Space-Time and Space-Frequency Coded
Orthogonal Frequency Division Multiplexing
Transmitter Diversity Techniques
King F,Lee
Georgia Institute of Technology Center for Signal and Image Processing
Introduction
? Frequency-selective fading is a dominant
impairment in mobile communications.
– Fading reduces receive signal-to-noise ratio
and degrades the bit-error-rate (BER).
– Frequency selectivity of the channel,i.e.,delay
spread,induces inter-symbol interference (ISI).
? To combat frequency-selective fading,diversity
techniques must be resilient to ISI.
? Transmitter diversity techniques are attractive,
especially for portable receivers where current
drain and physical size are important constraints.
Georgia Institute of Technology Center for Signal and Image Processing
Background
? Space-time block coding has emerged as an
efficient means of achieving near optimal
transmitter diversity gain [Alamouti 98,Tarokh 99].
? Existing implementations are sensitive to delay
spreads and,therefore,are limited to flat fading
environments,such as indoor wireless networks.
? Orthogonal frequency division multiplexing
(OFDM) with a sufficiently long cyclic prefix can
convert frequency-selective fading channels into
multiple flat fading subchannels.
Combine space-time block code and OFDM
Georgia Institute of Technology Center for Signal and Image Processing
Example
? Assume two transmit antennas and one
receive antenna.
? The space-time block code transmission
matrix is
? For each pair of symbols transmit
Antenna #1,Antenna #2:
Space-Time Block Code - I
*12xx? *21xx
12
2 **
21
xx
xx
???
?????G
Georgia Institute of Technology Center for Signal and Image Processing
? The received signals are
? Calculate the decision variables as
? Similar to that of a two-branch maximal ratio
combining receiver diversity system!
? Unfortunately,the technique is sensitive to
delays.
Space-Time Block Code - II
? ?
? ?
22* * *
1 1 1 2 2 1 2 1 1 1 2 2
22* * *
2 2 1 1 2 1 2 2 1 2 2 1
?
.
?
x y y x
x y y x
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
?
?
? ? ? ? ? ?
? ? ? ? ? ?
1 1 1 2 2 1
**
2 1 2 2 1 2
.y x xy x x? ? ?? ? ?? ? ?? ? ? ?
Georgia Institute of Technology Center for Signal and Image Processing
? Conventional orthogonal frequency division
multiplexing (OFDM) system.
OFDM - I
Serial to
Parallel
Parallel
to Serial
IDFT &
Cyclic
Prefix
Prefix
Removal
& DFT
X(m) X(n)
Equalizer
& DetectorX(m)
Channel
Estimator
Y(n)
Tx
Rx
h(n)
Georgia Institute of Technology Center for Signal and Image Processing
OFDM - II
? Serial to parallel converter collects K serial data
symbols X(m) into a data block or vector X(n).
? X(n) is modulated by an IDFT into OFDM symbol
vector x(n).
? A length G cyclic prefix is added to x(n) and
transmitted through a frequency-selective
channel h(n) of order L.
? At the receiver,the cyclic prefix is removed from
the received signal and the remaining signal is
demodulated by an DFT into Y(n).
Georgia Institute of Technology Center for Signal and Image Processing
OFDM - III
? Assuming the channel response remains constant
and G ? L,the demodulated signal is given by
or,equivalently,as
? Besides the noise component,the demodulated
symbol Y(n,k) is just the product of the complex
gain and the corresponding data symbol X(n,k).
? OFDM with a cyclic prefix transforms a frequency-
selective fading channel into K decoupled and
perfectly flat fading subchannels!
? ? ? ? ? ? ? ? ? ?,w h e r e i s d i a g o n a l,n n n n n??Y Λ X Z Λ
? ? ? ? ? ? ? ?,,,,,0 1,Y n k n k X n k Z n k k K?? ? ? ? ?
Georgia Institute of Technology Center for Signal and Image Processing
? Space-time coding on two adjacent blocks of
data symbols,i.e.,X(n) and X(n+1).
Space-Time Block-Coded OFDM - I
Serial to
Parallel
IDFT &
Cyclic
Prefix
Prefix
Removal
& DFT
X(m)
X(n)
Combiner
& Detector X(m)
Channel
Estimator
Y(n+1)
Tx1
Rx
h1(n)
Parallel
to Serial Y(n)
X(n+1)
IDFT &
Cyclic
Prefix
Tx2
h2(n)
-X(n+1)
X(n)
*
*
Georgia Institute of Technology Center for Signal and Image Processing
Space-Time Block-Coded OFDM - II
? Combine space-time block code with OFDM to
achieve spatial diversity gain over frequency-
selective fading channels.
? In effect,apply space-time coding on blocks of
data symbols instead of individual symbols.
? Space-time encoder takes two data vectors X(n)
and X(n+1) and transmits
Antenna #1,X(n) -X*(n+1)
Antenna #2,X(n+1) X*(n)
Georgia Institute of Technology Center for Signal and Image Processing
Space-Time Block-Coded OFDM - III
? Denote X(n) as Xe and X(n+1) as Xo,and Y(n) as
Ye and Y(n+1) as Yo,Assuming L1 and L2 remain
constant,the demodulated vectors are
? Calculate
which yields
12
**
12
.e e o e
o o e o
? ? ?
? ? ? ?
Y Λ X Λ X Z
Y Λ X Λ X Z
**
12
**
21
?
,? e e o
o e o
??
??
X Λ Y Λ Y
X Λ Y Λ Y? ?
? ?
22
1 2 1 2
22
1 2 2 1
?
.
?
e e e o
o o e o
??
??
? ? ? ?
? ? ? ?
X Λ Λ X Λ Z Λ Z
X Λ Λ X Λ Z Λ Z
Georgia Institute of Technology Center for Signal and Image Processing
STBC-OFDM Simulation Results
? STBC-OFDM achieves near optimal diversity
gain in slow fading.
? Still outperforms non-diversity OFDM system at
fD=100Hz.
0 5 10 15 20 25 30 35 40
10-8
10-6
10-4
10-2
100
Average Received SNR (dB)
Av
era
ge
Bi
t Err
or
Ra
te
fD =10Hz; K=256
Single OFDM transmitter (simulated)
STBC-OFDM transmitter diversity (simulated)
Two-branch transmitter diversity (ideal)
0 5 10 15 20 25 30 35 40
10-8
10-6
10-4
10-2
100
Average Received SNR (dB)
Av
era
ge
Bi
t Err
or
Ra
te
fD =20 and 100Hz; K=256
Single OFDM Transmitter; fD =20Hz
Single OFDM Transmitter; fD =100Hz
Two OFDM Transmitters; fD =20Hz
Two OFDM Transmitters; fD =100Hz
Georgia Institute of Technology Center for Signal and Image Processing
? Coding on adjacent DFT frequency bins of
each block of X(n).
Space-Frequency Block-Coded OFDM - I
Serial to
Parallel
IDFT &
Cyclic
Prefix
Prefix
Removal
& DFT
X(m)
X1(n)
Space-Freq
Decoder
X(m)
Channel
Estimator
Tx1
Rx
h1(n)
Parallel
to Serial Y(n)
IDFT &
Cyclic
Prefix
Tx2
h2(n)
Space-Freq
Encoder
X2(n)
Georgia Institute of Technology Center for Signal and Image Processing
Space-Frequency Block-Coded OFDM - II
? Space-frequency encoder codes each data
vector X(n),
into two vectors X1(n) and X2(n) as
or in terms of the even and odd polyphase
vectors as
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
1
2
,0,1,2,1
,
,1,0,1,2
T
T
n X n X n X n K X n K
n X n X n X n K X n K
??? ? ? ? ?
? ? ?
????X
X
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
1,1,
2,2,
,
.
,
e e o o
e o o e
n n n n
n n n n
?
?
? ? ?
??
X X X X
X X X X
? ? ? ? ? ? ? ? ? ?,,0,1,2,1 Tn X n X n X n K X n K? ? ?X
Georgia Institute of Technology Center for Signal and Image Processing
Space-Frequency Block-Coded OFDM - III
? The demodulated vector is
or,equivalently,as
? Calculate
? Assuming
yields
? ? ? ? ? ? ? ? ? ? ? ?1 1 2 2,n n n n n n? ? ?Y Λ X Λ X Z
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
*
1,2,
*
2,1,
?
.? e e e o o
o e e o o
n n n n n
n n n n n
?
?
??
??
X Λ Y Λ Y
X Λ Y Λ Y
? ?
? ?
22
1,2,1,2,
22
1,2,2,1,
?
.
?
e e e e e e o o
o o o o e e o o
??
??
? ? ? ?
? ? ? ?
X Λ Λ X Λ Z Λ Z
X Λ Λ X Λ Z Λ Z
? ? ? ? ? ? ? ?1,1,2,2,a n d,e o e on n n n??Λ Λ Λ Λ
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ?
1,1,2,2,
1,1,2,2,
.e e e e e e
o o o o o o
n n n n n n
n n n n n n
? ? ?
? ? ?
Y Λ X Λ X Z
Y Λ X Λ X Z
Georgia Institute of Technology Center for Signal and Image Processing
SFBC-OFDM Simulation Results - I
? SFBC-OFDM achieves similar diversity gain
as STBC-OFDM in slow fading.
? SFBC-OFDM performs better in fast fading.
0 5 10 15 20 25 30 35 40
10
-8
10
-6
10
-4
10
-2
10
0
A v e ra g e R e ce i v e d SN R (d B)
Ave
ra
g
e
Bi
t
Erro
r
R
a
t
e
f
D
=1 0 H z ; K=5 1 2
Si n g l e O F D M t ra n s m i t t e r (s i m u l a t e d )
ST BC -O F D M t ra n s m i t t e r d i v e rs i t y (s i m u l a t e d )
SF BC -O F D M t ra n s m i t t e r d i v e rs i t y (s i m u l a t e d )
T w o -b ra n ch t ra n s m i t t e r d i v e rs i t y (i d e a l )
0 5 10 15 20 25 30 35 40
10
-8
10
-6
10
-4
10
-2
10
0
A v e ra g e R e ce i v e d SN R (d B)
Ave
ra
g
e
Bi
t
Erro
r
R
a
t
e
f
D
=1 0 0 H z ; K=5 1 2
Si n g l e O F D M t ra n s m i t t e r (s i m u l a t e d )
ST BC -O F D M t ra n s m i t t e r d i v e rs i t y (s i m u l a t e d )
SF BC -O F D M t ra n s m i t t e r d i v e rs i t y (s i m u l a t e d )
T w o -b ra n ch t ra n s m i t t e r d i v e rs i t y (i d e a l )
Georgia Institute of Technology Center for Signal and Image Processing
SFBC-OFDM Simulation Results - II
? STBC-OFDM is more sensitive to channel gain
variation over time.
? SFBC-OFDM is more sensitive to channel gain
variation over frequency.
10
2
10
3
0
0, 0 5
0, 1
0, 1 5
0, 2
0, 2 5
0, 3
0, 3 5
Me
a
n
Su
b
ca
rri
e
r
G
a
i
n
Va
ri
a
t
i
o
n
Bl o ck Si z e (K)
TU
BU
0 5 10 15 20 25 30 35 40
10
-8
10
-6
10
-4
10
-2
10
0
A v e ra g e R e ce i v e d SN R (d B)
Ave
ra
g
e
Bi
t
Erro
r
R
a
t
e
f
D
=1 0 H z ; K=6 4
Si n g l e O F D M t ra n s m i t t e r (s i m u l a t e d )
SF BC -O F D M t ra n s m i t t e r d i v e rs i t y (s i m u l a t e d )
T w o -b ra n ch t ra n s m i t t e r d i v e rs i t y (i d e a l )
Georgia Institute of Technology Center for Signal and Image Processing
Future Work
? The cyclic prefix for OFDM can require up to 15~20%
bandwidth overhead,It is desirable to develop techniques
that eliminate or reduce the cyclic prefix.
? Channel estimation techniques for space-time and space-
frequency coded OFDM systems.
? Consider combining space-time codes with other
transforms to achieve other desirable characteristics such
as better performance in fast fading environments.
? Investigate optimum combination of error-correction code
with STBC-OFDM and SFBC-OFDM systems.
? Study the co-channel interference performance of STBC
and SFBC-OFDM systems.
Georgia Institute of Technology Center for Signal and Image Processing
References
? S,M,Alamouti,“A simple transmitter diversity scheme for wireless
communications,” IEEE J,Select,Areas Commun.,vol,16,no,8,pp,
1451-1458,Oct,1998.
? V,Tarokh,H,Jafarkhani,and A,R,Calderbank,“Space-time block
coding for wireless communications,performance results,” IEEE J,
Select,Areas Commun.,vol,17,no,3,pp,451-460,March 1999.
? K,F,Lee and D,B,Williams,“A space-time coded transmitter
diversity technique for frequency selective fading channels,” in Proc,
IEEE Sensor Array and Multichannel Signal Processing Workshop,
Cambridge,MA,March 2000,pp,149-152.
? K,F,Lee and D,B,Williams,“A Space-Frequency Transmitter
Diversity Technique for OFDM Systems,” in Proc,IEEE GLOBECOM,
San Francisco,CA,November 2000,pp,1473-1477.
? K,F,Lee and D,B,Williams,“A Multirate Pilot-Symbol-Assisted
Channel Estimator for OFDM Transmitter Diversity Systems,” in Proc,
IEEE ICASSP,Salt Lake City,UT,May 2001.
Orthogonal Frequency Division Multiplexing
Transmitter Diversity Techniques
King F,Lee
Georgia Institute of Technology Center for Signal and Image Processing
Introduction
? Frequency-selective fading is a dominant
impairment in mobile communications.
– Fading reduces receive signal-to-noise ratio
and degrades the bit-error-rate (BER).
– Frequency selectivity of the channel,i.e.,delay
spread,induces inter-symbol interference (ISI).
? To combat frequency-selective fading,diversity
techniques must be resilient to ISI.
? Transmitter diversity techniques are attractive,
especially for portable receivers where current
drain and physical size are important constraints.
Georgia Institute of Technology Center for Signal and Image Processing
Background
? Space-time block coding has emerged as an
efficient means of achieving near optimal
transmitter diversity gain [Alamouti 98,Tarokh 99].
? Existing implementations are sensitive to delay
spreads and,therefore,are limited to flat fading
environments,such as indoor wireless networks.
? Orthogonal frequency division multiplexing
(OFDM) with a sufficiently long cyclic prefix can
convert frequency-selective fading channels into
multiple flat fading subchannels.
Combine space-time block code and OFDM
Georgia Institute of Technology Center for Signal and Image Processing
Example
? Assume two transmit antennas and one
receive antenna.
? The space-time block code transmission
matrix is
? For each pair of symbols transmit
Antenna #1,Antenna #2:
Space-Time Block Code - I
*12xx? *21xx
12
2 **
21
xx
xx
???
?????G
Georgia Institute of Technology Center for Signal and Image Processing
? The received signals are
? Calculate the decision variables as
? Similar to that of a two-branch maximal ratio
combining receiver diversity system!
? Unfortunately,the technique is sensitive to
delays.
Space-Time Block Code - II
? ?
? ?
22* * *
1 1 1 2 2 1 2 1 1 1 2 2
22* * *
2 2 1 1 2 1 2 2 1 2 2 1
?
.
?
x y y x
x y y x
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
?
?
? ? ? ? ? ?
? ? ? ? ? ?
1 1 1 2 2 1
**
2 1 2 2 1 2
.y x xy x x? ? ?? ? ?? ? ?? ? ? ?
Georgia Institute of Technology Center for Signal and Image Processing
? Conventional orthogonal frequency division
multiplexing (OFDM) system.
OFDM - I
Serial to
Parallel
Parallel
to Serial
IDFT &
Cyclic
Prefix
Prefix
Removal
& DFT
X(m) X(n)
Equalizer
& DetectorX(m)
Channel
Estimator
Y(n)
Tx
Rx
h(n)
Georgia Institute of Technology Center for Signal and Image Processing
OFDM - II
? Serial to parallel converter collects K serial data
symbols X(m) into a data block or vector X(n).
? X(n) is modulated by an IDFT into OFDM symbol
vector x(n).
? A length G cyclic prefix is added to x(n) and
transmitted through a frequency-selective
channel h(n) of order L.
? At the receiver,the cyclic prefix is removed from
the received signal and the remaining signal is
demodulated by an DFT into Y(n).
Georgia Institute of Technology Center for Signal and Image Processing
OFDM - III
? Assuming the channel response remains constant
and G ? L,the demodulated signal is given by
or,equivalently,as
? Besides the noise component,the demodulated
symbol Y(n,k) is just the product of the complex
gain and the corresponding data symbol X(n,k).
? OFDM with a cyclic prefix transforms a frequency-
selective fading channel into K decoupled and
perfectly flat fading subchannels!
? ? ? ? ? ? ? ? ? ?,w h e r e i s d i a g o n a l,n n n n n??Y Λ X Z Λ
? ? ? ? ? ? ? ?,,,,,0 1,Y n k n k X n k Z n k k K?? ? ? ? ?
Georgia Institute of Technology Center for Signal and Image Processing
? Space-time coding on two adjacent blocks of
data symbols,i.e.,X(n) and X(n+1).
Space-Time Block-Coded OFDM - I
Serial to
Parallel
IDFT &
Cyclic
Prefix
Prefix
Removal
& DFT
X(m)
X(n)
Combiner
& Detector X(m)
Channel
Estimator
Y(n+1)
Tx1
Rx
h1(n)
Parallel
to Serial Y(n)
X(n+1)
IDFT &
Cyclic
Prefix
Tx2
h2(n)
-X(n+1)
X(n)
*
*
Georgia Institute of Technology Center for Signal and Image Processing
Space-Time Block-Coded OFDM - II
? Combine space-time block code with OFDM to
achieve spatial diversity gain over frequency-
selective fading channels.
? In effect,apply space-time coding on blocks of
data symbols instead of individual symbols.
? Space-time encoder takes two data vectors X(n)
and X(n+1) and transmits
Antenna #1,X(n) -X*(n+1)
Antenna #2,X(n+1) X*(n)
Georgia Institute of Technology Center for Signal and Image Processing
Space-Time Block-Coded OFDM - III
? Denote X(n) as Xe and X(n+1) as Xo,and Y(n) as
Ye and Y(n+1) as Yo,Assuming L1 and L2 remain
constant,the demodulated vectors are
? Calculate
which yields
12
**
12
.e e o e
o o e o
? ? ?
? ? ? ?
Y Λ X Λ X Z
Y Λ X Λ X Z
**
12
**
21
?
,? e e o
o e o
??
??
X Λ Y Λ Y
X Λ Y Λ Y? ?
? ?
22
1 2 1 2
22
1 2 2 1
?
.
?
e e e o
o o e o
??
??
? ? ? ?
? ? ? ?
X Λ Λ X Λ Z Λ Z
X Λ Λ X Λ Z Λ Z
Georgia Institute of Technology Center for Signal and Image Processing
STBC-OFDM Simulation Results
? STBC-OFDM achieves near optimal diversity
gain in slow fading.
? Still outperforms non-diversity OFDM system at
fD=100Hz.
0 5 10 15 20 25 30 35 40
10-8
10-6
10-4
10-2
100
Average Received SNR (dB)
Av
era
ge
Bi
t Err
or
Ra
te
fD =10Hz; K=256
Single OFDM transmitter (simulated)
STBC-OFDM transmitter diversity (simulated)
Two-branch transmitter diversity (ideal)
0 5 10 15 20 25 30 35 40
10-8
10-6
10-4
10-2
100
Average Received SNR (dB)
Av
era
ge
Bi
t Err
or
Ra
te
fD =20 and 100Hz; K=256
Single OFDM Transmitter; fD =20Hz
Single OFDM Transmitter; fD =100Hz
Two OFDM Transmitters; fD =20Hz
Two OFDM Transmitters; fD =100Hz
Georgia Institute of Technology Center for Signal and Image Processing
? Coding on adjacent DFT frequency bins of
each block of X(n).
Space-Frequency Block-Coded OFDM - I
Serial to
Parallel
IDFT &
Cyclic
Prefix
Prefix
Removal
& DFT
X(m)
X1(n)
Space-Freq
Decoder
X(m)
Channel
Estimator
Tx1
Rx
h1(n)
Parallel
to Serial Y(n)
IDFT &
Cyclic
Prefix
Tx2
h2(n)
Space-Freq
Encoder
X2(n)
Georgia Institute of Technology Center for Signal and Image Processing
Space-Frequency Block-Coded OFDM - II
? Space-frequency encoder codes each data
vector X(n),
into two vectors X1(n) and X2(n) as
or in terms of the even and odd polyphase
vectors as
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
1
2
,0,1,2,1
,
,1,0,1,2
T
T
n X n X n X n K X n K
n X n X n X n K X n K
??? ? ? ? ?
? ? ?
????X
X
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
1,1,
2,2,
,
.
,
e e o o
e o o e
n n n n
n n n n
?
?
? ? ?
??
X X X X
X X X X
? ? ? ? ? ? ? ? ? ?,,0,1,2,1 Tn X n X n X n K X n K? ? ?X
Georgia Institute of Technology Center for Signal and Image Processing
Space-Frequency Block-Coded OFDM - III
? The demodulated vector is
or,equivalently,as
? Calculate
? Assuming
yields
? ? ? ? ? ? ? ? ? ? ? ?1 1 2 2,n n n n n n? ? ?Y Λ X Λ X Z
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
*
1,2,
*
2,1,
?
.? e e e o o
o e e o o
n n n n n
n n n n n
?
?
??
??
X Λ Y Λ Y
X Λ Y Λ Y
? ?
? ?
22
1,2,1,2,
22
1,2,2,1,
?
.
?
e e e e e e o o
o o o o e e o o
??
??
? ? ? ?
? ? ? ?
X Λ Λ X Λ Z Λ Z
X Λ Λ X Λ Z Λ Z
? ? ? ? ? ? ? ?1,1,2,2,a n d,e o e on n n n??Λ Λ Λ Λ
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ?
1,1,2,2,
1,1,2,2,
.e e e e e e
o o o o o o
n n n n n n
n n n n n n
? ? ?
? ? ?
Y Λ X Λ X Z
Y Λ X Λ X Z
Georgia Institute of Technology Center for Signal and Image Processing
SFBC-OFDM Simulation Results - I
? SFBC-OFDM achieves similar diversity gain
as STBC-OFDM in slow fading.
? SFBC-OFDM performs better in fast fading.
0 5 10 15 20 25 30 35 40
10
-8
10
-6
10
-4
10
-2
10
0
A v e ra g e R e ce i v e d SN R (d B)
Ave
ra
g
e
Bi
t
Erro
r
R
a
t
e
f
D
=1 0 H z ; K=5 1 2
Si n g l e O F D M t ra n s m i t t e r (s i m u l a t e d )
ST BC -O F D M t ra n s m i t t e r d i v e rs i t y (s i m u l a t e d )
SF BC -O F D M t ra n s m i t t e r d i v e rs i t y (s i m u l a t e d )
T w o -b ra n ch t ra n s m i t t e r d i v e rs i t y (i d e a l )
0 5 10 15 20 25 30 35 40
10
-8
10
-6
10
-4
10
-2
10
0
A v e ra g e R e ce i v e d SN R (d B)
Ave
ra
g
e
Bi
t
Erro
r
R
a
t
e
f
D
=1 0 0 H z ; K=5 1 2
Si n g l e O F D M t ra n s m i t t e r (s i m u l a t e d )
ST BC -O F D M t ra n s m i t t e r d i v e rs i t y (s i m u l a t e d )
SF BC -O F D M t ra n s m i t t e r d i v e rs i t y (s i m u l a t e d )
T w o -b ra n ch t ra n s m i t t e r d i v e rs i t y (i d e a l )
Georgia Institute of Technology Center for Signal and Image Processing
SFBC-OFDM Simulation Results - II
? STBC-OFDM is more sensitive to channel gain
variation over time.
? SFBC-OFDM is more sensitive to channel gain
variation over frequency.
10
2
10
3
0
0, 0 5
0, 1
0, 1 5
0, 2
0, 2 5
0, 3
0, 3 5
Me
a
n
Su
b
ca
rri
e
r
G
a
i
n
Va
ri
a
t
i
o
n
Bl o ck Si z e (K)
TU
BU
0 5 10 15 20 25 30 35 40
10
-8
10
-6
10
-4
10
-2
10
0
A v e ra g e R e ce i v e d SN R (d B)
Ave
ra
g
e
Bi
t
Erro
r
R
a
t
e
f
D
=1 0 H z ; K=6 4
Si n g l e O F D M t ra n s m i t t e r (s i m u l a t e d )
SF BC -O F D M t ra n s m i t t e r d i v e rs i t y (s i m u l a t e d )
T w o -b ra n ch t ra n s m i t t e r d i v e rs i t y (i d e a l )
Georgia Institute of Technology Center for Signal and Image Processing
Future Work
? The cyclic prefix for OFDM can require up to 15~20%
bandwidth overhead,It is desirable to develop techniques
that eliminate or reduce the cyclic prefix.
? Channel estimation techniques for space-time and space-
frequency coded OFDM systems.
? Consider combining space-time codes with other
transforms to achieve other desirable characteristics such
as better performance in fast fading environments.
? Investigate optimum combination of error-correction code
with STBC-OFDM and SFBC-OFDM systems.
? Study the co-channel interference performance of STBC
and SFBC-OFDM systems.
Georgia Institute of Technology Center for Signal and Image Processing
References
? S,M,Alamouti,“A simple transmitter diversity scheme for wireless
communications,” IEEE J,Select,Areas Commun.,vol,16,no,8,pp,
1451-1458,Oct,1998.
? V,Tarokh,H,Jafarkhani,and A,R,Calderbank,“Space-time block
coding for wireless communications,performance results,” IEEE J,
Select,Areas Commun.,vol,17,no,3,pp,451-460,March 1999.
? K,F,Lee and D,B,Williams,“A space-time coded transmitter
diversity technique for frequency selective fading channels,” in Proc,
IEEE Sensor Array and Multichannel Signal Processing Workshop,
Cambridge,MA,March 2000,pp,149-152.
? K,F,Lee and D,B,Williams,“A Space-Frequency Transmitter
Diversity Technique for OFDM Systems,” in Proc,IEEE GLOBECOM,
San Francisco,CA,November 2000,pp,1473-1477.
? K,F,Lee and D,B,Williams,“A Multirate Pilot-Symbol-Assisted
Channel Estimator for OFDM Transmitter Diversity Systems,” in Proc,
IEEE ICASSP,Salt Lake City,UT,May 2001.
