imt advanced

Core Technologies for 4G: OFDM

Prof. Chung G. KangKOREA University

[email protected]

4G Mobile (IMT Advanced) System and Applications

OFDM: Overview

• High-speed wireless transmission technology

• Implemented as a useful means of multiple access to support the multi-user communication, as OFDMA(Orthogonal Frequency Division Multiple Access)

• Adopted for the candidate radio interface technologiesfor IMT-Advanced in ITU-R

• Rayleigh Fading Channel Model

• Time Dispersion due to Multi-path Fading

MOBILE Moving directionRoad

Buildings

i

2 ( cos )

1( ) Re ( ) c d i i

nj f f t

R ii

s t A s t e

cd fcvf where

RMS Delay Spread �(t)

t

t

( )t ( )t

Ideal Channel

Non-ideal Channel

Broadband Wireless Channel (1)

• Ideal Channel vs. Non-ideal Channel

+( )s t ( )s t

( )n t

( )h t

- Ideal channel

( )h t | ( ) |H f

- Non-ideal channel

ft

( )h t | ( ) |H f

ft

( )t ( )t

( )t


• Delay Spread and Inter-Symbol Interference (ISI)

Symbol 1

Ts

�s < Ts

0 �1 �2 �3

Symbol 1

�1

�2

�3

Symbol 2

�s >> Ts

Ts 0 �1 �2 �3

�1

�2

�3

( ) 0 1 1 2 2 3 3, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )h t t t t t= + - + - + -% % % % %t a d t a d t t a d t t a d t t


Higher-speed transmission suffers from the more multipath fading (more ISI)!

• Delay Spread and Frequency Selectivity

( )h t | ( ) |H f

ft

1( )t ( )t

( )h t

t

1( )t ( )t 2( )t

| ( ) |H f

f

Bc

Bc

~ �s

~ �s

Bs

- Frequency flat

- Frequency selective

Bs

Bs : Signal BandwidthBc: Coherence Bandwidth


Ts

Ts

( ) 1 2 2, ( ) ( ) ( ) ( )h t t tt a d t a d t t= + -% % %

• General Fading Channel


Channel varies with both frequency and time, i.e., frequency selectivity varies with the times, depending on the mobile speed

Equalizer

Channel Equalization

0 T

( )h t

{ }nx{ }ny

0h 1h

2 0 2 1 1

3 0 3 1 2

y h x h x ny h x h x n

• Optimum Channel Equalization

- Maximum likelihood sequence equalization (MLSE)

+

n

2 3 0 1

2 3

Given { , } and { , }, determine { , }

y y h hx x

2 3

2* * 22 3 2 0 2 1 1 3 0 3 1 2( , )

ˆ ˆ( , ) min ( ) { ( )}x x S

x x y h x h x y h x h x

- Illustrative example

{1, 1}nx

ˆ{ }nx

where {(1,1), (1, 1), ( 1,1), ( 1, 1)}S 2| | 2 4S

In general, | | LS M where M is the number of symbols andL is the number of multi-paths

Too complex!

Discrete Fourier Transform (DFT)

2( ) ( ) j ftX f x t e dt

( )X f( )x t

( )n s

nX f X fT

( )X fnx

sT1/ sT

2

0

kN j nN

k nn

X x e

nx

N

N

kX

f

f

k

DFT:

Serialto

ParallelConv.

x

x

x

+Modulator

RF

• Transmitter

sT

0cos 2 f t

1cos 2 f t

1cos 2 Nf t

OFDM: Basic Concept (1)

sN T

1/s sR T

sN T

{ }nx

0x

1x

1Nx

sN T

( )b t ( )s t

Orthogonality:

0

cos 2 cos 2 0sNT

i jf t f t dt

for all i j

1

0( ) cos 2

N

n nn

s t x f t

OFDM symbol

• Receiver


( )s t DownConv. x

0cos 2 f tsN T

x

x

1cos 2 f t

1cos 2 Nf t

1x

1Nx

Serialto

ParallelConv.

De-modulator

0x

0

0 0

1 1

2 ( ) cos(2 )2 cos(2 ) cos(2 )

2 cos(2 ) cos(2 ) 2 cos(2 ) cos(2 )

sNT

n

n

n n n

N N n

n

s t f t dtx f t f t

x f t f tx f t f t

x

Too many carriers….How to implement this?

0f

• OFDM = N Parallel Narrowband Channels

0x


1f 3f2f

1x 2x


0

• Time Domain: OFDM Symbol

• Frequency Domain: Subcarriers( ) cos(2 ) (0, )n n ns t x f t rect T

( ) ( )*sinc( ) sinc( ( ))

n n n

n n

S f x f f fTx f f

(0, )rect T

T

sT N T

0x 1x 1Nx

0 t T 1cos(2 )f t

2cos(2 )f t

3cos(2 )f t

OFDM: Implementation (1)• Block Diagram

12 ( / )

0

Nj k N n

n kk

x X e

1 2 ( / )0

1 2 ( / )0

N j k N nk nk

N j k N nn kk

Y y e

a x e aX

{ }kX { }kY0x

1x

1Nx

- Illustration: single-path channelˆ/k kX Y a

• Block Diagram

kX kH kY

?k k kY H X

{ }kX { }kY0x

1x

1Nx

- Illustration: multi-path channel

OFDM: Implementation (2)

Cyclic Prefix (1)

1

0

2exp2k n

nH h jk n

0

1

20

HH

2

0

2exp3k n

nX x jk n

0

1

2

300

XXX

2

0

2exp3k n

n

Y y jk n

0

1

2

5

1 2 3

1- 2 3

Y

Y

Y

k k kY H X

• Effect of Multi-path Channel- Illustrating example

1

0

2exp2k n

nH h jk n

0

1

20

HH

2

0

2exp3k n

n

X x jk n

2

0 32exp][

nn njkykY

0

1

2

600

YYY

, 1,2 k k kY H X k

0

1

2

300

XXX

Cyclic Prefix (2)• Effect of Multi-path Channel

- Illustrating example

Cyclic prefix

• Guard Interval vs. Cyclic Prefix- Inter-symbol Interference (ISI) & guard Interval

- Inter-carrier Interference & cyclic prefix

Zero-valued guard interval

FFT intervalGuardinterval

Cyclic prefix

Guardinterval

FFT interval

No ICI and no ISI

No ISI but ICI

Guard interval

Cyclic Prefix (3)

subTGT

sym sub GT T T

No guard interval

Orthogonality maintained by inserting CP

ISI can be avoided by the guard

interval

Cyclic Prefix (4)• Effect of CP: Illustration

FFT period FFT periodGI

Subcarrier #1

Subcarrier #2

CP

DelayedSubcarrier #2

f

t

Effecti

ve BWFFT si

ze

Guard interval

TG

Effectivesymbol duration

Tsub

copy

1 1 0 1 2 1 1{ , , , , , , , , , }N L N N N L N L N NX X X X X X X X X X

0x1x

1Nx

OFDM: Overall Picture• OFDM Symbol in 3D

OFDM Symbol

OFDM: Performance• Effect of Delay Spread

(b) Delay exceeds guard time by 3% of the FFT interval.(c) Delay exceeds guard time by 10% of the FFT interval.

- What if delay exceeds the guard time (CP)?

Windowing• Power Spectrum Density

- The side-lobe of spectrum decreases with the

larger number of subcarriers

- The out-of-band spectrum decreases slowly,

due to a sinc function

- Raised cosine windowing

Guard Band Guard BandData Subcarrier BandGuard Band Guard BandData Subcarrier Band

- Adjacent Channel Interference (ACI)

- Guard Band

Guard Band & ACI• Illustrative Example: N = 1024 (IEEE 802.16e)

Channel 1 Channel 2 Channel 3

Adjacent channel interference

Channel 2

UnusedSubcarriers for

guard band

SNR

Coded OFDM

- Some subcarriers suffered by frequency selective fading must be protected by forward error correction (FEC) coding

• Why Coded OFDM?

OFDM: Block Diagram• Overall Block Diagram

Water-filling (1)

{ }kX { }kY0x

1x

1Nx

• System Model

, 1, 2, , 1n n n ny h x n N

- The frequency selective channel transformed to a parallel channel

• AWGN Capacity

21

0 0

| |log 1

Nn

n

P hC

N

- Total capacity = sum capacity of each channel

where 2{| | }, 0,1,2, , 1nP E x n N

What if we allocate the different power to each

subcarrier?

Water-filling (2)• Power Allocation Problem for a Parallel Channel

- Assume that each subcarrier is allocated with power Pn.

- Problem statement

- Optimal power allocation:

where the Lagrange multiplier � is chosen such that the power constraint is

met:

0 1

21

,..., 0 0

m ax lo g 1 ,c

cN c

Nn n

N P P n

P hC

N

1,...,0 ,0 ,1

0

cnc

N

nn NnPPNP

c

2

0*~

1

n

nh

NP

.~1 1 1

02

0 Ph

NN

cN

nnc

subject to

Water-filling (3)• Water-filling Interpretation

- If P units of water per sub-carrier are filled into the vessel, the depth of the water at subcarrier n is the power allocated to that sub-carrier

Height of the water surface

- Optimal power allocation:

The better a channel, the more power!

Inverse ofChannel gain

2

0*~

1

n

nh

NP

• Illustrative Example

x x

Rb bps/Wb Hz

DigitalModulation

Base Station

x x

DigitalDemodulation

Information bitsfor User 1

Rc >> Rb bps

x

+C1

C2

Rb bps/Wb Hz

User 1

User 2

Multiple Access: CDMA (1)

C1

• Processing Gain & Interference

0 b b

required required

EC RI N W

1b

b

RT

1

c

WT

Processing Gain = b

b c

W TR T

0

6

10 3

(dB) (dB)

1.2288 10 6 10 log 6 21.1 15.1dB9.6 10

b

required brequired

EC WI N R

- Example: 09,600Hz; 1.2288M Hz; / 6dBb b requiredR W E N


• Processing Gain & Data Rate- Processing gain varies with the data rate for the fixed chip rate system

- Example: Rc = 1.2288Mcps

The higher the data rate is, the lower the processing gain is! To maintain the processing gain, more bandwidth is required for higher data rate

Rb = 9.6kbps PG = 128

Rb = 4.8kbps PG = 256

- Example: For W = 20Mbps with PG = 128,Rb = W/PG ~ 150kbps The maximum possible data is limited to

150kbps with CDMA!

Rc

Rb

2Rb


• Illustrative ExampleChip

Serial toParallel

Converter

X

X

X

+Modulator RF

sT

0cos 2 f t

1cos 2 f t

1cos 2 Nf t

sNT

sNT

sNT

• Orthogonal Frequency Division Multiplexing (OFDM)

X

X

X

+ RF)(ts

0cos 2 f t

1cos 2 f t

1cos 2 Nf t

sNT• Orthogonal Frequency Division Multiple Access (OFDMA)

sNT

User 0

User 1

User N-1

Modulator

Modulator

Modulator

Multiple Access: OFDMA (1)

0x

1x

1Nx

( )s t

0x

1x

1Nx

User #2

User #1

• OFDMA Concept Multiuser OFDM (OFDM + FDMA)- Subchannel: a set of subcarrier as a basic resource allocation unit

- Why OFDMA?


• Multiple Access with OFDM- Resource units: Subchannels or Resource Block

Frequency

Time OFDM symbol

Subchannel


Subframe

SubcarrierUser 1

User 2

User 3 User 4

By assigning different time/frequency slots to users, they can be kept orthogonal, no matter how much the delay spread is….

Cellular OFDMA (1)

0

max max 0 0

2max

( )( ) ( )( ) ( )( )u u k k

k k kk

P dN N d dC

PNI N d p ddN

• Co-channel Interference in OFDMA Network

max

uNpN

maxN

Cell F0 Cell F1

Fully loaded Loading factor = p

uN

0

bEC RI N W

cf) CDMA 1/Processing Gain

0( )d

1( )d

2( )d

- C/I ratio for subcarrier

P

-500 0 500-800

-600

-400

-200

0

200

400

600

800

in meter

in m

eter

10

20

30

40

50

60

- Downlink

• Subcarrier Allocation for Interference Averaging- Example

x1x2

X1 X2Withoutfrequency hopping

Withfrequency hopping

- Interference averaging with frequency hopping interference diversity

Cellular OFDMA (2)

• Hopping Pattern for Subcarrier Allocation- To design the hopping patterns with a period of Nc OFDM symbols

that are as apart as possible for neighbor BSs (Nc: prime number) Every user hops over all the sub-carriers in each period frequency diversity Each user occupies different sub-carriers in any OFDM symbol time

- Latin square Nc x Nc matrix

Example: Nc = 5

Cellular OFDMA (3)

• Orthogonal Latin Squares- Latin squares that gives exactly one time/sub-carrier collision for every pair

of virtual channels of two base stations

Ra and Rb are orthogonal if a is not equal to b

- Generation rule:

Example: a = 2 & Nc = 5

• Inter-BS Synchronization- OFDM symbol-level synchronization required

Cellular OFDMA (4)

• OFDM Parameters: Numerology (TDD)Nominal Channel Bandwidth (W) 8.75MHz

Over-sampling Factor (n) 8/7Sampling Frequency (Fs) 10 MHz

FFT Size (Nfft) 1,024Sub-Carrier Spacing (�f) 9.765625kHzUseful Symbol Time (Tb ) 102.4 µs

Cyclic Prefix (CP)Tg=1/8 Tb

Symbol Time (Ts ) 115.2 µs

TDDNumber of OFDM

symbols per Frame 42

TTG + RTG (µs) 161.6

Number of Guard Sub-Carriers

Left 80

Right 79

Number of Used Sub-Carriers 865

IEEE 802.16e: PHY Parameters

Tg Tb

Ts

sF nW

1/bT f

/s fftf F N

1/ 9.765625 kHzbf T

2 8.75MHz 9.765625kHz 896mfftN 1024fftN

(9.765625)(1024) 10MHzs fftF f N

/ 10 / 8.75 8/ 7sn F W

102.4 μsbT

• TDD Frame Structure

115.2us

IEEE 802.16e: Frame Structure

24 symbols 12 symbols

• Downlink Syntax Value Notes

Total # of subcarriers 768 768 = 24 bands * 4 bins/band * 8 subcarriers/bin

# of frames / sec 200 1 / 5 ms/frame = 200 (frames/sec)

OFDM symbols / frame 42 42 symbols = 27 DL symbols + 15 UL symbols

OFDM symbol rate 5400 200 (frames/sec) * 27 (symbols/frame) = 5400 (symbols/sec)

Data subcarrier rate 4.1472 5400 (symbols/sec)* 768 (subcarriers/symbol) = 4.1472 (Msubcarriers/sec)

Max. bits/subcarrierMin. bits/subcarrier

55/36

MAX: R = 5/6 coding & 64 QAM 5/6 * log2(64) = 5 (bits/subcarrier)MIN: R = 1/12 coding & QPSK 1/12 * log2(4) = 5/36 (bits/subcarrier)

Max. data rate (Mbps)Min. data rate (Mbps)

20.7360.576

4.1472 (Msubcarriers/sec) * 5 (bits/subcarrier) = 20.736 (Mbps)4.1472 (Msubcarriers/sec) * 5/36 (bits/subcarrier) = 576 (kbps)

IEEE 802.16e: Data Rate

• Uplink Syntax Value Notes

OFDM symbol rate 3000 200 (frames/sec) * 15 (symbols/frame) = 3000 (symbols/sec)

Data subcarrier rate 2.3040 3000 (symbols/sec)* 768 (subcarriers/symbol) = 2.304 (Msubcarriers/sec)

Max. bits/subcarrierMin. bits/subcarrier

10/35/36

MAX: R = 5/6 coding & 16 QAM 5/6 * log2(16) = 10/3 (bits/subcarrier)MIN: R = 1/12 coding & QPSK 1/12 * log2(4) = 5/36 (bits/subcarrier)

Max. data rate (Mbps)Min. data rate (Mbps)

7.680.320

2.304 (Msubcarriers/sec) * 10/3 (bits/subcarrier) = 7.68 (Mbps)2.304 (Msubcarriers/sec) * 5/36 = 320 (kbps)

IEEE 802.16m (1)• Basic Frame Structure

- The number of OFDMA symbols varies with the length of CP.

- Type-1, type-2, type-3, type-4 subframes

IEEE 802.16m (2)• Frame Structure with Type-1 Subframe (FDD)

- 5MHz, 10MHz, 20MHz bandwidth

IEEE 802.16m (3)• Frame Structure with Type-1 Subframe (TDD)

• OFDM Parameters: Numerology (FDD)Nominal Channel Bandwidth (MHz) 5 7 8.75 10 20

Over-sampling Factor 28/25 8/7 8/7 28/25 28/25Sampling Frequency (MHz) 5.6 8 10 11.2 22.4

FFT Size 512 1024 1024 1024 2048Sub-Carrier Spacing (kHz) 10.937500 7.812500 9.765625 10.937500 10.937500Useful Symbol Time Tu (µs) 91.429 128 102.4 91.429 91.429

Cyclic Prefix (CP)Tg=1/8 Tu

Symbol Time Ts (µs) 102.857 144 115.2 102.857 102.857

FDDNumber of OFDM

symbols per Frame 48 34 43 48 48

Idle time (µs) 62.857 104 46.40 62.857 62.857


Symbol Time Ts (µs) 97.143 136 108.8 97.143 97.143

FDDNumber of OFDM


Idle time (µs) 45.71 104 104 45.71 45.71


Symbol Time Ts (µs) 114.286 160 128 114.286 114.286

FDDNumber of OFDM


Idle time (µs) 85.694 40 8 85.694 85.694


Left 40 80 80 80 160

Right 39 79 79 79 159

Number of Used Sub-Carriers 433 865 865 865 1729Number of Physical Resource Unit (18x6)

in a type-1 sub-frame 24 48 48 48 96

IEEE 802.16m (4)

• OFDM Parameters: Numerology (TDD)Nominal Channel Bandwidth (MHz) 5 7 8.75 10 20

Over-sampling Factor 28/25 8/7 8/7 28/25 28/25Sampling Frequency (MHz) 5.6 8 10 11.2 22.4

FFT Size 512 1024 1024 1024 2048Sub-Carrier Spacing (kHz) 10.937500 7.812500 9.765625 10.937500 10.937500Useful Symbol Time Tu (µs) 91.429 128 102.4 91.429 91.429


Symbol Time Ts (µs) 102.857 144 115.2 102.857 102.857

TDDNumber of OFDM


TTG + RTG (µs) 165.714 248 161.6 165.714 165.714


Symbol Time Ts (µs) 97.143 136 108.8 97.143 97.143

TDDNumber of OFDM


TTG + RTG (µs) 142.853 240 212.8 142.853 142.853


Symbol Time Ts (µs) 114.286 160 128 114.286 114.286

TDDNumber of OFDM


TTG + RTG (µs) 199.98 200 136 199.98 199.98


Left 40 80 80 80 160Right 39 79 79 79 159

Number of Used Sub-Carriers 433 865 865 865 1729Number of Physical Resource Units (18x6)

in a type-1 sub-frame 24 48 48 48 96

IEEE 802.16m (5)

• Frame Structure

- FDD

- TDD

3GPP LTE (1)

Subframe #0

Dw

PTS Subframe

#2Subframe

#3Subframe

#4Subframe

#5Subframe

#7Subframe

#8Subframe

#9GP

Uw

PTS

Dw

PTS

GP

Uw

PTS

Subframe #0

Dw

PTS Subframe

#2Subframe

#3Subframe

#4Subframe

#5Subframe

#7Subframe

#8Subframe

#9GP

Uw

PTS Subframe

#6

One radio frame (10 ms)

10 ms switch-point periodicty

5 ms switch-pointperiodicty

: DL subframe : UL subframe

Dw

PTS

GP

Uw

PTS : Special subframe

Configuration

0123455

Switch-point periodicity

5 ms5 ms5 ms

10 ms10 ms10 ms10 ms

Subframe number0 1 2 3 4 5 6 7 8 9DDDDDDD

SSSSSSS

UUUUUUU

UUDUUDU

UDDUDDU

DDDDDDD

SSSDDDS

UUUDDDU

UUDDDDU

UDDDDDD

Uplink-downlink allocations

• Periodic Switch-Point Operation for TDD Frame Structure

3GPP LTE (2)

DLsymbN

slotT

0l 1DLsymb Nl

RB

scD

LR

BN

N

RB

scN

RBsc

DLsymb NN

),( lk

0k

1RBsc

DLRB NNk

• Slot Structure and Physical Resource Element: Downlink

( , )k l

RBsc

DLRB NN

- Resource grid

subcarriers and DLsymbN OFDM symbols

- Resource element

Each element in the resource grid,uniquely defined by the index pair

- Resource block

RBscNDL

symbN

To describe the mapping of certain physical channels to resource elements, in terms of

OFDM symbols and consecutive subcarriers

3GPP LTE (3)

Nominal Channel Bandwidth (MHz) 1.4 3 5 10 15 20Over-sampling Factor 48/35 96/75 43/28 43/28 43/28 43/28

Sampling Frequency (MHz) 1.92 3.84 7.68 15.36 23.04 30.72FFT Size 128 256 512 1024 1536 2048

Sub-Carrier Spacing (kHz) 15 15 15 15 15 15Useful Symbol Time Tu (µs) 66.7 66.7 66.7 66.7 66.7 66.7

NormalCyclic Prefix (CP)

Tg=4.7us

Symbol Time Ts (µs) 71.4 71.4 71.4 71.4 71.4 71.4

FDD

Number of OFDM symbols per Half Frame

70 70 70 70 70 70

Idle time (µs) . . . . . .

ExtendedCyclic Prefix (CP)

Tg=16.7us

Symbol Time Ts (µs) 83.4 83.4 83.4 83.4 83.4 83.4

FDD


60 60 60 60 60 60

Idle time (µs) . . . . . .


Left 28 38 106 212 318 424Right 28 38 106 212 318 424

Number of Used Sub-Carriers 72 180 300 600 900 1200Number of Physical Resource elements (12x7)

in a resource block 6 15 25 50 75 100

• OFDM Parameters: FDD

3GPP LTE (1)

Nominal Channel Bandwidth (MHz) 1.4 3 5 10 15 20Over-sampling Factor 48/35 96/75 43/28 43/28 43/28 43/28

Sampling Frequency (MHz) 1.92 3.84 7.68 15.36 23.04 30.72FFT Size 128 256 512 1024 1536 2048

Sub-Carrier Spacing (kHz) 15 15 15 15 15 15Useful Symbol Time Tu (µs) 66.7 66.7 66.7 66.7 66.7 66.7

NormalCyclic Prefix (CP)

Tg=4.7us

Symbol Time Ts (µs) 71.4 71.4 71.4 71.4 71.4 71.4

TDD


68 68 68 68 68 68

GP (µs) 142.8 142.8 142.8 142.8 142.8 142.8

ExtendedCyclic Prefix (CP)

Tg=16.7us

Symbol Time Ts (µs) 83.4 83.4 83.4 83.4 83.4 83.4

TDD


59 59 59 59 59 59

GP (µs) 83.4 83.4 83.4 83.4 83.4 83.4


Left 28 38 106 212 318 424Right 28 38 106 212 318 424

Number of Used Sub-Carriers 72 180 300 600 900 1200Number of Physical Resource elements (12x7)

in a resource block 6 15 25 50 75 100

• OFDM Parameters: TDD

3GPP LTE (2)

imt advanced

Technology

h t t t t t

t t h t t

t t st n t

n n ns t x f t

n n x x jk n

h t t tt

n nx x

n n x x e nx n n kx