9. Multi Carrier Modulation and OFDM

Transmission of Data Through Frequency Selective Time Varying Channels

We have seen a wireless channel is characterized by time spread and frequency spread.

Time Spread

Frequency Spread ),( FS

F

MEAN

MAXDF

RMSRMS

• if symbol duration >> time spread then there is almost no Inter Symbol Interference (ISI).

1 0 time

channel

1 0phase still recognizable

ST

Problem with this: Low Data Rate!!!

Single Carrier Modulation in Flat Fading Channels

• this corresponds to Flat Fading

Frequency Frequencychannel

ST/1Flat Freq. Response

Frequency

… in the Frequency Domain

• if symbol duration ~ time spread then there is considerable Inter Symbol Interference (ISI).

1 0time

channel

? ?phase not recognizable

Single Carrier Modulation in Frequency Selective Channels

One Solution: we need equalization

channel equalizer

1 0time

1 0time

Channel and Equalizer

Problems with equalization:• it might require training data (thus loss of bandwidth)• if blind, it can be expensive in terms computational effort• always a problem when the channel is time varying

• let symbol duration >> time spread so there is almost no Inter Symbol Interference (ISI);

• send a block of data using a number of carriers (Multi Carrier)

1 0

time channel

time

time

0

0

1

1

“symbol” “symbol”

The Multi Carrier Approach

Compare Single Carrier and Multi Carrier Modulation

Frequency Frequency

channel

0 1 0 1 1 1

Block of symbols

subcarriers

Each subcarrier sees a Flat Fading

Channel: Easy Demod

MC

Frequency

1

One symbol

Frequency

Flat Fading Channel: Easy Demod

SC

101 1

0 1 0 1 1 1

In MC modulation each “MC symbol” is defined on a time interval and it contains a block of data

gT bT

SymbolT

data interval

t

guard interval

time

OFDM Symbol

data datadatadata

data

MAXgT MAX channel time spreadwith

Structure of Multi Carrier Modulation

the “guard time” is long enough, so the multipath in one block does not affect the next block

Data BlockData Block

TX RX

We leave a “guard time” between blocks to allow multipath

gTGuard Time

bT

SymbolTdata+guard

Guard Time

TX

RX

NO Inter Block Interference!

gT

2

20

2)(FN

FN

k

kk

tFkjkectx

datakc

offsetfrequency subcarrierFk

SymbolTt 0

Baseband Complex Signal:

MC Signal

Transmitted Signal:

)(Re)( 2 txets tFj Cfrequencycarrier CF

“Orthogonal” Subcarriers and OFDM

gT bT data intervalt

guard interval

bTF 1

kk

dteT

dteeT

bb

k

Tt

t

Ftkj

b

Tt

t

tFjtFj

b if 0 if 111 0

0

0

0

)(222

Choose:

Orthogonality:

FCF

F

FkFF Ck

FN F

still orthogonal at the receiver!!!

bg

g

k

TT

T

tFj

bkk dtety

TFHc 2)(1

)(1

Orthogonality at the Receiver

)(tht0

0

transient response

bg TT

bgg TTtT

tFj ke 2

gT

bg TT

Transmitted subcarrier Channel

(LTI)

Received subcarrier

k

tFjk

kectx 2)( k

tFjkk

keFHcty 2)()(

bg TTt 0

steady state response

)()( thFTFH

t

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

Lnjkk

N

Nk

LnkjkS ec

Nec

NnTx

1,..,0 NLn

FNN

with the guard time.Sg TLT

OFDM symbols in discrete time

Summary OFDM Symbol

SS FT /1t0 gT

L

bT

FNN

Sampling Interval

guard data

TIME:

NFF S /

FNFN SF

2

Freq spacing

FREQUENCY:2/SF2/SF

NFN SF

2

0

# samples# subcarriers

OFDM Symbol and FFT

][][1

11

1][

1

0

1

2

)(2

1

2

2

2

22

2

kXIFFTekXN

ecN

ecN

ecN

Lnx

N

k

njk

Nk

nkNjk

N

k

njkk

N

Nk

njkk

N

F

N

F

N

F

F

N

otherwise ,0][2/,...,1 ,][

2/,...,1 ,][

kXNkckNX

NkckX

Fk

Fk

Where:positive subcarriers

negative subcarriers

unused subcarriers

][][ nNxnx

]1[]1[...

]1[]1[][]0[

NLxLx

NxxNxx

Guard Time with Cyclic Prefix (CP)

1,...,0],[]1[],...,[ NkkXIFFTNLxLx

N

0 L 1 NL

CP from the periodicity

IFFT{ X }CP

OFDM Demodulator

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 k X k e IFFT H k X kN

]1[],...,[][][ NLyLyFFTkXkH

with [ ] [0],..., [ 1],0,...,0H k FFT h h L 1,...,0 Nk

See each block:

n0 1L 1 NL

No Inter Block Interference

][ny

Overall Structure of OFDM Comms System

]1[

]1[]0[

NX

XX

X

IFFT +CP P/S

][nh

FFT -CP S/P

N N LN LN

LN

LN NN

W

NXNH

XHXH

Y

]1[]1[

]1[]1[]0[]0[

][nw

To recover the transmitted signal you need a very simple one gain equalization:

][][][][ kWkXkHkY

received transm. noise

channel

Use simple Wiener Filter:

][][

][][ˆ22

*

kYkH

kHkXW

Simple One Gain Equalization

OFDM as Parallel Flat Fading Channels

Significance: a Freq. Selective Channel becomes N Flat 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]mW

[ 1]mX N [ 1]H N

[ 1]mW N

N Flat Fading

Channels

( )h t

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

FN N

N/ St T

data

Ltime

SFF /0

data

/FN Nfrequency

guard guard guard

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

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

Channel Parameters: Example IEEE802.11

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

CF 99 1111 2020 3030

dB0

20dB

28dB

40dB

)(MHzF

Typical Signal Spectrum

Typical BW~16 MHz

In either case:

MHzFS 20 Sampling frequency

64N16L

FFT sizeCyclic Prefix

64N16N64 / 20 3.2 secbT

16 / 20 0.8 secgT

DATACP

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

52FN 64N

k2638 64 26

20 / 64 312.5F MHz kHz

( )F MHz

8.1258.125

CARRIERF)(MHzF

MHz25.16

DATA

Frequencies:

sTMHz /120

163 Subcarriers index

10CARRIERF 10CARRIERF

Time Block:

sec2.3 FFTT

sec105064/ 9 FFTs TT

sec8.0 GT

sec0.4 FRAMET

time

Overall Implementation (IEEE 802.11a with 16QAM).

1. Map encoded data into blocks of 192 bits and 48 symbols:

data Encode Interleave

…010011010101…

Buffer (192 bits)

111001111000

…

1101

4x48=192 bits

Map to 16QAM

…48

4

+1+j3-1+j

+3-j3…

+1-j

a

48

Overall Implementation (IEEE 802.11a with 16QAM).

2. Map each block of 48 symbols into 64 samples

[ ]mX k

+1+j3…

-3-j+3-j3

…+1-j

01

2627

6427

6426

[0]mx

IFFT

012

6362

time domainfrequency domainnull

null

24 data 2 pilots

24 data 2 pilots

k1 2626

641

1

[ ]ma [ ]mx n1: 48 0 : 63k 0 : 63n

[1]mx

[62]mx[63]mx

Constraints on OFDM Symbol Duration:

to minimize CP overhead

1/MAXMAX g b DT T F

sec10 6 sec10 3 roughly!!!

Frequency Spread

Time Spread

),( FS F

kHzF

MAXD

indoor sec5010outdoor sec101

nMAX

MAX

for channel Time Invariant

Channel Parameters: Physical

Summary of OFDM and Channel Parameters

Channel:

1. Max Time Spread sec

2. Doppler Spread Hz

3. Bandwidth Hz

4. Channel Spacing Hz

OFDM (design parameters):

1. Sampling Frequency

2. Cyclic Prefix

3. FFT size (power of 2)

4. Number of Carriers

MAX

MAXDF

BW

SF

SF

integerMAX SL F

4 / integerMAXS DL N F F

/ integerF SN N BW F

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 of 2)

4. Number of Carriers

0.5 secMAX

50MAXDF Hz

16BW MHz

20SF MHz

20SF MHz

16 0.5 20 10L

664 20 10 / 50 integerN

52 64 16 / 20 integerFN

Example: IEEE802.11a

According to the applications, we define three “Area Networks”:

• Personal Area Network (PAN), for communications within a few meters. This is the typical Bluetooth 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. Mobility is 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

More Applications

1. WLAN (Wireless Local Area Network) standards and WiFi. In particular:• IEEE 802.11a in Europe and North America• HiperLAN /2 (High Performance LAN type 2) in Europe and North America• MMAC (Mobile Multimedia Access Communication) in Japan

2. WMAN (Wireless Metropolitan Network) and WiMax• IEEE 802.16

3. Digital Broadcasting• Digital Audio and Video Broadcasting (DAB, DVB) in Europe

4. Ultra Wide Band (UWB) Modulation• a very large bandwidth for a very short time.

5. Proposed for IEEE 802.20 (to come) for high mobility communications (cars, trains …)