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?

12. 0f
• OFDM = N Parallel Narrowband Channels
0x
OFDM: Basic Concept (3)
1f 3f2f
1x 2x

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

20. FFT period FFT periodGI
Subcarrier #1
Subcarrier #2
CP
Delayed
Subcarrier #2

21. f
t
Effective
BW
FFT
size
Guard
interval
TG
Effective
symbol 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       
0x
1x
1Nx 
OFDM: Overall Picture
• OFDM Symbol in 3D
OFDM Symbol

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?

26. OFDM: Block Diagram
• Overall Block Diagram

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 

41. • TDD Frame Structure
115.2us
IEEE 802.16e: Frame Structure
24 symbols 12 symbols

42. • 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/subcarrier
Min. bits/subcarrier
5
5/36
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)
20.736
0.576
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/subcarrier
Min. bits/subcarrier
10/3
5/36
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)
7.68
0.320
2.304 (Msubcarriers/sec) * 10/3 (bits/subcarrier) = 7.68 (Mbps)
2.304 (Msubcarriers/sec) * 5/36 = 320 (kbps)

43. 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

44. IEEE 802.16m (2)
• Frame Structure with Type-1 Subframe (FDD)
- 5MHz, 10MHz, 20MHz bandwidth

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

46. • 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 28/25
Sampling Frequency (MHz) 5.6 8 10 11.2 22.4
FFT Size 512 1024 1024 1024 2048
Sub-Carrier Spacing (kHz) 10.937500 7.812500 9.765625 10.937500 10.937500
Useful 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
FDD
Number of OFDM
symbols per Frame
48 34 43 48 48
Idle time (µs) 62.857 104 46.40 62.857 62.857
Cyclic Prefix (CP)
Tg=1/16 Tu
Symbol Time Ts (µs) 97.143 136 108.8 97.143 97.143
FDD
Number of OFDM
symbols per Frame
51 36 45 51 51
Idle time (µs) 45.71 104 104 45.71 45.71
Cyclic Prefix (CP)
Tg=1/4 Tu
Symbol Time Ts (µs) 114.286 160 128 114.286 114.286
FDD
Number of OFDM
symbols per Frame
43 31 39 43 43
Idle time (µs) 85.694 40 8 85.694 85.694
Number of
Guard Sub-Carriers
Left 40 80 80 80 160
Right 39 79 79 79 159
Number of Used Sub-Carriers 433 865 865 865 1729
Number of Physical Resource Unit (18x6)
in a type-1 sub-frame
24 48 48 48 96
IEEE 802.16m (4)

47. • 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 28/25
Sampling Frequency (MHz) 5.6 8 10 11.2 22.4
FFT Size 512 1024 1024 1024 2048
Sub-Carrier Spacing (kHz) 10.937500 7.812500 9.765625 10.937500 10.937500
Useful 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
TDD
Number of OFDM
symbols per Frame
47 33 42 47 47
TTG + RTG (µs) 165.714 248 161.6 165.714 165.714
Cyclic Prefix (CP)
Tg=1/16 Tu
Symbol Time Ts (µs) 97.143 136 108.8 97.143 97.143
TDD
Number of OFDM
symbols per Frame
50 35 44 50 50
TTG + RTG (µs) 142.853 240 212.8 142.853 142.853
Cyclic Prefix (CP)
Tg=1/4 Tu
Symbol Time Ts (µs) 114.286 160 128 114.286 114.286
TDD
Number of OFDM
symbols per Frame
42 30 38 42 42
TTG + RTG (µs) 199.98 200 136 199.98 199.98
Number of
Guard Sub-Carriers
Left 40 80 80 80 160
Right 39 79 79 79 159
Number of Used Sub-Carriers 433 865 865 865 1729
Number of Physical Resource Units (18x6)
in a type-1 sub-frame
24 48 48 48 96
IEEE 802.16m (5)

48. • Frame Structure
- FDD
- TDD
3GPP LTE (1)

49. Subframe
#0
DwPTS
Subframe
#2
Subframe
#3
Subframe
#4
Subframe
#5
Subframe
#7
Subframe
#8
Subframe
#9
GP
UwPTS
DwPTS
GP
UwPTS
Subframe
#0
DwPTS
Subframe
#2
Subframe
#3
Subframe
#4
Subframe
#5
Subframe
#7
Subframe
#8
Subframe
#9
GP
UwPTS
Subframe
#6
One radio frame (10 ms)
10 ms switch-point
periodicty
5 ms switch-point
periodicty
: DL subframe : UL subframe
DwPTS
GP
UwPTS
: Special subframe
Configuration
0
1
2
3
4
5
5
Switch-point periodicity
5 ms
5 ms
5 ms
10 ms
10 ms
10 ms
10 ms
Subframe number
0 1 2 3 4 5 6 7 8 9
D
D
D
D
D
D
D
S
S
S
S
S
S
S
U
U
U
U
U
U
U
U
U
D
U
U
D
U
U
D
D
U
D
D
U
D
D
D
D
D
D
D
S
S
S
D
D
D
S
U
U
U
D
D
D
U
U
U
D
D
D
D
U
U
D
D
D
D
D
D
Uplink-downlink allocations
• Periodic Switch-Point Operation for TDD Frame Structure
3GPP LTE (2)

50. DL
symbN
slotT
0l 1DL
symb  Nl
RB
sc
DL
RBNN
RB
scN
RB
sc
DL
symb NN 
),( lk
0k
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)