Ofdm Handout

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Orthogonal Frequency Division Multiplexing

(OFDM): Concept and System-Modeling

Klaus Witrisal

Signal Processing and Speech Communication Lab

Technical University Graz, Austria

VL: Mobile Radio Systems, Ch. 5: “Wideband Systems”

24-Nov-05

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

f

PSD

*f

PSD

f c-f c

Multipath Radio Channel

Multipath Propagation

• Reflections from walls,etc.

• Time dispersive channel

– Impulse response:

• Problem with high rate data

transmission: – inter-symbol-interference

τ [ns]

p (τ ) (PDP)




Inter-Symbol-Interference

Transmitted signal:

Received Signals:

Line-of-sight:

Reflected:

The symbols add upon the channel

Æ Distortion!

Delays

Outline

• Introduction






• Summary

OFDM Technology

Concept of parallel transmission (1)

Channel impulseresponse

1 Channel (serial)

2 Channels

8 Channels

Time

In practice: 50 … 8000

Channels (sub-carriers)

Channels are transmittedat different frequencies(sub-carriers)


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 impulseresponse

1 Channel (serial)

Channeltransfer function

Channels are“narrowband”

2 ChannelsFrequency

Frequency

8 Channels Frequency

Frequency Time

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




• 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)()( ,,, kT t f i j xkT t wt s k ik i BB −∆⋅⋅−= π

Re

Im xi,k

Window function Sub-carrier



resemblesIDFT!

Spectrum of the modulated data symbols

• Rectangular Windowof duration T

0

• Has a sinc-spectrumwith zeros at 1/ T

0

• Other carriers are put

in these zeros

• Æ sub-carriers are

orthogonalFrequency

Magnitude

∑−

=

−∆−=

1

0

)(2

,, )()( N

i

kT t f i j

k ik BB e xkT t wt sπ

Nsub-carriers:

T0

Generating the OFDM signal (2)

serial-to-

parallel xn

IDFT

(IFFT)

x0,k

x1 ,k

x N,k

parallel-

to-serial

s0,k

s1 ,k

s N,k

sn

Re

Im xi,k

N data symbols:(in frequency-domain)

Base-bandsignal

(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 signalwith channel impulse response

Æ 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 Postfixeffective TX-time

k ⋅T

T win T guard T FFT

T FFT

τ excess delay timeτ 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

x N /2-1,k

h N /2-1,k n N /2-1,k

y N /2-1,k

iiii nh x y +=

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


• OFDM Implementation and System Model• Advantages and Disadvantages

• OFDM System Design

– Parameter selection

– Implementation Issues

• Summary and Applications



Introduction

Design of an OFDM System

Channelimpulse

response

Guardintervallength

Channel

Parameters

are needed

x(4 … 10) FFTsymbollength

Nr. of carriers

Data rate;modulation

order

Other constraints:

•Nr. of carriers should match FFT sizeand 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 Postfixeffective TX-time

k ⋅T

T win T guard T FFT

T FFT

τ excess delay timeτ 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

p o w e r s p e c t r u m m

a g n i t u d e [ 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 – f s/2 f s/2

Transfer function of

transmitter/receiver

useable sub-carriers useable sub-carriers

…, –1, 0, 1, … – N /2, … …, N /2–1

frequency

sub-carrier

index i



Outline

• Introduction






• 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

– All 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 domainsignal (baseband)

samplenr.

imaginaryreal

δ 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.

Σ

... … (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

i

Liiopt r r P

)/2exp( N i f jsr ii δ π =



Outline

• Introduction






• 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

Documents

Ofdm Handout