude may increase or decrease

Cyclic PrefixPath delay

Signal on Path 2

Signal on Path 1

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Frequency selective fading

Main signal +Delayed signal

TransmittedSignal

Main signal +Delayed signal

TransmittedSignal

0 0.5 1 1.5 2-1

0

1

Symbol Duration

Am

plit

ud

e

0 0.5 1 1.5 2-2

0

2

Symbol Duration

Am

plit

ud

e

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Spectrum of Received Signal

! Multipath fading causessome frequencies to beattenuated

! Fading is approximatelyconstant over narrow band

! This is corrected in thereceiver

W

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Amplitude and phase change! Multipath delay causes

change in amplitude andphase of each subcarrier

! Change depends onsubcarrier frequency

! Corrected in receiver byone complex multiplicationper subcarrier

Main signal +Delayed signal

TransmittedSignal

Main signal +Delayed signal

TransmittedSignal

0 0.5 1 1.5 2-1

0

1

Symbol Duration

Am

plit

ud

e

0 0.5 1 1.5 2-2

0

2

Symbol Duration

Am

plit

ud

e

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Multipath fading corrected by‘single tap equalizer’

! Change in phase and amplitude corrected bycomplex multiplication

! Receiver structure suited to DSPimplementation

Received high speed data

Parallel

to Serial

Serial

to Parallel

FFT

A/D Conver

-ter

Low-Pass Filter-

ing

One Tap

Equali-zer

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Digital Video Broadcasting(DVB)

! OFDM is used in the Australiandigital television system

! 2048 point IFFT! 1705 subcarriers used

! Flexible standard! variable error coding! variable cyclic prefix! variable constellation

! 4QAM, 16QAM, 64QAM

! Broadcast system! mode determined by broadcaster

TV

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DVB - single frequencynetwork

! DVB designed to allow thesame frequency to be used forthe same channel throughouta region

! Single Frequency Network! More than one received signal

! like extreme multipath

! Reason for large number ofsubcarriers! 8000 subcarrier option allows

greater distance betweentransmitters

TVAntenna Antenna

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OFDM in ADSL

! OFDM used in ADSL is usually called ‘DiscreteMultitone’ (DMT)

! Two way transmission! transmission can be tailored to the particular

channel

! Baseband system! only real (not complex signal can be transmitted)

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Frequencies used for ADSL

Frequency

0-4kHz Downstream 25-1104 kHz

Ups

trea

m

PO

TS

Pow

er S

pect

ral

Den

sity

ADSL with Echo Cancelling (EC)

Ups

trea

m

PO

TS

Pow

er S

pect

ral

Den

sity

FrequencyDownstream 138-1104 kHz

ADSL with Frequency Division

Duplexing (FDD)

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OFDM/DMT in ADSL

! 256 subcarriers! Test signals transmitted

! received signal and noise level of each tonemeasured

! Large constellations used on good tones

Ups

trea

m

PO

TS

Pow

er S

pect

ral

Den

sity

FrequencyDownstream 138-1104 kHz

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Hiperlan-2 - Wireless LAN! 64 point FFT, 52 subcarriers used! Different modes

! signal constellation, error coding, cyclic prefix

! Two way channel! feedback be used to determine transmission mode

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OFDM Problems! High peak-to-average power ratio

! peak signals power much greater than averagesignal power

! need very linear amplifiers with large dynamicrange

! Very sensitive to frequency errors! tight specifications for local oscillators! Doppler limitation

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High peak-to-average power

! OFDM signal is sumof many separatesinusoids

! In worst case mayall addconstructively

! High peaks occurrarely

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Solutions to peak-to-averagepower

! Coding to avoid the peaks - Monash! Clip the peaks - La Trobe! Predistort the signal to compensate for the

amplifier nonlinearity - Victoria University

High speed data (complex)

Serial

to Parallel

IFFT

Parallel to Serial

D/A

Conver-ter

Low-Pass Filter-

ing

Transmitter

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Frequency Sensitivity

! Individual subcarriers have sin(x)/x spectrum! Large sidelobes result in sensitivity to frequency

offset! Subcarriers no longer orthogonal! Tight specifications on local oscillators

Frequency

W/N

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Research at La TrobeUniversity! Peak-to-average power reduction

! clipping! effect on signal constellation! clipping noise added at transmitter

! Alternative modulation schemes based onOFDM! polynomial cancellation coded OFDM (PCC-OFDM)

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PCC-OFDM - solution tofrequency sensitivity

! By coding the subcarriers in pairs frequencysensitivity can be reduced

! Would have been a better basis for DVB

-5 0 5 10-1

-0.5

0

0.5

1

Frequncy-5 0 5 10

-1

-0.5

0

0.5

1

Frequncy-5 0 5 10

-1

-0.5

0

0.5

1

Frequncy

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ISI/ICI of OFDM and PCC-OFDM

OFDM PCC-OFDM! Concentration of subchannels in time and

frequency domain reduce ICI and ISI

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PCC with overlapping symbolperiods

! Symbols are overlapped! ISI is deliberately introduced! equalizer required in receiver to recover data

0 T/2 T 3T/2 2T

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PCC-OFDM receiver structure

! Requires two dimensional equalizer! Properties of PCC-OFDM mean that only a

few terms along the diagonal are significant

Two-Dimensional

Equalizer

1−iV

iV

1+iViD̂

"

"

BPFLPFand

ADCX

( )( )tffj c ∆+− π2exp

iN

i

y

y

,1

,0

−

"DFT

iN

i

z

z

,1

,0

−

" Weightandsum i

i

Nv

v

,1

,0

2−

"T/2

Delay 1,1

1,0

2−−

−

i

i

Nv

v"

T/2Delay

2,1

2,0

2 −−

−

i

i

Nv

v"Delay

line

Data clockedin at rate T/N

One DFToperationevery T/2

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Performance in a multipathchannel

! PCC-OFDMoutperforms OFDM

! Advantages increaseas delay spreadincreases

! tolerance to delayspread depends onequalizer length, notlength of cyclic prefix

N=64, OFDM cyclic prefix length=6T/64

0 5 10 15 20 25 3010

-6

10-5

10-4

10-3

10-2

10-1

100

de lay spread (T/64)

Bit

Err

or R

ate

four linear s tages - 10dBfour linear s tages - 15dBOFDM - 10dBOFDM - 15dB

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Conclusions

! OFDM is used in many applications! solution to multipath! good digital signal processing algorithms

! Any questions?

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Baseband OFDM system

High speed data (complex)

Serial

to Parallel

IFFT

Parallel to Serial

D/A

Conver-ter

Low-Pass Filter-

ing

Received high speed data

Parallel to

Serial

Serial to

Parallel

FFT

A/D Conver

-ter

Low-Pass Filter-

ing

Transmitter

Receiver