Lecture Two- OfDMI

7/29/2019 Lecture Two- OfDMI

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EECE5984CE5984

Orthogonal Frequency Division MultiplexingOrthogonal Frequency Division Multiplexing

TechnologiesTechnologies

Fall 2007Fall 2007

Mohamed Essam Khedr

OFDM Basics I


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TextbookTextbook

OFDM and MC-CDMA for broadband multi

communications by Lajos Hanzo et al

Additional Readings:

Richard van Nee and Ramjee Prasad, OFDM

Multimedia Communications, Artech House: OR90065306)

Orthogonal Frequency Division Multiplexing Communications by Ye (Geoffrey) Li (EditorStuber (Editor), ISBN 0387290958

Ahmad Bahai and Burton Saltzberg, Multi-C

Communications: Theory and Applications ofPlenum Publishing Corporation: 1999, ISBN:


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SyllabusSyllabus

Wireless channels characteristics (7.5%)

wireless channel modeling and characteristics

Large scale and small scale models

Common channel models

Channel categories and parameter calculation.

Prob. of error calculations

OFDM Basics (10%)

History of OFDM OFDM System model

Discrete-time signals & systems and DFT

Generation of subcarriers using the IFFT

Guard time, cyclic extension

Windowing

Choice of OFDM parameters & OFDM signal processing

Implementation complexity of OFDM versus single carrier m Modulation and Coding (10%)

Linear and nonlinear modulation

Interleaving and channel coding

Optimal bit and power allocation

Adaptive modulation


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SyllabusSyllabus

Analysis of OFDM systems (15%) RF subsystems, amplifier classification and distortion

Crest factor (PAPR) reduction techniques

Pre-distortion & adaptive pre-distortion techniques

clipping

coding techniques

partial transmit sequences (PTS) & modified PTS v. sel

nonlinear quantization (companding) Phase noise and I&Q imbalance for QAM

Performance of OFDM in Gaussian channels

Performance of OFDM in Wide-band channels

Synchronization and Estimation (15%)

ICI and OISI problems

Timing estimation

Frequency synchronization Frequency error estimation algorithms

Carrier phase tracking

Frequency domain and time domain approaches for channe

coherent detection

differential detection


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SyllabusSyllabus

Multi-user OFDM Techniques (10%) 2 Adaptive modulations in OFDM

Power and bit allocations in OFDM

Scalable OFDM

Flash OFDM

Diversity (7.5%) 1

Limits of capacity in fading environments Channel models for multiple-input-multiple-output (MIMO)

Receiver diversity techniques

Transmit diversity techniques and design criteria for fading c

Block, trellis and layered space-time codes

Multi-carrier CDMA (10%)

MC-CDMA versus DS-CDMA

MC-CDMA versus orthogonal frequency division multiple a

OFDMA and MC-CDMA performance evaluation in wide-b


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SyllabusSyllabus

Physical and Medium Access Control (MAC) for IEEE 80(7.5%) 1

Physical modeling of 802.11 networks

MAC system architecture

Frame exchange with RTS/CTS

Power management

Synchronization

Physical and Medium Access Control (MAC) for IEEE 80(7.5%) 1

Physical modeling of 802.16 networks

MAC system architecture

QoS guarantees in Wimax

Power management

Synchronization


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GradingGrading

Type of assignment Percent of Grade

Home works 20%

Matlab Assignments 20%

Midterm 20%

Final project presentation and term paper 20%Final Exam 20%


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MatlabMatlab Assignment 1Assignment 1

Develop a WGN channel that accepts symbol

noise to it with certain SNR and produces the

Develop a Flat Fading Channel following Ray

ricean distribution

Develop a Frequency selective channel followi

and ricean distribution All inputs to the channel are baseband signals.

Compare with the matlab functions (if exist)

Plot the probability of error vs SNR


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ecture one a ng c anne secture one a ng c anne s


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ImpulseImpulse RResponseesponse CCharacterizationharacterization

t0

t2

t1

Time spreading property

Timev

ariat

ionsp

roperty

Impulse response: Time-spreading : multipa

and time-variations: time-varying enviro


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C

A

D

BReceiverTransmitter

A: freeB: reflC: diffD: sca


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Multipath PropagationMultipath Propagation Simple MSimple M

hc(t) = k k (t - k)where k = 0, , K-1

k : path gain (complex)

0 = 0 normalize relative

delay of first path

k = k - 0 difference in

time-of-flight

| | | | 0 ||||

1

0

1

2

path attenuationpath attenuation path phasepath phase

( ) ( ) ( ) (1

0

, iL

j t

i

i

h t a t e

=

=


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Impact ofImpact ofMultipathMultipath: Delay Spread: Delay Spread

-6 -4 -2 0 2 4 6-0.2

0

0.2

0.4

0.6

0.8

1

t/Ts

2Ts 4Ts

Ts

-6 -4 -2 0

-0.5

0

0.5

1

-6 -4 -2 0

-0.2

0

0.2

0.4

0.6

0.8

Max delay spread = effective number of symbol periods occu

Requires equalization to remove resultin


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!

"#$ Tm

"#$$$%

&' ("$

( )

( )

( )

( )

2

h h

h h

d d

d d

=

h

Tm


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!

1m mB TBm

0)

)*!

Bm ' %

)*$Bm %


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!

"#

+,-!%+

Bd

0B

HS

cos cosdV

f

= =


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$,

$

0

L ./0

$,

L ./0

$,

Bd

( ) ( )

( )

( )

12

0

, i iL

j t

i ii

h t a t e

+

=

=


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Statistical ModelsStatistical Models Design and performance analysis based on statistical en

channels rather than specific physical channel.

Rayleigh flat fading model: many small scattered paths

Complex circular symmetric Gaussian .

Rician model: 1 line-of-sight plus scattered paths


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&($

( )2 22

2

aa

p a e

= ( )1

2p

=

( ) ( ) ( ) ( ) ( ) (j t

i

i

c t a t e x t j y t a

= = + =

)',!)(,!#

* $1'

($ ($


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&(

) %%'23! # 1 '

&!

( ( "

-

" -

( ) ( ) ( ) ( )0 0j t

i

i

c t a a t e a a t e

= + = +

( )( )22 20 2 0

02 2

a aa aap a e I

+ =


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Channel ClassificationChannel Classification

Based on Time-Spreading

Flat Fading1. BS < BC Tm < Ts2. Rayleigh, Ricean distrib.3. Spectral char. of transmitted

signal preserved

Frequency Sele1. BS > BC Tm2. Intersymbol In3. Spectral chara

signal not pres4. Multipath com

Signal

Channel

freq.BS

BC

BC

BS

Channel


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Channel ClassificationChannel Classification

Based on Time-Variations

Fast Fading1. High Doppler Spread

2. 1/Bd TC < Ts

Slow Fadin1. Low Dop

2. 1/Bd T

Signal

BSfreq.BS

BD

Doppler

Signal


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Multicarrier ModulationMulticarrier Modulation

Divide broadband channel into narrowband s

No ISI in subchannels if constant gain in every subchasampling

Orthogonal Frequency Division Multiplexing

Based on the fast Fourier transform

Standardized for DAB, DVB-T, IEEE 802.11a, 802.16

Considered for fourth-generation mobile communicati

ma

gnitude

carrie

channel

Subchannels are 312 kHz wide in 802.11a and Hype


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An OFDM SymbolAn OFDM Symbol

N-pointInverse

FFT

X1X2

x0x2

x3

xN-1XN-1

X0

Nsubsymbolsone

Ncsa

Nsamplesv samples CP: Cyclic Prefix

CP CPs y m b o l i s y m b o l

copy copy

Bandpass transmission allows for complex wa Transmit: y(t) = Re{(I(t)+j Q(t)) exp(j2 fc t)}

= I(t) cos(2 fc t) Q(t) sin(2 fc t)


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Introduction to OFDMIntroduction to OFDM


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P/SQAM

decoder

invertchannel

=frequencydomain

equalizer

S/P

quadratureamplitudemodulation

(QAM)encoder

N-IFFTadd

cyclicprefix

P/S

N-FFT S/Premovecyclicprefix

TRANSMITTER

RECEIVER

Nsubchannels Ncomplex samples

Ncomplex samplesNsubchannels

An OFDM ModemAn OFDM Modem

Bits

00110


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Coded OFDM (COFDM)Coded OFDM (COFDM)

Error correction is necessary in OFDM system

Forward error correction (FEC)

Adds redundancy to data stream

Examples: convolutional codes, block codes

Mitigates the effects of bad channels

Reduces overall throughput according to the coding ra

Automatic repeat request (ARQ)

Adds error detecting ability to data stream

Examples: 16-bit cyclic redundancy code

Used to detect errors in an OFDM symbol

Bad packets are retransmitted (hopefully the channel c

Usually used with FEC

Minus: Ineffective in broadcast systems


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Typical Coded OFDM EncodeTypical Coded OFDM Encode

FEC

Bitwise

Interleaving

Symbol

Mapping

Reed-Solomon and/or convolu

Intersperse coded and uncoded bit

Data bits Parity bits

Rate 1/2

Map bits to symbols


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Typical Coded OFDM DecodeTypical Coded OFDM Decode

Frequency-domain

equalization

Symbol

Demapping

Deinterleaving

Decoding

Symbol demapping Produce soft estimate of each

Improves decoding


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OFDM Mathematics

12

0( )

k

Nj f t

kk

s t X e

==

t

Orthogonality Condition

*

1 2

0

( ). ( ) 0

T

g t g t dt =In our case

2 2

0

. 0p qT

j f t j f te e d t

=

For p q Where fk=k/T

os

os

os


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Transmitted Spectrum


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r

Spectrum of the modulated data symbSpectrum of the modulated data symb

Rectangular Window of

duration T0

Has a sinc-spectrum with

zeros at 1/T0

Other carriers are put in

these zeros

sub-carriers areorthogonal

Magnitude

=

=1

0

)(2

,, )()(N

i

kTtfij

kikBB exkTtwts

Nsub-carriers:

Subcarrier orthogonality must be preserved

Compromised by timing jitter, frequency offset, and fading


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OFDM terminology

Orthogonal carriers referred to as subcarrier

OFDM symbol period {Tos=N x Ts}.

Subcarrier spacing f = 1/Tos.


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OFDM and FFT

Samples of the multicarrier signal can be obthe IFFT of the data symbols - a key issue.

FFT can be used at the receiver to obtain th

No need for N oscillators,filters etc.

Popularity of OFDM is due to the use of IFF

have efficient implementations.


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OFDM Signal

1

,

0

( ) ( (N

n k k os

n k

s t X g t nT

= =

= 2

( )0

kj f t

k

eg t

=

t [ 0,os]

Otherwise

k

o s

kf

T= K=0,......


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By sampling the low pass equivalent signal at

higher than the OFDM symbol rate 1/Tos, OFD

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 k

Nn n k n k

k

F m X e N IDFT X

=

= =


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Interpretation of IFFT&FFTInterpretation of IFFT&FFT

IFFT at the transmitter & FFT at the receiver

Data symbols modulate the spectrum and the time d

symbols are obtained using the IFFT.

Time domain symbols are then sent on the channel.

FFT at the receiver to obtain the data.


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Lecture Two- OfDMI

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