EC744 Wireless CommunicationsSpring 2007

Mohamed Essam KhedrDepartment of Electronics and Communications

OFDMwww.aast.edu/~khedr

Motivation

• High bit-rate wireless applications in a multipath radio environment.

• OFDM can enable such applications without a high complexity receiver.

• OFDM is part of WLAN, DVB, and BWA standardsand is a strong candidate for some of the 4G wireless technologies.

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 Transmission

• Fading due to constructive and destructive addition of multipath signals.

• Channel delay spread can cause ISI.

• Flat fading occurs when the symbol period is large comparedto the delay spread.

• Frequency selective fading and ISI go together.

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)

Delay Spread

• Power delay profile conveys the multipath delay spread effects of the channel.

• RMS delay spread quantifies the severity of the ISIphenomenon.

• The ratio of RMS delay spread to the data symbol period determines the severity of the ISI.

Multipath Radio Channel

� �����������

Inter-Symbol-Interference

Transmitted signal:Received Signals:

Line-of-sight:

Reflected:

The symbols add up on the

channel Delays

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

A Solution for ISI channels

• Conversion of a high-data rate stream into several low-ratestreams.

• Parallel streams are modulated onto orthogonal carriers.

• Data symbols modulated on these carriers can be recoveredwithout mutual interference.

• Overlap of the modulated carriers in the frequency domain -different from FDM.

OFDM

• OFDM is a multicarrier block transmission system.

• Block of ‘N’ symbols are grouped and sent parallely.

• No interference among the data symbolssent in a block.

OFDM Mathematics1

2

0

( ) k

Nj f t

kk

s t X e π−

=

= � t ≡ [ 0,Τos]

Orthogonality Condition

*1 2

0

( ). ( ) 0T

g t g t dt =�In our case

2 2

0

. 0p q

Tj f t j f te e dtπ π− =�

For p ≠ q Where fk=k/T

Transmitted Spectrum

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 π

N sub-carriers:

T0

OFDM terminology

• Orthogonal carriers referred to as subcarriers {fi,i=0,....N-1}.

• OFDM symbol period {Tos=N x Ts}.

• Subcarrier spacing ∆f = 1/Tos.

OFDM and FFT

• Samples of the multicarrier signal can be obtained using the IFFT of the data symbols - a key issue.

• FFT can be used at the receiver to obtain the data symbols.

• No need for ‘N’ oscillators,filters etc.

• Popularity of OFDM is due to the use of IFFT/FFT which have efficient implementations.

OFDM Signal1

,0

( ) ( ( ))N

n k k osn k

s t X g t nT∞ −

=−∞ =

= −� �2

( )0

kj f t

k

eg t

π�= �

�

t ≡ [ 0,Τos]

Otherwise

ko s

kf

T= K=0,..........N-1

By sampling the low pass equivalent signal at a rate N times

higher than the OFDM symbol rate 1/Tos, OFDM frame

can be expressed as:

1

,0

( ) ( ) ( )N

n n k k os osk

mF m X g t nT t n T

N

−

=

= − = +�

{ }1 2

, ,0

( ) .mN j kN

n n k n kk

F m X e N IDFT Xπ−

=

��= =� ��

m = 0....N-1

Interpretation of IFFT&FFT

• IFFT at the transmitter & FFT at the receiver

• Data symbols modulate the spectrum and the time domain symbols are obtained using the IFFT.

• Time domain symbols are then sent on the channel.

• FFT at the receiver to obtain the data.

Interference between OFDM Symbols

• Transmitted Signal

• Due to delay spread ISI occurs

Delay Spread

IOSI

OS1 OS2 OS3

• Solution could be guard interval between OFDM symbols

Cyclic Prefix

• Zeros used in the guard time can alleviate interference between OFDM symbols (IOSI problem).

• Orthogonality of carriers is lost when multipath channels are involved.

• Cyclic prefix can restore the orthogonality.

Cyclic Prefix

• Convert a linear convolution channel into a circular convolution channel.

• This restores the orthogonality at the receiver.

• Energy is wasted in the cyclic prefix samples.

Cyclic Prefix Illustration

TosTg

Cyclic Prefix

OS 1 OS 2

OS1,OS2 - OFDM Symbols

Tg - Guard Time Interval

Ts - Data Symbol Period

Tos - OFDM Symbol Period - N * Ts

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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

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 N

win = 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

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 domain signal (baseband)

sample nr.

imaginaryreal

δf frequency offset

frequency

amplitude

Serialto Parallel

X0

XN-1

x0

xN-1

IFFT

Parallel to

Serialand

add CP

Add CP

WindowingDACRF Section

InputSymbols

OFDM Transmitter

ADCandRemoveCP

Serial toParallel FFT

Parallel to Serialand Decoder

X0

XN-1

x0

xN-1

OutputSymbols

OFDM Receiver

Synchronization

• Timing and frequency offset can influence performance.

• Frequency offset can influence orthogonality of subcarriers.

• Loss of orthogonality leads to Inter Carrier Interference.

Peak to Average Ratio

• Multicarrier signals have high PAR as compared to singlecarrier systems.

• PAR increases with the number of subcarriers.

• Affects power amplifier design and usage.

Peak to Average Power Ratio