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Coded Modulation for Orthogonal Transmit Diversity. Motivation. Wireless Communication Environment Noise Multipath Fading MAI Demands Multimedia applications High rate Data communication Reliability. Challenges. Problems - PowerPoint PPT Presentation
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Mohammad Jaber Borran, Mahsa Memarzadeh, and Behnaam Aazhang
June 29, 2001
Coded Modulation for Orthogonal Transmit Diversity
Motivation
Wireless Communication EnvironmentNoise
Multipath
Fading
MAI
DemandsMultimedia applications High rate
Data communication Reliability
Challenges
ProblemsLow achievable rates if single transmit and
receive antenna systems are used
Less reliability due to low SNR and fading
Some Possible SolutionsUse more bandwidth (limited resource!)
Use strong codes (computational complexity!)
Use multiple antennas (hardware complexity!)
Multiple-Antenna Systems
Capacity min(nT, nR) Higher rate
Potential spatial diversity More reliability
Data ChannelEncoder ...
ChannelDecoder
RecoveredData
[I. E. Telatar]
Space-Time Coding
Slowly fadingSpatial diversity and coding gain
Fast fadingSpatial and temporal diversity, and coding gain
DataSpace-TimeEncoder ...
Space-TimeCode matrix
Spac
eTime
Space-TimeDecoder
RecoveredData
Space-Time Code Design
Previous approaches Jointly maximizing spatial and temporal
diversity and coding gain No systematic code design method, difficult
Suggested approach Decouples the problem into simpler ones Simplifies code design procedure Provides systematic code construction method Performs better than existing codes
System Model
Decouples the problems of maximizing
Spatial diversity
Temporal diversity and/or coding gain
[S. Alamouti]
*
*
cc
-cc
12
21
c
OTDTransmitter TX antenna 1
TX antenna 2
RX antenna
1*2 cc
2*1 cc
12 cc
AlamoutiEncoder
Orthogonal Transmit Diversity
Achieves full diversity (2) Provides full rate (R = 1) No capacity loss Simple ML decoder
Slowly Fading Channels
Upper bound for pairwise error probability
No temporal diversity
2
01
2
4)(
N
EecP s
L
lllec
spatialdiversit
y
coding gain
Design Criteria
Maximization of coding gain
Same as design criterion for single antenna systems in AWGN channels
Codes designed for optimum performance in AWGN channels are optimum outer codes
L
llle ecd
1
2)e,c(
(Standard Euclidean distance)
Simulation Results (1)
9 10 11 12 13 14 15 16 17 1810
-3
10-2
10-1
100
SNR (dB)
Fra
me
Err
or P
roba
bilit
y
AT&T 4-state space-time trellis code Concatenated orthogonal space-time trellis codeOutage Probability
R = 2 b/s/Hz
1 dB gain
4-state TCM outer code optimum for AWGN
0, 2, 4, 6
1, 3, 5, 7
2, 0, 6, 4
3, 1, 7, 5
Better performance with same complexity
Simulation Results (2)
9 10 11 12 13 14 15 16 17 1810
-3
10-2
10-1
100
SNR (dB)
Fra
me
Err
or P
roba
bilit
y
AT&T 8-state space-time trellis code Concatenated orthogonal space-time trellis codeOutage Probability
R = 2 b/s/Hz
2 dB gain
8-state TCM outer codeoptimum for AWGN
0, 2, 4, 6
1, 3, 5, 7
2, 0, 6, 4
3, 1, 7, 5
4, 6, 0, 2
5, 7, 1, 3
6, 4, 2, 0
7, 5, 3, 1
Better performance with same complexity
Fast Fading Channels
Upper bound for pairwise error probability
),(),(;
2
0
2
22
2
1212
2122124
)(kkkk eecck
skkkk N
EececP ec
spatialdiversit
y
coding gain
component
temporaldiversity
Design Criteria (1)
Maximization of
Hamming distance Product distance
between pairs of consecutive symbols:
(c2k-1, c2k) , (e2k-1, e2k)
Design for an Expanded Constellation
Constellation Expansion (1)
In dimension In size
c2k-1
c2k
Ck=(c2k-1, c2k)
Original M-aryconstellation
Expanded M2-aryconstellation
(2D coordinate 1)
(2D coordinate 2)
(4D point)
c2k
c2k-1 Ck=(c2k-1, c2k)
Design Criteria (2)
Design for expanded constellation based on maximizing
• Symbol Hamming distance• Product of squared distances
Same as design criteria for single antenna systems in fast fading channels
Expanded constellation
Ck
OTDTransmitter
c2k c2k-1
122 k*
k cc
k*
k cc 212
[D. Divsalar]
Simulation Results (1)
Comparison with AT&T smart-greedy code
Better performance with same complexity
R = 1 b/s/Hz
0 2 4 6 8 10 12 14 16 18 2010
-3
10-2
10-1
100
SNR per Bit (dB)
Fra
me
Err
or P
roba
bilit
yAT&T smart-greedy space-time trellis code
Concatenated orthogonal space-time code
Slowly fading channel
-2 0 2 4 6 8 10 12 14 1610
-5
10-4
10-3
10-2
10-1
100
SNR per Bit (dB)
Sym
bol E
rror
Pro
babi
lity
Fast fading channel
Diversity 4
Diversity 3
AT&T smart-greedy space-time trellis codeConcatenated orthogonal space-time code
Simulation Results (2)
8 10 12 14 16 18 2010
-5
10-4
10-3
10-2
10-1
SNR per Bit
Sym
bol E
rror
Pro
babi
lity
Uncoded Orthogonal Transmission (R = 3 bits/s/Hz)MLC for Orthogonal Transmission (R = 3 bits/s/Hz)
Diversity 4
Diversity 2
Comparison of simple OTD with concatenated ST code(Outer code: 4-dimensional MLC)
OTD systems with nT>2 and nR1
Achieve maximum diversity order (nTnR)
Not full rate (R < 1)Full rate, full diversity, complex orthogonal
designs exist only if nT=2
Generalized OTD
Slowly Fading Channels
Upper bound for pairwise error probability
Design criteria
Maximization of free Euclidean distance
RT nn
sRL
lll N
EecP
01
2
4)( ec
spatialdiversit
y
coding gain
Fast Fading Channels
Upper bound for pairwise error probability
Design criteria Maximizing Hamming and product distances
in expanded constellation
Concatenation of RQ points in original signal
setCk = (c(k-1)RQ+1, …, ckRQ)
Point in expanded
constellation
),...,(),...,(; 01
2
)1()1(
1)1(1)1(4
)(kRQRQkkRQRQk
RT
eecck
nn
sRQ
qqRQkqRQk N
EecP ec
coding gain component
temporal diversity
Simulation Results
Slowly fading channel Fast fading channel
2 4 6 8 10 12 14 1610
-4
10-3
10-2
10-1
100
SNR per Bit (dB)
Fra
me
Err
or P
roba
bilit
y
6 7 8 9 10 11 12 13 1410
-6
10-5
10-4
10-3
10-2
10-1
SNR per Bit (dB)
Sym
bol E
rror
Pro
babi
lity
R = 1.5 b/s/Hz R = 1 b/s/Hz
3 & 4 transmit,1 receive
3 & 4 transmit,2 receives
3 transmit,Diversity 6
4 transmit,Diversity 8
MTCM outer code8-state TCM outer code optimum for AWGN
Summary
Concatenated orthogonal space-time code
Decouples the problems of maximizing spatial diversity, temporal diversity and/or coding gain
Simplifies code design procedure and provides a systematic method for code construction
Has better performance compared to existing space-time codes