Orthogonal Frequency Division Multiplexing (OFDM): Concept and System-Modeling

Klaus Witrisal

Signal Processing and Speech Communication LabTechnical University Graz, Austria

VL: Mobile Radio Systems, Ch. 5: “Wideband Systems”15-Dec-10

Outline

• Introduction– What is OFDM?– Multipath fading radio-channel

• Principle of OFDM• OFDM Implementation and System Model• Advantages and Disadvantages• OFDM in Practice• Summary

What is OFDM?

• Modulation technique – Requires channel coding– Solves multipath problems

OFDM modulation

Source coding

I/Q-mod., up-

converter

I/Q RFChannel coding /

interleaving

Transmitter:

InfoSource

OFDM de-modulation

Source decoding

Down-converter,

I/Q-demod.I/Q RF

Decoding / deinter-leaving

Receiver:Radio-channel

InfoSink

e.g. Audio 0110 01101101

fPSD

* fPSD

fc-fc

Multipath Radio Channel

Multipath Propagation

• Reflections from walls, etc.

• Time dispersive channel– Impulse response:

• Problem with high rate data transmission:– inter-symbol-interference

[ns]

p () (PDP)

Multipath Radio Channel

Inter-Symbol-Interference

Transmitted signal:

Received Signals:Line-of-sight:

Reflected:

The symbols add upon the channel

Distortion!Delays

Outline

• Introduction– What is OFDM?– Multipath fading radio-channel

• Principle of OFDM• OFDM Implementation and System Model• Advantages and Disadvantages• OFDM in Practice• Summary

OFDM Technology

Concept of parallel transmission (1)Channel impulse response

1 Channel (serial)

2 Channels

8 Channels

Time

In practice: 50 … 8000Channels (sub-carriers)

Channels are transmitted at different frequencies (sub-carriers)

Multipath Radio Channel

The Frequency-Selective Radio Channel

• Interference of reflected (and LOS) radio waves– Frequency-dependent fading

-10

-5

0

5

10

15

20

Frequency

Power response [dB]

OFDM Technology

Concept of parallel transmission (2)Channel impulse response

1 Channel (serial)

Channeltransfer function

Channels are “narrowband”

2 ChannelsFrequency

Frequency

8 ChannelsFrequency

FrequencyTime

Signal is “broadband”

Implementation and System Model

Concept of an OFDM signal

Ch.1

Ch.2 Ch.3 Ch.4 Ch.5 Ch.6 Ch.7 Ch.8 Ch.9 Ch.10

Saving of bandwidth

Ch.3 Ch.5 Ch.7 Ch.9Ch.2 Ch.4 Ch.6 Ch.8 Ch.10

Ch.1

Conventional multicarrier techniques

Orthogonal multicarrier techniques

50% bandwidth saving

frequency

frequency

Outline

• Introduction– What is OFDM?– Multipath fading radio-channel

• Principle of OFDM• OFDM Implementation and System Model• Advantages and Disadvantages• OFDM in Practice• Summary

Generating the OFDM signal (1)

• Symbol (QPSK) of sub-carrier i at time k– Other symbol-alphabets can be used as well (BPSK, m-QAM)

• Baseband signal is generated by DSP

)(2exp)()( ,,, kTtfijxkTtwts kikiBB

Re

Imxi,k

Window function Sub-carrier

resemblesIDFT!

Spectrum of the modulated data symbols

• Rectangular Window of duration T0

• Has a sinc-spectrum with zeros at 1/ T0

• Other carriers are put in these zeros

• sub-carriers are orthogonal Frequency

Magnitude

1

0

)(2,, )()(

N

i

kTtfijkikBB exkTtwts

N sub-carriers:

T0

Generating the OFDM signal (2)

serial-to-parallelxn

IDFT

(IFFT)

x0,k

x1,k

xN,k

parallel-to-serial

s0,k

s1,k

sN,k

sn

Re

Imxi,k

N data symbols:(in frequency-domain)

Base-band signal

(time-domain)

Introduction

Idea of Guard Interval (GI)

FFT-part

time

Insertion of guard interval (cyclic prefix):

Channel impulse response (shorter than GI):

t

1 OFDM symbol

Cyclic convolution of transmitted signal with channel impulse response

multiplication in frequency-domain

Guard interval (2) - Cyclic extension

System Proposal

OFDM Symbol Configuration (1)Transmitter pulse prototype w(t) Channel impulse response Receiver filter (implemented by FFT)

time

time

Prefix Postfix effective TX-time

kT

Twin Tguard TFFT

TFFT

excess delay time max

T

Introduction

OFDM System Model• Multiplication of data symbols with (complex-valued)

channel transfer-function:

x-N/2,k

h-N/2,k n-N/2,k

y-N/2,k

xN/2-1,k

hN/2-1,k nN/2-1,k

yN/2-1,k

iiii nhxy

OFDM Technology

OFDM Block Diagram

OFDM modulation

(IFFT)

Channel coding /

interleaving

Guard interval

I/Q I/QSymbol mapping

(modulation)

Transmitter

0101010010110

OFDM demod. (FFT)

Decoding / deinter-leaving

Guard interval removal

Time sync.

I/Q I/Q

symbol de-mapping

(detection)

Channel est.

Receiver

RF modulation;TX antenna;Multipath channel;RX antenna;RF demodulation

Outline

• Introduction• Principle of OFDM• OFDM Implementation and System Model• Advantages and Disadvantages• OFDM System Design

– Parameter selection– Implementation Issues

• Summary and Applications

Introduction

Design of an OFDM System

Channel impulse

response

Guard intervallength

Channel Parametersare needed

x(4 … 10) FFTsymbollength

Nr. ofcarriers

Data rate;modulation

order

Other constraints:•Nr. of carriers should match FFT size

and data packet length

•considering coding and modulation schemes

OFDM System Design

OFDM Symbol Configuration (1)Transmitter pulse prototype w(t) Channel impulse response Receiver filter (implemented by FFT)

time

time

Prefix Postfix effective TX-time

kT

Twin Tguard TFFT

TFFT

excess delay time max

T

OFDM System Design

Spectral Shaping by Windowing

−60 −40 −20 0 20 40 60−90

−80

−70

−60

−50

−40

−30

−20

−10

0

10

OFDM spectrum for NFFT

= 64, Nguard

= 16, oversampling = 2

frequency in sub−carriers

pow

er s

pect

rum

mag

nitu

de [d

B]

Nwin

= 2

Nwin

= 0

Nwin

= 16

Design of an OFDM System

OFDM Symbol Configuration (2)

• Not all FFT-points can be used for data carriers– Lowpass filters for AD- and DA-conversion

• oversampling required

– DC offsets; carrier feedtrough; etc.

DC–fs/2 fs/2

Transfer function oftransmitter/receiver

useable sub-carriers useable sub-carriers…, –1, 0, 1, … –N/2, … …, N/2–1

frequency

sub-carrierindex i

Outline

• Introduction– What is OFDM?– Multipath fading radio-channel

• Principle of OFDM• OFDM Implementation and System Model• Advantages and Disadvantages• OFDM in Practice• Summary

Advantages of OFDM

• Solves the multipath-propagation problem– Simple equalization at receiver

• Computationally efficient– For broadband systems more efficient than SC

• Supports several multiple access schemes– TDMA, FDMA, MC-CDMA, etc.

• Supports various modulation schemes– Adaptability to SNR of sub-carriers is possible

• Elegant framework for MIMO-systems– Any interference among symbols is removed

OFDM Technology

Problems of OFDM (Research Topics)

• Synchronization issues:– Time synchronization

• Find start of symbols

– Frequency synchr.• Find sub-carrier positions

• Non-constant power envelope– Linear amplifiers needed

• Channel estimation:

– To retrieve data

– Channel is time-variant

0 20 40 60 80 100 120 140 160 180 200-0.2

-0.1

0

0.1

0.2time domain signal (baseband)

sample nr.

imaginaryreal

f frequency offset

frequency

amplitude

Introduction

Correlation-based Frequency-sync.• Correlation of duplicated parts of OFDM signal

– e.g.: Cyclic prefix (Guard interval - GI):

Guard interval (M samples)

FFT-part (L samples)

conj.

conj.

... … (M times)

...

si:

• Peak at optimum position • Phase frequency-offset

• Received signal with f-offset:– Constant phase offset between samples spaced by L

1

0

*M

iLiiopt rrP

)/2exp( Nifjsr ii

Outline

• Introduction– What is OFDM?– Multipath fading radio-channel

• Principle of OFDM• OFDM Implementation and System Model• Advantages and Disadvantages• OFDM in Practice• Summary

Summary and Applications

Applications of OFDM

• Wireless LAN– IEEE802.11a/g

– HYPERLAN

• DAB, DVB, etc.– Digital Audio/Video Broadcasting

• xDSL (Digital Subscriber Line)– uses Discrete Multitone (DMT)

Summary – Essential “Ingredients”

• IFFT & FFT– For efficient implementation

• Guard interval insertion– Obtaining simple equalization – Removing all IS- & IC-interferences

• Error correction coding– To restore bits that are lost on weak sub-carriers