9-mc modulation and ofdm

8/3/2019 9-MC Modulation and OFDM

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9. Multi Carrier Modulation and OFDM


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ifsymbol duration >>time spreadthen there is almost no InterSymbol Interference (ISI).

1 0 time

channel

1 0

phase still recognizable

ST

Problem with this: Low Data Rate!!!

Single Carrier Modulation in Flat Fading Channels


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this corresponds to Flat Fading

Frequency Frequency

channel

ST/1

Flat Freq. Response

Frequency

in the Frequency Domain


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ifsymbol duration ~time spreadthen there is considerable InterSymbol Interference (ISI).

1 0

time

channel

? ?

phase not recognizable

Single Carrier Modulation in Frequency Selective Channels


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In MC modulation each MC symbol is defined on a time interval and it contains a

block of data

gT bT

Symbol

T

data interval

t

guard interval

. .time

OFDM Symbol

data datadatadata

data

MAXgT X" MAX channel time spreadwith

Structure of Multi Carrier Modulation


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. .

the guardtimeislong

enough,so the multipath inoneblockdoesnotaffect the

nextblock

Data BlockData Block

TX RX

We leave a guard time

between blocks to allowmultipath

gT

Guard Time

bT

SymbolT

data+guard

Guard Time

. .

_

TX

RX

NO Inter Block Interference!

gT


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!

{!

(!2

20

2)(

FN

FN

k

k

k

tFkj

kectxT

data!kc

offsetfrequencysubcarrier!(Fk

SymbolTtee0

Baseband Complex Signal:

MC Signal

Transmitted Signal:

_ a)(Re)( 2 txets tFj CT!frequencycarrierCF


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Orthogonal Subcarriers and OFDM

gT

bT data intervalt

guard interval

bTF

1

!(

{

!!!

(

N

NNN

k

kdte

T

dtee

T

bb

k

Tt

t

Ftkj

b

Tt

t

tFjtFj

b if0

if111 0

0

0

0

)(222 TTT

Choose:

Orthogonality:

FCF

F(

FkFF Ck (!

FN F(


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Let

be the sampling frequency;

be the number of data samples in each symbol;

the subcarriers spacing

Then:

SF

NFTNF SS //1 !!(

!

!

!!

( 2

2

)(2

2

)(2 211)(

F

F

N

F

F

sFF

N

Nk

Lnjk

k

N

Nk

Lnkj

kS ec

N

ec

N

nTxTT 1,..,0 ! NLn

FNN"

with the guard time.Sg TLT v!

OFDM symbols in discrete time


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Summary OFDM Symbol

SS

FT /1!

t0 gT

L

bT

FNN"

Sampling Interval

guard data

TIME:

NFF S /!(

F

N

FN SF

2

Freq spacing

FREQUENCY:

2/SF2/SF

N

FN SF

2

0

# samples

# subcarriers


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OFDM Symbol and FFT

_ a][][1

11

1][

1

0

1

2

)(2

1

2

2

2

22

2

kXIFFTekXN

ec

N

ec

N

ecN

Lnx

N

k

njk

Nk

nkNj

k

N

k

njk

k

N

Nk

njkk

N

F

N

F

N

F

F

N

!

!

!

!

!!

!

!

T

TT

T

otherwise,0][

2/,...,1,][

2/,...,1,][

!

!!

!!

kX

NkckNX

NkckX

Fk

Fk

Where:positive subcarriers

negative subcarriers

unused subcarriers


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OFDM Demodulator

_ a

21

0

21

0

[ ] [ ]* [ ]1

[ ]* [ ]

1 [ ] [ ] [ ] [ ]

N j knN

k

N j knN

k

y n L h n x n L

h n X k eN

H kX k e IFFT H kX k

N

T

T

!

!

!

!

! !

_ a]1[],...,[][][ ! NLyLyFFTkXkH

with_ a[ ] [0],..., [ 1],0,..., 0H k FFT h h L! 1,...,0 ! Nk

See each block:

n

0 1L 1 NL

No InterBlock Interference

][ny


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Overall Structure of OFDM Comms System

-

!

]1[

]1[]0[

NX

XX

X/

IFFT +CP P/S

][nh

FFT -CP S/P

N NLN

LN

LN

LN NN

W

NXNH

XH

XH

Y

-

!

]1[]1[

]1[]1[

]0[]0[

/

][nw


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OFDM as Parallel Flat Fading Channels

Significance: a Freq. Selective Channel becomes NFlat Fading

Channels

OFDM

Mod

OFDM

Demod/ /

)(tx ( )y t

Frequency

Selective

channel

]0[mX

[ 1]mX N/

[0]mY

[ 1]mY N/

/

]0[mX [0]mY

[ 1]mY N

( )w t

]0[H

[0]m

W

[ 1]mX N [ 1]H N

[ 1]m

W N/ /

NFlat

Fading

Channels

( )h t


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OFDM Parameters

Summarize basic OFDM Parameters:

sampling rate in Hz

N length of Data Field in number of samples

L length of Cyclic Prefix in number of samples

total number of Data Subcarriers

SF

F

N Ne

N

/St T

data

Ltime

SFF/0

data

/F

N N

frequency

guard guard guard


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IEEE 802.11a:

Frequency Bands: 5.150-5.350 GHz and 5.725-5.825 GHz (12 channels)

Modulation OFDM

Range: 100m

IEEE 802.11g

Frequency Bands: 2.412-2.472GHz

Modulation: OFDM

Range: 300m


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Channel Parameters: FCC

Example: the Unlicensed Band 5GHz U-NII (Unlicensed National

Information Infrastructure)

4 channels in the range 5.725-5.825GHz

8 channels in the range 5.15-5.35GHz

)(MHzF5150 5350

MHz30 MHz3020MHz

5180 5200

.

5300 5320

CF


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Channel Parameters: Example IEEE802.11

In terms of a Transmitter Spectrum Mask (Sec. 17.3.9.2 inIEEE Std 802.11a-1999)

CF99 1111 2020 3030

dB0

20dB

28dB

40dB

)(MHzF

Typical Signal

Spectrum

Typical BW~16 MHz


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In either case:

MHzFS 20! Sampling frequency

64!N

16!L

FFT size

Cyclic Prefix

64!N16!N

64 / 20 3.2 secbT Q! !16 / 20 0.8 sec

gT Q! !

DATACP


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Sub-carriers: (48 data + 4 pilots) + (12 nulls) = 64

Pilots at: -21, -7, 7, 21

01

26

38

63

/

/

/

NULL

NULL

0

63

/

/

/

/

Frequency Time

1c

26c

26c

1c

0x

63x

IFFT

52!FN 64!N


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k2638 64 26

20 /64 312.5 F MHz kHz( ! !

( ) F MHz

8.1258.125

CARRIERF

)(MHzF

MHz25.16

DATA

Frequencies:

sTMHz /120 !

163 Subcarriersindex

10CARRIER

F 10CARRIERF


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Overall Implementation (IEEE 802.11a with 16QAM).

1. Map encoded data into blocks of192bits and 48 symbols:

data EncodeInterleave

010011010101

Buffer

(192 bits)

1110

0111

1000

1101

4x48=192 bits

Map to

16QAM

48

4

+1+j3

-1+j

+3-j3

+1-j

a"

48


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Overall Implementation (IEEE 802.11a with 16QAM).

2. Map each block of48 symbols into 64 samples

[ ]mX k

+1+j3

-3-j

+3-j3

+1-j

/

01

2627

6427 /

/

6426 /

[0]mx

IFFT

0

12

63

62

time domainfrequency domain

null

null

24 data

2 pilots

24 data

2 pilots

/

..

k1 2626

641

1

[ ]m

a " [ ]m

x n

1:48!" 0:63k ! 0:63n !

[1]mx

[62]mx[63]mx


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Constraints on OFDM Symbol Duration:

to minimize CP overhead

1 /MAXMAX g b D

T T FX

sec10 6 sec10 3 roughly!!!

Frequency Spread

Time Spread

),( FSXF

X

kHzFMAXD

indoorsec5010

outdoorsec101

nMAX

MAX

}

}

X

QX

for channel Time Invariant

Channel Parameters: Physical


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Summary of OFDM and Channel Parameters

Channel:

1. Max Time S pread sec

2. Doppler S pread Hz

3. Bandwidth Hz

4. Channel S pacing Hz

OFDM (design parameters):

1. Sampling Frequency

2. Cyclic Prefix

3. FFT size (power of2)

4. Number of Carriers

MAXX

MAXDF

BW

SF

SF

integerMAX S L FXu

4 / integerMAXS D

L N F F e

? A/ integerF S N N BW F ! v


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Channel:

1. Max Time Spread

2. Doppler Spread

3. Bandwidth

4. Channel Spacing

OFDM (design parameters):

1. Sampling Frequency

2. Cyclic Prefix

3. FFT size (power of2)

4. Number of Carriers

0.5 secMAXX Q!50

MAXDF Hz!

16BW MHz!

20SF MHz!

20SF MHz!

16 0.5 20 10L ! " v !664 20 10 / 50 integerN! v

? A52 64 16 / 20 integerFN ! ! v

Example: IEEE802.11a


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According to the applications, we define three AreaNetworks:

Personal Area Network (PAN), for communications within a few meters. This is the typicalBluetooth or Zigbee application between between personal devices such as your cell phone,

desktop, earpiece and so on;

Local Area Network (LAN), for communications up 300 meters. Access points at the

airport, coffee shops, wireless networking at home. Typical standard is IEEE802.11 (WiFi) or

HyperLan in Europe. It is implemented by access points, but it does not support mobility;

Wide Area Network (WAN), for cellular communications, implemented by towers. Mobilityis fully supported, so you can move from one cell to the next without interruption. Currently it

is implemented by Spread Spectrum Technology via CDMA, CDMA-2000,TD-SCDMA,

EDGE and so on. The current technology, 3G, supports voice and data on separate networks.

For(not so) future developments, 4G technology will be supporting both data and voice on the

same network and the standard IEEE802.16 (WiMax) seems to be very likely

Applications: various Area Networks


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9-mc modulation and ofdm

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