space-time and space-frequency coded orthogonal frequency division multiplexing transmitter...
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Space-Time and Space-Frequency Coded
Orthogonal Frequency Division Multiplexing
Transmitter Diversity Techniques
King F. Lee
![Page 2: Space-Time and Space-Frequency Coded Orthogonal Frequency Division Multiplexing Transmitter Diversity Techniques King F. Lee](https://reader036.vdocuments.us/reader036/viewer/2022082711/56649f085503460f94c1d4cd/html5/thumbnails/2.jpg)
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.
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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
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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
*1 2x x *
2 1x x
1 22 * *
2 1
x x
x x
G
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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
2 2* * *1 1 1 2 2 1 2 1 1 1 2 2
2 2* * *2 2 1 1 2 1 2 2 1 2 2 1
ˆ.
ˆ
x y y x
x y y x
1 1 1 2 2 1* *
2 1 2 2 1 2
.y x x
y x x
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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 & Detector
X(m)
Channel Estimator
Y(n)
Tx
Rx
h(n)
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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).
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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!
, where is diagonal,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
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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)
*
*
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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)
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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 1 and 2 remain constant, the demodulated vectors are
• Calculate
which yields
1 2* *
1 2
.e e o e
o o e o
Y Λ X Λ X Z
Y Λ X Λ X Z
* *1 2
* *2 1
ˆ,
ˆe e o
o e o
X Λ Y Λ Y
X Λ Y Λ Y
2 2
1 2 1 2
2 2
1 2 2 1
ˆ
.ˆ
e e e o
o o e o
X Λ Λ X Λ Z Λ Z
X Λ Λ X Λ Z Λ Z
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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 4010
-8
10-6
10-4
10-2
100
Average Received SNR (dB)
Ave
rag
e B
it E
rro
r R
ate
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 4010
-8
10-6
10-4
10-2
100
Average Received SNR (dB)
Ave
rag
e B
it E
rro
r R
ate
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
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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)
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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 , 1T
n X n X n X n K X n K X
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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,
ˆ.
ˆe 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
2 2
1, 2, 1, 2,
2 2
1, 2, 2, 1,
ˆ
.ˆ
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,and ,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
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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 4010
-8
10-6
10-4
10-2
100
Average Received SNR (dB)
Ave
rag
e B
it E
rro
r R
ate
fD
=10Hz; K=512
Single OFDM transmitter (simulated) STBC-OFDM transmitter diversity (simulated)SFBC-OFDM transmitter diversity (simulated)Two-branch transmitter diversity (ideal)
0 5 10 15 20 25 30 35 4010
-8
10-6
10-4
10-2
100
Average Received SNR (dB)
Ave
rag
e B
it E
rro
r R
ate
fD
=100Hz; K=512
Single OFDM transmitter (simulated) STBC-OFDM transmitter diversity (simulated)SFBC-OFDM transmitter diversity (simulated)Two-branch transmitter diversity (ideal)
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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.
102
103
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Me
an
Su
bca
rrie
r G
ain
Va
ria
tion
Block Size (K)
TUBU
0 5 10 15 20 25 30 35 4010
-8
10-6
10-4
10-2
100
Average Received SNR (dB)
Ave
rag
e B
it E
rro
r R
ate
fD
=10Hz; K=64
Single OFDM transmitter (simulated) SFBC-OFDM transmitter diversity (simulated)Two-branch transmitter diversity (ideal)
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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.
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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.