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Introduction to Orthogonal Frequency
Division Multiplexing Technique
Gwo-Ruey Lee
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
Outlines
 Introduction to Orthogonal Frequency Division
Multiplexing (OFDM) Technique
Introduction
The History of OFDM
OFDM and Multicarrier Transmission
The Applications of OFDM
 DAB
 HDTV
 Wireless LAN
 IEEE 802.16
 IEEE 802.20
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
Introduction
 Because of its high-speed data transmission and
effectiveness in combating the frequency selective
fading channel, OFDM technique is widely used in
wireless communication nowadays.
 Orthogonal frequency division multiplexing (OFDM)
is a multi-carrier transmission technique, which
divides the available spectrum into many
subcarriers, each one being modulated by a low
data rate stream.
1/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
Introduction
 OFDM can be viewed as either a modulation
technique or a multiplex technique.
 Modulation technique
 Viewed by the relation between input and
output signals
 Multiplex technique
 Viewed by the output signal which is the
linear sum of the modulated signals
Input Signal
OFDM System
Output Signal
S/P

2/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
Introduction
 The employment of discrete Fourier transform to
replace the banks of sinusoidal generator and the
demodulation significantly reduces the
implementation complexity of OFDM modems.
IFFT
1
cos(2 )
f t

2
cos(2 )
f t

cos(2 )
N
f t

( )
s t

( )
s t
3/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
Introduction
 Intersymbol interference is eliminated almost
completely by introducing a guard interval with
zero padding in every OFDM symbol.
 Guard interval with zero padding
 The way to eliminate ISI
GuardInterval
(Zeropadding)
GuardInterval
(Zeropadding)
GuardInterval
(Zeropadding)
Guard Interval
(Zero padding)
4/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
Introduction
 In the guard time , the OFDM symbol is cyclically
extended to avoid intercarrier interference.
 Guard interval with cyclic extension (cyclic prefix)
Guard Interval
(Cyclic Extension)
5/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
Introduction
 The way to avoid ICI
Guard time FFT integration time=1/carrier spacing Guard time FFT integration time=1/carrier spacing
OFDM symbol time OFDM symbol time
Subcarrier #1
Delayed subcarrier #2
Part of subcarrier #2
causing ICI on
subcarrier #1
6/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
Introduction – FFT-based OFDM
Serial-to-
Parallel
Converter
Signal
Mapper
IFFT
Parallel-
to-Serial
Converter
Guard
Interval
Insertion
Serial
Data
Input
x bits
0
d
1
d
1

n
d
0
s
1
s
1

n
s
D/A &
Low pass
Filter
Up-
Converter
Down-
Converter
A/D
Guard
Interval
Removal
Serial-to-
Parallel
Converter
FFT
One-tap
Equalizer
Signal
Demapper
Parallel-
to-Serial
Converter
Serial
Data
Output
0
d̂
x bits
1
ˆ
d
1
ˆ

n
d
0
ŝ
1
ŝ
1
ˆ 
n
s
Channel
)
(t
s
Time
Frequency
Subchannels
Fast Fourier
Transform
Guard
Intervals
Symbols
7/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
Introduction
 The advantages of OFDM
 Immunity to delay spread and multipath
 Resistance to frequency selective fading
 Simple equalization
 Efficient bandwidth usage
 The disadvantages of OFDM
 Synchronization
 Need FFT units at transmitter, receiver
 Sensitive to carrier frequency offset
 High peak to average power ratio
8/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The History of OFDM
 The idea, which was proposed in mid-1960s, used
parallel data transmission and frequency division
multiplexing (FDM) [1,14].
 In the 1960s, the OFDM technique was used in
several high-frequency military system
 KINEPLEX [15]
 ANDEFT [16]
 KATHRYN [17]
1/4
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The History of OFDM
 In 1971,Weinstein and Ebert applied the Discrete Fourier
Transform (DFT) to parallel data transmission systems as
part of modulation and demodulation process[1,4,18].
 FFT-based OFDM
 In the 1980s, OFDM was studied for high-speed modems
digital mobile communication, and high-density recording.
 Pilot tone is used to stabilize carrier and frequency control
 Trellis code is implemented
 COFDM
 In 1980, Hirosaki suggested an equalization algorithm in order
to suppress both intersymbol and intercarrier interference
caused by the channel impulse response or timing and
frequency errors[4,19].
 In 1980. Hirosaki also introduced the DFT-based
implementation of Saltzburg’s O-QAM OFDM system[4,20].
2/4
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The History of OFDM
 In the 1990s, OFDM was exploited for wideband data
communications [1-7]
 Mobile radio FM channels
 Fix-wire network [7,26]
 High-bit-rate digital subscriber line (HDSL)
 Asymmetric digital subscriber line (ADSL)
 Very-high-speed digital subscriber line (VDSL)
 Digital audio broadcasting (DAB) [9,21]
 Digital video broadcasting (DVB)
 High-definition television (HDTV) terrestrial broadcasting [10,22]
 There exist three mechanisms about the digital terrestrial television
broadcasting system in European (COFDM), North America (8-VSB),
and Japan (BST-OFDM).
 Wireless LAN [11-13,23-25]
 HIPERLAN2 (European)
 IEEE 802.11a (U.S.A)
 IEEE 802.11g (U.S.A)
3/4
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The History of OFDM
 Now, OFDM technique has been adopted as the new
European DAB standard, and HDTV standard.
 A candidate of 4G mobile communication [27]
 OFDM/UWB (802.15.3a)
 IEEE 802.16 broadband wireless access system
 IEEE 802.20 mobile broadband wireless access
(MBWA)
4/4
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
OFDM and Multicarrier Transmission
 OFDM is a special case of multicarrier
transmission , where a single data stream is
transmitted over a number of lower rate
subcarrier[1,4].
 Single carrier transmission
 The concept of single-carrier is that each user transmits
and receives data stream with only one carrier at any time.
 Multicarrier transmission
 The concept of multi-carrier transmission is that a user
can employ a number of carriers to transmit data
simultaneously.
1/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
OFDM and Multicarrier Transmission
 Single and multicarrier transmission
Single carrier transmission
1
cos(2 )
f t

i
b ( )
s t
S/P
1
cos(2 )
f t

2
cos(2 )
f t

cos(2 )
N
f t

i
b ( )
s t

Multicarrier carrier transmission
2/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
OFDM and Multicarrier Transmission
 Orthogonality
 Time domain Frequency domain
 Bandpass signal
where is the equivalent lowpass signal of
if , n is a non-zero integer, i.e. , then
*
1 2
( ) ( ) 0
x t x t dt




*
1 2
( ) ( ) 0
X f X f df




   
2 ( ) 2
( ) cos(2 ( ) ) Re Re ( )
c m c
i f f t i f t
m c m lm
x t f f t e x t e
 
 
    
2
( ) m
i f t
lm
x t e 

1 2 1 2
2 2 2 ( )
*
12
0 0
sin( )
( )
T T
i f t i f t i f f t i fT
fT
e e dt e dt e
f
   



 

  

 
f T n
  
n
f
T
  12 0
 

3/8
( )
m
x t
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
OFDM and Multicarrier Transmission
(A)
(E)
(D)
(C)
(B)
1
c
f f
 2
c
f f
 3
c
f f
 4
c
f f
 5
c
f f

1
T
1
T
Orthogonal
Non-orthogonal
Orthogonal, n=3
Orthogonal, n=2
Orthogonal, n=1
(OFDM)
4/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
-10 -5 0 5 10
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-1
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0
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1
OFDM and Multicarrier Transmission
1
subcarrier f
2
subcarrier f
3
subcarrier f
4
subcarrier f
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0
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1
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0
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1
1.5
2
2.5
3
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
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-1
0
1
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4
-10 -5 0 5 10
-0.4
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0
0.2
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1
1.2
5/8
Time domain Frequency domain
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
OFDM and Multicarrier Transmission
 Multicarrier CDMA system
CDMA + OFDM system
Three types of Multicarrier CDMA system
 MC-CDMA system
 Multi-carrier DS-CDMA system
 Multi-tone CDMA system
6/8
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
OFDM and Multicarrier Transmission
 Multicarrier CDMA system
 Frequency domain spreading
 MC-CDMA system
 The spreading operation in the frequency domain
 It spreads the original data streams using a given spreading code, and then
modulates a different subcarriers with each chip
7/8
1
3
2
5
6
7
8
9
10
f
1
f
10
f
9
f
8
f
7
f
6
f
5
f
4
f
3
f
2
f
t
a1
a1
a1
a1
a1
a1
a1
a1
a1
a1
4
1
cos(2 )
f t

2
cos(2 )
f t

( )
MC
s t

Copier
1
c
2
c
t
t
Data Stream
cos(2 )
N
f t

N
c
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
OFDM and Multicarrier Transmission
 Time domain spreading
 Multi-carrier DS-CDMA system
 Multi-tone CDMA system
 The spreading operation in the time domain
 It spreads the serial-to-parallel (s/p) converted data streams using a
given spreading code, and then modulates a different subcarrier with
each data stream.
8/8
f
f1
f10
f9
f8
f7
f6
f5
f4
f3
f2
t
1 3
2 4
5
6
7
8
9
10
t
1 3
2 4
5
6
7
8
9
10
t
1 3
2 4
5
6
7
8
9
10
1
cos(2 )
f t

2
cos(2 )
f t

( )
or
( )
MD
MT
s t
s t

Serial to
Parallel
Converter
( )
c t
t
(a) Transmitter
Data Stream
cos(2 )
N
f t

t
( )
c t
( )
c t
Multi-carrier DS-
CDMA System
t
( )
c t
Multi-tone CDMA
System
t
( )
c t
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM
 DAB
 HDTV
 Wireless LAN
 IEEE 802.16
 IEEE 802.20
1/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM – DAB
 Digital Audio Broadcasting (DAB) [9,21]
 DAB is a digital technology offering considerable
advantages over today's FM radio, both to listeners and
broadcasting.
 DAB's flexibility will also provide a wider choice of
programs, including many not available on FM.
 A single station might offer its listeners a choice of mono
voice commentaries on three or four sporting events at
the same time, and then combine the bitstreams to
provide high-quality sound for the concert which follows.
2/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM – HDTV
 High-definition Television (HDTV) Terrestrial
Broadcasting [10,22]
 Commercial television station is first published by England.
 There exist three mechanisms about the digital
terrestrial television broadcasting system in European
(COFDM), North America (8-VSB), and Japan (BST-
OFDM).
 The European introduces the COFDM modulation scheme into
the system structure.
 American develops the system based on 8-level vestigial side-
band (8-VSB) modulation scheme.
 Japan is zealous to develop the band segmented transmission
Orthogonal Frequency Division Multiplexing (BST-OFDM)
system, which nature is based on COFDM modulation scheme.
3/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM – Wireless LANs
 Wireless LANs [11-13,23-25]
 HIPERLAN2 (European)
 IEEE 802.11a (U.S.A)
 IEEE 802.11g (U.S.A)
4/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM – Wireless LANs
HIPERLAN2
 ETSI has developed a new WLAN technology called HiperLAN
type 2 (HiperLAN2)[23].
 HiperLAN2 provides:
 High and scalable capacity as the number of users increase in the
system
 Managed bandwidth with predictable performance for each user
and application
 Robust protocols that also optimize the overall throughput of
the available radio resource, making it the most spectrum-
efficient WLAN technology operating at 5 GHz
 A high level of security
 QoS capabilities to support virtually any type of service or
application
 Ease-of-use through a set of auto-configuration tools.
 HipperLan2 standard achieves its 54 Mbps data rate through a
OFDM technique.
5/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM – Wireless LANs
IEEE 802.11a Standards
 IEEE 802.11a, 1999
 5GHz band
 Orthogonal frequency division multiplexing (OFDM)
 6Mbps to 54Mbps
6/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM – Wireless LANs
IEEE 802.11g Standards
 IEEE 802.11g [28]
 IEEE 802.11g will use the same 2.4 GHz radio spectrum as
current 802.11b equipment, but with the higher data rates,
packet structure, and modulation technology of 802.11a.
 IEEE 802.11g standard achieves its 54 Mbps data rate
through a OFDM technique.
 IEEE 802.11b and IEEE 802.11g are operated in the same
2.4 GHz frequency band. When their devices are used in
the same area, they will coexist, sharing the airspace
between them.
7/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM – Wireless LANs
IEEE 802.11g Standards
 Operational modes
 802.11b Mode
 OFDM Mode (Support of 6, 12 and 24 Mbit/s data rates is
mandatory )
 PBCC-22 and PBCC-33 Modes (Optional)
 CCK-OFDM Modes (Optional)
模式 資料速率(Mbit/s) 調變技術
802.11b 1, 2, 5.5, 11 DSSS, CCK, PBCC
OFDM 6, 9, 12, 18, 24, 36, 48, 54 OFDM
PBCC-22 and PBCC-33 2, 5.5, 11, 22, 33 DSSS, PBCC
CCK-OFDM 6, 9, 12, 18, 24, 36, 48, 54 DSSS, OFDM
8/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM – Wireless LANs
IEEE 802.11a/b/g Standards
 Maximum Data rate
 IEEE 802.11a
 54 Mbps
 For example, an 802.11a network, which broadcasts on the 5GHz
frequency band, supports 12 simultaneous channel (in North
American).
 maximum data rate 12*54=648 Mbps.
 IEEE 802.11b
 11Mbps
 For example, a standalone 802.11b network supports three non-
overlapping channel (worldwide), each with a peak data rate of 11
Mbps.
 maximum data rate 3*11=33 Mbps.
 IEEE 802.11g
 54 Mbps
 For example, an 802.11g installation supports three channels, each
with a peak rate of 54 Mbps.
 maximum data rate 3*54=162 Mbps.
 Mixed mode
9/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM – Wireless LANs
IEEE 802.11a/b/g Standards
Mixed-Mode Data Rate vs. 802.11g Data
Rate
Maximum Theoretical Data
Rate
54 Mbps IEEE 802.11 Wireless LAN at 2.4 GHz
Deploying standards-based Wireless LAN solutions
December 2002 Intel white paper
10/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM –
IEEE 802.16
 IEEE 802.16 broadband wireless access system [29]
 Broadband wireless access (BWA) is a term referring to a range
of fixed radio systems, used primarily to convey broadband
services between users’ premises and core networks.
 The term “broadband” is usually taken to mean the capability to
deliver significant bandwidth to each user (in ITU terminology,
greater than around 1.5 Mbps, though many BWA networks
support significantly higher data rates).
 A typical BWA network supports connection to many user
premises within a radio coverage area.
 The IEEE 802.16 standard should provides the solution to access
systems based on DSL, cable, and eventually fiber optics.
 The applications of IEEE 802.16
 The range of applications is very wide and evolving quickly. It
includes voice, data and entertainment services of many kinds.
11/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM –
IEEE 802.16
 IEEE 802.16 wireless MAN background
 Target: FBWA (fixed broadband wireless access)
 Fast local connection to network
 Project development since 1998
12/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM –
IEEE 802.16
 802.16 bit rate and channel size
134.4
89.6
44.8
22.4
28
120
80
40
20
25
96
64
32
16
20
64-QAM
bit rate
(Mbps)
16-QAM
bit rate
(Mbps)
QPSK
bit rate
(Mbps)
Symbol
Rate
(Msym/s
)
Channel
Width
(MHz)
13/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM –
IEEE 802.20
 IEEE 802.20 mobile broadband wireless access
 Mission
 The mission of IEEE 802.20 is to develop the
specification for an efficient packet based
air interface that is optimized for the
transport of IP based services.
 The goal is to enable worldwide deployment of
affordable, ubiquitous, always-on and
interoperable multi-vendor mobile broadband
wireless access networks that meet the needs
of business and residential end user markets.
14/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM –
IEEE 802.20
 IEEE 802.20 mobile broadband wireless access
 MBWA Scope
 Specification of physical and medium access control layers of
an air interface for interoperable mobile broadband wireless
access systems, operating in licensed bands below 3.5 GHz,
optimized for IP-data transport, with peak data rates per
user in excess of 1 Mbps.
 It supports various vehicular mobility classes up to 250 Km/h
in a MAN environment and targets spectral efficiencies,
sustained user data rates and numbers of active users that
are all significantly higher than achieved by existing mobile
systems.
 The applications of MBWA
 This allows applications including, but not limited to, video,
full graphical web browsing, e-mail, file uploading and
downloading without size limitations (e.g., FTP), streaming
video and streaming audio, IP multicast, telematics, location
based services, VPN connections, VoIP, instant messaging and
on- line multiplayer gaming
15/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM –
IEEE 802.20
Work
Domain
Home
Domain
Seamless
Seamless
Ubiquitous
Ubiquitous
Experience
Experience
Mobile
Domain
Portable Remote
Access Services
Field Service Apps
Hotel/Motel
Portable Services
Mobile Commerce
Services
Mobile Office (Voice
and Data Apps)
High BW Connectivity
Video Streaming -
Conferencing Apps
Portable
Office
Reservations-Listings
Directions Services
Video Streaming -
Conferencing Apps
Video Streaming -
Conferencing Apps
Mobile Broadband
Wireless Access
16/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
The Applications of OFDM –
IEEE 802.20
 IEEE 802.20 mobile broadband wireless access
 Peak data rates
 These peak data rate targets are independent
of channel conditions, traffic loading, and
system architecture.
Parameter Bandwidth
1.25 MHz 5 MHz
Downlink Uplink Downlink Uplink
Peak User Data Rate 4.5 Mbps 2.25 Mbps 18 Mbps 9 Mbps
17/17
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
Introduction to Orthogonal Frequency Division
Multiplexing Technique
 Readings
 Pandharipande A., “Principles of OFDM,” Potentials, IEEE
Vol. 21, Issue 2, pp.16 – 19, Apr-May 2002.
 Zou, W.Y.; Yiyan Wu, “ COFDM: An overview ”
Broadcasting, IEEE Transactions on, Vol. 41 Issue: 1, pp.
1 –8, Mar. 1995.
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
References
 [1] Richard van Nee, Ramjee Prasad, OFDM wireless multimedia communication, Artech
House Boston London, 2000.
 [2] Ahmad R. S. Bahai and Burton R. Saltzberg, Multi-carrier digital communications -
Theory and applications of OFDM, Kluwer Academic / Plenum Publishers New York,
Boston, Dordrecht, London, Moscow 1999.
 [3] Ramjee Prasad, “OFDM based wireless broadband multimedia communication,” Letter
Notes on ISCOM’99, Kaohsiung, Taiwan, Nov 7-10, 1999.
 [4] L. Hanzo, W. Webb and T. Keller, Single- and multi-carrier quadrature amplitude
modulation – Principles and applications for personal communications, WLANs and
broadcasting, John Wiley & Sons, Ltd, 2000.
 [5] Mark Engels, Wireless Ofdm Systems: How to Make Them Work? Kluwer Academic
Publishers.
 [6] Lajos Hanzo, William Webb, Thomas Keller, Single and Multicarrier Modulation:
Principles and Applications, 2nd edition, IEEE Computer Society.
 [7] John A. C. Bingham, ADSL, VDSL, and Multicarrier Modulation, Wiley-Interscience.
 [8] Lajos Hanzo, Choong Hin Wong, Mong-Suan Yee, Adaptive Wireless Transceivers:
Turbo-Coded, Turbo-Equalized and Space-Time Coded TDMA, CDMA and OFDM
Systems , John Wiley & Sons.
 [9] Wolfgang Hoeg, Thomas Lauterbach, Digital Audio Broadcasting: Principles and
Applications, John Wiley & Sons.
 [10] Robert Goodman , The Guide To Digital Television, second edition, Miller Freeman
PSN, Inc
 [11] John Terry, Juha Heiskala, OFDM Wireless LANs: A Theoretical and Practical Guide,
Sams.
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
References
 [12] Jim Geier, Wireless LANS, Implementing High Performance IEEE 802.11 Networks,
second edition, Sams.
 [13] Neil Reid and Ron Seide, 802.11(Wi-Fi) Networking Handbook, Mc Graw Hill.
 [14] Zou, W.Y.; Yiyan Wu, “ COFDM: An overview ” Broadcasting, IEEE Transactions on,
Vol. 41 Issue: 1, pp. 1 –8, Mar. 1995.
 [15] Mosier, R. R., and R. G. Clabaugh, “ Kineplex, a bandwidth efficient binary
transmission system ” AIEE Trans., Vol. 76, pp. 723-728, Jan. 1958.
 [16] Porter, G. C., “ Error distribution and diversity performance of a frequency
differential PSK HF, modem ” IEEE Trans. Comm. Vol., COM-16, pp. 567-575 Aug. 1968
 [17] Zimmerman, M. S., and A. L. Kirsch, “ The AN/GSC-10 (KATHRYN) variable rate
data modem for HF radio ” IEEE Trans. Comm. Vol., COM-15, pp. 197-205 Apr. 1967.
 [18] S. Weinstein and P. Ebert, “ Data transmission by frequency division multiplexing
using the discrete Fourier transform ” IEEE Trans. Comm., Vol. COM-19, pp. 628-634,
October 1971.
 [19] B. Hirosaki, “ An analysis of automatic equalizers for orthogonally multiplexed QAM
system ” IEEE Trans. Comm., Vol. COM-28, pp. 73-83, Jan. 1980
 [20] B. Hirosaki, “ An orthogonally multiplexed QAM system using the discrete fourier
transform ” IEEE Trans. Comm., Vol., COM-29 pp. 73-83, Jan. 1980
 [21] Radio broadcasting system: Digital Audio Broadcasting (DAB) to mobile, portable
and fixed receivers. ETS 300 401, ETSI-European Telecommunication Standards
Institute, Valbonne, France, Feb. 1995.
 [22] Digital broadcasting systems for television, sound and data services. European
Telecommunication Standard, prETS 300 744 (Draft, version 0.0.3), Apr. 1996.
Wireless Access Tech. Lab.
CCU
Wireless Access Tech. Lab.
References
 [23] Khun-Jush, J.; Malmgren, G.; Schramm, P.; Torsner, J. “ Overview and
performance of HIPERLAN type 2-a standard for broadband wireless
communications ” Vehicular Technology Conference Proceedings, 2000. VTC
2000-Spring Tokyo. 2000 IEEE 51st, Vol. 1 pp. 112 -117 Vol.1, 2000.
 [24] IEEE Standards Department, “ IEEE 802.11 draft standard for wireless
LAN medium access control (MAC) and physical layer (PHY) specification ”
P802.11 D6.1, May 1997.
 [25] IEEE P802.11a/D2.0. “ Draft supplement to standard for telecommunications and
information exchange between systems – LAN/MAN specific requirement-Part II:
Wireless MAC and PHY Specifications: High speed physical layer in the 5GHz band ”
1997.
 [26] Chow, P. S., J. C. Tu and J. M. Cioffi, “ Performance evaluation of a multichannel
transceiver system for ADSL and VHDSL services ” IEEE Journal on Selected Areas in
Communications, Vol. 9 Issue: 6 pp. 909 -919, Aug. 1991
 [27] “ Universal mobile telecommunications system (UMTS); UMTS terrestrial radio
access (UTRA); Concept evaluation,” tech, rep., ETSI, 1997. TR 101 146.
 [28] “54 Mbps IEEE 802.11 Wireless LAN at 2.4 GHz, Deploying standards-based
Wireless LAN solutions ” White Paper, Dec. 2002.
 [29] “IEEE 802.16.2, Recommended Practices to Facilitate the Coexistence of
Broadband Wireless Access (BWA) Systems: Working Document, Draft 5, ” IEEE
802.16.2-00/01r5, 2000.

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Introduction to OFDM.ppt

  • 1. Introduction to Orthogonal Frequency Division Multiplexing Technique Gwo-Ruey Lee
  • 2. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. Outlines  Introduction to Orthogonal Frequency Division Multiplexing (OFDM) Technique Introduction The History of OFDM OFDM and Multicarrier Transmission The Applications of OFDM  DAB  HDTV  Wireless LAN  IEEE 802.16  IEEE 802.20
  • 3. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. Introduction  Because of its high-speed data transmission and effectiveness in combating the frequency selective fading channel, OFDM technique is widely used in wireless communication nowadays.  Orthogonal frequency division multiplexing (OFDM) is a multi-carrier transmission technique, which divides the available spectrum into many subcarriers, each one being modulated by a low data rate stream. 1/8
  • 4. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. Introduction  OFDM can be viewed as either a modulation technique or a multiplex technique.  Modulation technique  Viewed by the relation between input and output signals  Multiplex technique  Viewed by the output signal which is the linear sum of the modulated signals Input Signal OFDM System Output Signal S/P  2/8
  • 5. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. Introduction  The employment of discrete Fourier transform to replace the banks of sinusoidal generator and the demodulation significantly reduces the implementation complexity of OFDM modems. IFFT 1 cos(2 ) f t  2 cos(2 ) f t  cos(2 ) N f t  ( ) s t  ( ) s t 3/8
  • 6. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. Introduction  Intersymbol interference is eliminated almost completely by introducing a guard interval with zero padding in every OFDM symbol.  Guard interval with zero padding  The way to eliminate ISI GuardInterval (Zeropadding) GuardInterval (Zeropadding) GuardInterval (Zeropadding) Guard Interval (Zero padding) 4/8
  • 7. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. Introduction  In the guard time , the OFDM symbol is cyclically extended to avoid intercarrier interference.  Guard interval with cyclic extension (cyclic prefix) Guard Interval (Cyclic Extension) 5/8
  • 8. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. Introduction  The way to avoid ICI Guard time FFT integration time=1/carrier spacing Guard time FFT integration time=1/carrier spacing OFDM symbol time OFDM symbol time Subcarrier #1 Delayed subcarrier #2 Part of subcarrier #2 causing ICI on subcarrier #1 6/8
  • 9. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. Introduction – FFT-based OFDM Serial-to- Parallel Converter Signal Mapper IFFT Parallel- to-Serial Converter Guard Interval Insertion Serial Data Input x bits 0 d 1 d 1  n d 0 s 1 s 1  n s D/A & Low pass Filter Up- Converter Down- Converter A/D Guard Interval Removal Serial-to- Parallel Converter FFT One-tap Equalizer Signal Demapper Parallel- to-Serial Converter Serial Data Output 0 d̂ x bits 1 ˆ d 1 ˆ  n d 0 ŝ 1 ŝ 1 ˆ  n s Channel ) (t s Time Frequency Subchannels Fast Fourier Transform Guard Intervals Symbols 7/8
  • 10. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. Introduction  The advantages of OFDM  Immunity to delay spread and multipath  Resistance to frequency selective fading  Simple equalization  Efficient bandwidth usage  The disadvantages of OFDM  Synchronization  Need FFT units at transmitter, receiver  Sensitive to carrier frequency offset  High peak to average power ratio 8/8
  • 11. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The History of OFDM  The idea, which was proposed in mid-1960s, used parallel data transmission and frequency division multiplexing (FDM) [1,14].  In the 1960s, the OFDM technique was used in several high-frequency military system  KINEPLEX [15]  ANDEFT [16]  KATHRYN [17] 1/4
  • 12. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The History of OFDM  In 1971,Weinstein and Ebert applied the Discrete Fourier Transform (DFT) to parallel data transmission systems as part of modulation and demodulation process[1,4,18].  FFT-based OFDM  In the 1980s, OFDM was studied for high-speed modems digital mobile communication, and high-density recording.  Pilot tone is used to stabilize carrier and frequency control  Trellis code is implemented  COFDM  In 1980, Hirosaki suggested an equalization algorithm in order to suppress both intersymbol and intercarrier interference caused by the channel impulse response or timing and frequency errors[4,19].  In 1980. Hirosaki also introduced the DFT-based implementation of Saltzburg’s O-QAM OFDM system[4,20]. 2/4
  • 13. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The History of OFDM  In the 1990s, OFDM was exploited for wideband data communications [1-7]  Mobile radio FM channels  Fix-wire network [7,26]  High-bit-rate digital subscriber line (HDSL)  Asymmetric digital subscriber line (ADSL)  Very-high-speed digital subscriber line (VDSL)  Digital audio broadcasting (DAB) [9,21]  Digital video broadcasting (DVB)  High-definition television (HDTV) terrestrial broadcasting [10,22]  There exist three mechanisms about the digital terrestrial television broadcasting system in European (COFDM), North America (8-VSB), and Japan (BST-OFDM).  Wireless LAN [11-13,23-25]  HIPERLAN2 (European)  IEEE 802.11a (U.S.A)  IEEE 802.11g (U.S.A) 3/4
  • 14. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The History of OFDM  Now, OFDM technique has been adopted as the new European DAB standard, and HDTV standard.  A candidate of 4G mobile communication [27]  OFDM/UWB (802.15.3a)  IEEE 802.16 broadband wireless access system  IEEE 802.20 mobile broadband wireless access (MBWA) 4/4
  • 15. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. OFDM and Multicarrier Transmission  OFDM is a special case of multicarrier transmission , where a single data stream is transmitted over a number of lower rate subcarrier[1,4].  Single carrier transmission  The concept of single-carrier is that each user transmits and receives data stream with only one carrier at any time.  Multicarrier transmission  The concept of multi-carrier transmission is that a user can employ a number of carriers to transmit data simultaneously. 1/8
  • 16. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. OFDM and Multicarrier Transmission  Single and multicarrier transmission Single carrier transmission 1 cos(2 ) f t  i b ( ) s t S/P 1 cos(2 ) f t  2 cos(2 ) f t  cos(2 ) N f t  i b ( ) s t  Multicarrier carrier transmission 2/8
  • 17. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. OFDM and Multicarrier Transmission  Orthogonality  Time domain Frequency domain  Bandpass signal where is the equivalent lowpass signal of if , n is a non-zero integer, i.e. , then * 1 2 ( ) ( ) 0 x t x t dt     * 1 2 ( ) ( ) 0 X f X f df         2 ( ) 2 ( ) cos(2 ( ) ) Re Re ( ) c m c i f f t i f t m c m lm x t f f t e x t e          2 ( ) m i f t lm x t e   1 2 1 2 2 2 2 ( ) * 12 0 0 sin( ) ( ) T T i f t i f t i f f t i fT fT e e dt e dt e f                 f T n    n f T   12 0    3/8 ( ) m x t
  • 18. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. OFDM and Multicarrier Transmission (A) (E) (D) (C) (B) 1 c f f  2 c f f  3 c f f  4 c f f  5 c f f  1 T 1 T Orthogonal Non-orthogonal Orthogonal, n=3 Orthogonal, n=2 Orthogonal, n=1 (OFDM) 4/8
  • 19. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. -10 -5 0 5 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 OFDM and Multicarrier Transmission 1 subcarrier f 2 subcarrier f 3 subcarrier f 4 subcarrier f -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -10 -5 0 5 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -10 -5 0 5 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -10 -5 0 5 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -10 -5 0 5 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -1.5 -1 -0.5 0 0.5 1 1.5 2 -10 -5 0 5 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -10 -5 0 5 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -2 -1 0 1 2 3 4 -10 -5 0 5 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 5/8 Time domain Frequency domain
  • 20. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. OFDM and Multicarrier Transmission  Multicarrier CDMA system CDMA + OFDM system Three types of Multicarrier CDMA system  MC-CDMA system  Multi-carrier DS-CDMA system  Multi-tone CDMA system 6/8
  • 21. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. OFDM and Multicarrier Transmission  Multicarrier CDMA system  Frequency domain spreading  MC-CDMA system  The spreading operation in the frequency domain  It spreads the original data streams using a given spreading code, and then modulates a different subcarriers with each chip 7/8 1 3 2 5 6 7 8 9 10 f 1 f 10 f 9 f 8 f 7 f 6 f 5 f 4 f 3 f 2 f t a1 a1 a1 a1 a1 a1 a1 a1 a1 a1 4 1 cos(2 ) f t  2 cos(2 ) f t  ( ) MC s t  Copier 1 c 2 c t t Data Stream cos(2 ) N f t  N c
  • 22. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. OFDM and Multicarrier Transmission  Time domain spreading  Multi-carrier DS-CDMA system  Multi-tone CDMA system  The spreading operation in the time domain  It spreads the serial-to-parallel (s/p) converted data streams using a given spreading code, and then modulates a different subcarrier with each data stream. 8/8 f f1 f10 f9 f8 f7 f6 f5 f4 f3 f2 t 1 3 2 4 5 6 7 8 9 10 t 1 3 2 4 5 6 7 8 9 10 t 1 3 2 4 5 6 7 8 9 10 1 cos(2 ) f t  2 cos(2 ) f t  ( ) or ( ) MD MT s t s t  Serial to Parallel Converter ( ) c t t (a) Transmitter Data Stream cos(2 ) N f t  t ( ) c t ( ) c t Multi-carrier DS- CDMA System t ( ) c t Multi-tone CDMA System t ( ) c t
  • 23. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM  DAB  HDTV  Wireless LAN  IEEE 802.16  IEEE 802.20 1/17
  • 24. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – DAB  Digital Audio Broadcasting (DAB) [9,21]  DAB is a digital technology offering considerable advantages over today's FM radio, both to listeners and broadcasting.  DAB's flexibility will also provide a wider choice of programs, including many not available on FM.  A single station might offer its listeners a choice of mono voice commentaries on three or four sporting events at the same time, and then combine the bitstreams to provide high-quality sound for the concert which follows. 2/17
  • 25. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – HDTV  High-definition Television (HDTV) Terrestrial Broadcasting [10,22]  Commercial television station is first published by England.  There exist three mechanisms about the digital terrestrial television broadcasting system in European (COFDM), North America (8-VSB), and Japan (BST- OFDM).  The European introduces the COFDM modulation scheme into the system structure.  American develops the system based on 8-level vestigial side- band (8-VSB) modulation scheme.  Japan is zealous to develop the band segmented transmission Orthogonal Frequency Division Multiplexing (BST-OFDM) system, which nature is based on COFDM modulation scheme. 3/17
  • 26. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – Wireless LANs  Wireless LANs [11-13,23-25]  HIPERLAN2 (European)  IEEE 802.11a (U.S.A)  IEEE 802.11g (U.S.A) 4/17
  • 27. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – Wireless LANs HIPERLAN2  ETSI has developed a new WLAN technology called HiperLAN type 2 (HiperLAN2)[23].  HiperLAN2 provides:  High and scalable capacity as the number of users increase in the system  Managed bandwidth with predictable performance for each user and application  Robust protocols that also optimize the overall throughput of the available radio resource, making it the most spectrum- efficient WLAN technology operating at 5 GHz  A high level of security  QoS capabilities to support virtually any type of service or application  Ease-of-use through a set of auto-configuration tools.  HipperLan2 standard achieves its 54 Mbps data rate through a OFDM technique. 5/17
  • 28. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – Wireless LANs IEEE 802.11a Standards  IEEE 802.11a, 1999  5GHz band  Orthogonal frequency division multiplexing (OFDM)  6Mbps to 54Mbps 6/17
  • 29. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – Wireless LANs IEEE 802.11g Standards  IEEE 802.11g [28]  IEEE 802.11g will use the same 2.4 GHz radio spectrum as current 802.11b equipment, but with the higher data rates, packet structure, and modulation technology of 802.11a.  IEEE 802.11g standard achieves its 54 Mbps data rate through a OFDM technique.  IEEE 802.11b and IEEE 802.11g are operated in the same 2.4 GHz frequency band. When their devices are used in the same area, they will coexist, sharing the airspace between them. 7/17
  • 30. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – Wireless LANs IEEE 802.11g Standards  Operational modes  802.11b Mode  OFDM Mode (Support of 6, 12 and 24 Mbit/s data rates is mandatory )  PBCC-22 and PBCC-33 Modes (Optional)  CCK-OFDM Modes (Optional) 模式 資料速率(Mbit/s) 調變技術 802.11b 1, 2, 5.5, 11 DSSS, CCK, PBCC OFDM 6, 9, 12, 18, 24, 36, 48, 54 OFDM PBCC-22 and PBCC-33 2, 5.5, 11, 22, 33 DSSS, PBCC CCK-OFDM 6, 9, 12, 18, 24, 36, 48, 54 DSSS, OFDM 8/17
  • 31. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – Wireless LANs IEEE 802.11a/b/g Standards  Maximum Data rate  IEEE 802.11a  54 Mbps  For example, an 802.11a network, which broadcasts on the 5GHz frequency band, supports 12 simultaneous channel (in North American).  maximum data rate 12*54=648 Mbps.  IEEE 802.11b  11Mbps  For example, a standalone 802.11b network supports three non- overlapping channel (worldwide), each with a peak data rate of 11 Mbps.  maximum data rate 3*11=33 Mbps.  IEEE 802.11g  54 Mbps  For example, an 802.11g installation supports three channels, each with a peak rate of 54 Mbps.  maximum data rate 3*54=162 Mbps.  Mixed mode 9/17
  • 32. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – Wireless LANs IEEE 802.11a/b/g Standards Mixed-Mode Data Rate vs. 802.11g Data Rate Maximum Theoretical Data Rate 54 Mbps IEEE 802.11 Wireless LAN at 2.4 GHz Deploying standards-based Wireless LAN solutions December 2002 Intel white paper 10/17
  • 33. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – IEEE 802.16  IEEE 802.16 broadband wireless access system [29]  Broadband wireless access (BWA) is a term referring to a range of fixed radio systems, used primarily to convey broadband services between users’ premises and core networks.  The term “broadband” is usually taken to mean the capability to deliver significant bandwidth to each user (in ITU terminology, greater than around 1.5 Mbps, though many BWA networks support significantly higher data rates).  A typical BWA network supports connection to many user premises within a radio coverage area.  The IEEE 802.16 standard should provides the solution to access systems based on DSL, cable, and eventually fiber optics.  The applications of IEEE 802.16  The range of applications is very wide and evolving quickly. It includes voice, data and entertainment services of many kinds. 11/17
  • 34. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – IEEE 802.16  IEEE 802.16 wireless MAN background  Target: FBWA (fixed broadband wireless access)  Fast local connection to network  Project development since 1998 12/17
  • 35. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – IEEE 802.16  802.16 bit rate and channel size 134.4 89.6 44.8 22.4 28 120 80 40 20 25 96 64 32 16 20 64-QAM bit rate (Mbps) 16-QAM bit rate (Mbps) QPSK bit rate (Mbps) Symbol Rate (Msym/s ) Channel Width (MHz) 13/17
  • 36. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – IEEE 802.20  IEEE 802.20 mobile broadband wireless access  Mission  The mission of IEEE 802.20 is to develop the specification for an efficient packet based air interface that is optimized for the transport of IP based services.  The goal is to enable worldwide deployment of affordable, ubiquitous, always-on and interoperable multi-vendor mobile broadband wireless access networks that meet the needs of business and residential end user markets. 14/17
  • 37. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – IEEE 802.20  IEEE 802.20 mobile broadband wireless access  MBWA Scope  Specification of physical and medium access control layers of an air interface for interoperable mobile broadband wireless access systems, operating in licensed bands below 3.5 GHz, optimized for IP-data transport, with peak data rates per user in excess of 1 Mbps.  It supports various vehicular mobility classes up to 250 Km/h in a MAN environment and targets spectral efficiencies, sustained user data rates and numbers of active users that are all significantly higher than achieved by existing mobile systems.  The applications of MBWA  This allows applications including, but not limited to, video, full graphical web browsing, e-mail, file uploading and downloading without size limitations (e.g., FTP), streaming video and streaming audio, IP multicast, telematics, location based services, VPN connections, VoIP, instant messaging and on- line multiplayer gaming 15/17
  • 38. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – IEEE 802.20 Work Domain Home Domain Seamless Seamless Ubiquitous Ubiquitous Experience Experience Mobile Domain Portable Remote Access Services Field Service Apps Hotel/Motel Portable Services Mobile Commerce Services Mobile Office (Voice and Data Apps) High BW Connectivity Video Streaming - Conferencing Apps Portable Office Reservations-Listings Directions Services Video Streaming - Conferencing Apps Video Streaming - Conferencing Apps Mobile Broadband Wireless Access 16/17
  • 39. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. The Applications of OFDM – IEEE 802.20  IEEE 802.20 mobile broadband wireless access  Peak data rates  These peak data rate targets are independent of channel conditions, traffic loading, and system architecture. Parameter Bandwidth 1.25 MHz 5 MHz Downlink Uplink Downlink Uplink Peak User Data Rate 4.5 Mbps 2.25 Mbps 18 Mbps 9 Mbps 17/17
  • 40. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. Introduction to Orthogonal Frequency Division Multiplexing Technique  Readings  Pandharipande A., “Principles of OFDM,” Potentials, IEEE Vol. 21, Issue 2, pp.16 – 19, Apr-May 2002.  Zou, W.Y.; Yiyan Wu, “ COFDM: An overview ” Broadcasting, IEEE Transactions on, Vol. 41 Issue: 1, pp. 1 –8, Mar. 1995.
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