How to Troubleshoot Apps for the Modern Connected Worker
IMT Advanced
1. Core Technologies for 4G: OFDM
Prof. Chung G. Kang
KOREA University
ccgkang@korea.ac.kr
4G Mobile (IMT Advanced) System and Applications
2. 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 technologies
for IMT-Advanced in ITU-R
3. • Rayleigh Fading Channel Model
• Time Dispersion due to Multi-path Fading
MOBILE Moving directionRoad
Buildings
i
2 ( cos )
1
( ) Re ( ) c d i i
n
j f f t
R i
i
s t As t e
cd f
c
v
f where
RMS Delay Spread
(t)
t
t
( )t ( )t
Ideal
Channel
Non-ideal
Channel
Broadband Wireless Channel (1)
4. • 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
Broadband Wireless Channel (2)
5. • 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
Broadband Wireless Channel (3)
Higher-speed
transmission suffers
from the more
multipath fading
(more ISI)!
6. • 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 Bandwidth
Bc: Coherence Bandwidth
Broadband Wireless Channel (4)
Ts
Ts
7. ( ) 1 2 2, ( ) ( ) ( ) ( )h t t tt a d t a d t t= + -% % %
• General Fading Channel
Broadband Wireless Channel (5)
Channel varies with
both frequency and
time, i.e., frequency
selectivity varies with
the times, depending
on the mobile speed
8. 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 n
y 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 h
x x
2 3
2* * 2
2 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, | | L
S M where M is the number of symbols and
L is the number of multi-paths
Too
complex!
9. Discrete Fourier Transform (DFT)
2
( ) ( ) j ft
X f x t e dt
( )X f
( )x t
( )
n s
n
X f X f
T
( )X f
nx
sT
1/ sT
2
0
kN j n
N
k n
n
X x e
nx
N
N
kX
f
f
k
DFT:
10. Serial
to
Parallel
Conv.
x
x
x
+
Modulator
RF
• Transmitter
sT
0cos2 f t
1cos2 f t
1cos2 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
cos2 cos2 0
sNT
i jf t f t dt
for all i j
1
0
( ) cos2
N
n n
n
s t x f t
OFDM
symbol
11. • Receiver
OFDM: Basic Concept (2)
( )s t Down
Conv. x
0cos2 f t
sN T
x
x
1cos2 f t
1cos2 Nf t
1x
1Nx
Serial
to
Parallel
Conv.
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 dt
x f t f t
x f t f t
x f t f t
x
Too many carriers….
How to implement this?
13. OFDM: Basic Concept (4)
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 fT
x 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
14. OFDM: Implementation (1)
• Block Diagram
1
2 ( / )
0
N
j k N n
n k
k
x X e
1 2 ( / )
0
1 2 ( / )
0
N j k N n
k nk
N j k N n
n kk
Y y e
a x e aX
{ }kX { }kY
0x
1x
1Nx
- Illustration: single-path channel
ˆ/k kX Y a
15. • Block Diagram
kX kH kY
?k k kY H X
{ }kX { }kY
0x
1x
1Nx
- Illustration: multi-path channel
OFDM: Implementation (2)
16. Cyclic Prefix (1)
1
0
2
exp
2
k n
n
H h jk n
0
1
2
0
H
H
2
0
2
exp
3
k n
n
X x jk n
0
1
2
3
0
0
X
X
X
2
0
2
exp
3
k 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
17. 1
0
2
exp
2
k n
n
H h jk n
0
1
2
0
H
H
2
0
2
exp
3
k n
n
X x jk n
2
0 3
2
exp][
n
n njkykY
0
1
2
6
0
0
Y
Y
Y
, 1,2k k kY H X k
0
1
2
3
0
0
X
X
X
Cyclic Prefix (2)
• Effect of Multi-path Channel
- Illustrating example
Cyclic
prefix
18. • Guard Interval vs. Cyclic Prefix
- Inter-symbol Interference (ISI) & guard Interval
- Inter-carrier Interference & cyclic prefix
Zero-valued guard interval
FFT interval
Guard
interval
Cyclic prefix
Guard
interval
FFT interval
No ICI
and no ISI
No ISI
but ICI
Guard
interval
Cyclic Prefix (3)
19. 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
22. 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)?
23. 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
24. 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
Unused
Subcarriers for
guard band
25. SNR
Coded OFDM
- Some subcarriers suffered by frequency selective fading must be protected
by forward error correction (FEC) coding
• Why Coded OFDM?
27. Water-filling (1)
{ }kX { }kY
0x
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
N
n
n
P h
C
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?
28. 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
2
1
,...,
0 0
m ax log 1 ,
c
c
N c
N
n n
N
P P
n
P h
C
N
1,...,0,0,
1
0
cnc
N
n
n NnPPNP
c
2
0*
~
1
n
n
h
N
P
.~
11 1
0
2
0
P
h
N
N
cN
n
n
c
subject to
29. 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 of
Channel gain
2
0*
~
1
n
n
h
N
P
30. • Illustrative Example
x x
Rb bps/Wb Hz
Digital
Modulation
Base
Station
x x
Digital
Demodulation
Information bits
for User 1
Rc >> Rb bps
x
+
C1
C2
Rb bps/Wb Hz
User 1
User 2
Multiple Access: CDMA (1)
C1
31. • Processing Gain & Interference
0
b b
required required
EC R
I N W
1
b
b
R
T
1
c
W
T
Processing Gain =
b
b c
W T
R T
0
6
10 3
(dB) (dB)
1.2288 10
6 10 log 6 21.1 15.1dB
9.6 10
b
required brequired
EC W
I N R
- Example: 0
9,600Hz; 1.2288MHz; / 6dBb b required
R W E N
Multiple Access: CDMA (2)
32. • 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
Multiple Access: CDMA (3)
• Illustrative Example
Chip
33. Serial to
Parallel
Converter
X
X
X
+
Modulator
RF
sT
0cos2 f t
1cos2 f t
1cos2 Nf t
sNT
sNT
sNT
• Orthogonal Frequency Division Multiplexing (OFDM)
X
X
X
+ RF
)(ts
0cos2 f t
1cos2 f t
1cos2 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
34. 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: OFDMA (2)
35. • Multiple Access with OFDM
- Resource units: Subchannels or Resource Block
Frequency
Time OFDM symbol
Subchannel
Multiple Access: OFDMA (3)
Subframe
Subcarrier
User 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….
36. Cellular OFDMA (1)
0
max max 0 0
2
max
( )
( ) ( )
( ) ( )
( )u u k k
k k k
k
P d
N N d dC
PNI N d p d
d
N
• Co-channel Interference in OFDMA Network
max
uN
p
N
maxN
Cell F0 Cell F1
Fully loaded Loading factor = p
uN
0
bEC R
I 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
inmeter
10
20
30
40
50
60
- Downlink
37. • Subcarrier Allocation for Interference Averaging
- Example
x1
x2
X1 X2
Without
frequency
hopping
With
frequency
hopping
- Interference averaging with frequency hopping
interference diversity
Cellular OFDMA (2)
38. • 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)
39. • 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)
40. • OFDM Parameters: Numerology (TDD)
Nominal Channel Bandwidth (W) 8.75MHz
Over-sampling Factor (n) 8/7
Sampling Frequency (Fs) 10 MHz
FFT Size (Nfft) 1,024
Sub-Carrier Spacing ( f) 9.765625kHz
Useful Symbol Time (Tb ) 102.4 µs
Cyclic Prefix (CP)
Tg=1/8 Tb
Symbol Time (Ts ) 115.2 µs
TDD
Number 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 896m
fftN 1024fftN
(9.765625)(1024) 10MHzs fftF f N
/ 10/8.75 8/ 7sn F W
102.4 μsbT
50. DL
symbN
slotT
0l 1DL
symb Nl
RB
sc
DL
RBNN
RB
scN
RB
sc
DL
symb NN
),( lk
0k
1RB
sc
DL
RB NNk
• Slot Structure
and Physical Resource Element: Downlink
( , )k l
RB
sc
DL
RB NN
- Resource grid
subcarriers and
DL
symbN OFDM symbols
- Resource element
Each element in the resource grid,
uniquely defined by the index pair
- Resource block
RB
scNDL
symbN
To describe the mapping of certain physical
channels to resource elements, in terms of
OFDM symbols and consecutive subcarriers
3GPP LTE (3)
51. Nominal Channel Bandwidth (MHz) 1.4 3 5 10 15 20
Over-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 30.72
FFT Size 128 256 512 1024 1536 2048
Sub-Carrier Spacing (kHz) 15 15 15 15 15 15
Useful Symbol Time Tu (µs) 66.7 66.7 66.7 66.7 66.7 66.7
Normal
Cyclic 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) . . . . . .
Extended
Cyclic Prefix (CP)
Tg=16.7us
Symbol Time Ts (µs) 83.4 83.4 83.4 83.4 83.4 83.4
FDD
Number of OFDM
symbols per
Half Frame
60 60 60 60 60 60
Idle time (µs) . . . . . .
Number of
Guard Sub-Carriers
Left 28 38 106 212 318 424
Right 28 38 106 212 318 424
Number of Used Sub-Carriers 72 180 300 600 900 1200
Number of Physical Resource elements (12x7)
in a resource block
6 15 25 50 75 100
• OFDM Parameters: FDD
3GPP LTE (1)
52. Nominal Channel Bandwidth (MHz) 1.4 3 5 10 15 20
Over-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 30.72
FFT Size 128 256 512 1024 1536 2048
Sub-Carrier Spacing (kHz) 15 15 15 15 15 15
Useful Symbol Time Tu (µs) 66.7 66.7 66.7 66.7 66.7 66.7
Normal
Cyclic Prefix (CP)
Tg=4.7us
Symbol Time Ts (µs) 71.4 71.4 71.4 71.4 71.4 71.4
TDD
Number of OFDM
symbols per
Half Frame
68 68 68 68 68 68
GP (µs) 142.8 142.8 142.8 142.8 142.8 142.8
Extended
Cyclic Prefix (CP)
Tg=16.7us
Symbol Time Ts (µs) 83.4 83.4 83.4 83.4 83.4 83.4
TDD
Number of OFDM
symbols per
Half Frame
59 59 59 59 59 59
GP (µs) 83.4 83.4 83.4 83.4 83.4 83.4
Number of
Guard Sub-Carriers
Left 28 38 106 212 318 424
Right 28 38 106 212 318 424
Number of Used Sub-Carriers 72 180 300 600 900 1200
Number of Physical Resource elements (12x7)
in a resource block
6 15 25 50 75 100
• OFDM Parameters: TDD
3GPP LTE (2)
