Transcript No Slide Title

Coded Modulation for Orthogonal
Transmit Diversity
Mohammad Jaber Borran, Mahsa Memarzadeh,
and Behnaam Aazhang
June 29, 2001
Motivation
Wireless Communication Environment
Noise
Multipath
Fading
MAI
Demands
Multimedia applications  High rate
Data communication
 Reliability
Challenges
Problems
Low achievable rates if single transmit and
receive antenna systems are used
Less reliability due to low SNR and fading
Some Possible Solutions
Use more bandwidth (limited resource!)
Use strong codes (computational complexity!)
Use multiple antennas (hardware complexity!)
Multiple-Antenna Systems
Data
Channel
Encoder
..
Channel
Decoder
Recovered
Data
Capacity   min(nT, nR)  Higher rate
[I. E. Telatar]
Potential spatial diversity  More reliability
Space-Time Coding
Space
Space-Time
Code matrix
Data Space-Time
Encoder
Time
..
Space-Time Recovered
Data
Decoder
Slowly fading
Spatial diversity and coding gain
Fast fading
Spatial and temporal diversity, and coding gain
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
Orthogonal Transmit Diversity
[S. Alamouti]
 c2*
c2
c1
OTD
Transmitter
Alamouti
Encoder
c1
TX antenna 1
c1*
c2
RX antenna
TX antenna 2
 Achieves full diversity (2)
 Provides full rate (R = 1)
c1
c  
 No capacity loss
c2
 Simple ML decoder
-c*2 
*
c1 
Slowly Fading Channels
 Upper bound for pairwise error probability

2   Es  

P(c  e)    cl  el  
  4 N 0 
 l 1
L
coding gain
 No temporal diversity
2
spatial
diversity
Design Criteria
 Maximization of coding gain
L
d e (c, e)   cl  el
2
l 1
(Standard Euclidean distance)
 Same as design criterion for single antenna
systems in AWGN channels
 Codes designed for optimum performance in
AWGN channels are optimum outer codes
Simulation Results (1)
R = 2 b/s/Hz
0
10
1, 3, 5, 7
2, 0, 6, 4
3, 1, 7, 5
4-state TCM outer code
optimum for AWGN
Frame Error Probability
0, 2, 4, 6
1 dB gain
-1
10
-2
10
-3
10
9
AT&T 4-state space-time trellis code
Concatenated orthogonal space-time trellis code
Outage Probability
10
11
12
13
14
15
16
17
18
SNR (dB)
Better performance with same complexity
Simulation Results (2)
R = 2 b/s/Hz
0
0, 2, 4, 6
10
2, 0, 6, 4
3, 1, 7, 5
4, 6, 0, 2
5, 7, 1, 3
6, 4, 2, 0
Frame Error Probability
1, 3, 5, 7
2 dB gain
-1
10
-2
10
AT&T 8-state space-time trellis code
Concatenated orthogonal space-time trellis code
Outage Probability
7, 5, 3, 1
-3
10
8-state TCM outer code
optimum for AWGN
9
10
11
12
13
14
15
16
17
18
SNR (dB)
Better performance with same complexity
Fast Fading Channels
 Upper bound for pairwise error probability
spatial
diversity
temporal
diversity


2
P(c  e) 
c

e
 2 k 1 2 k 1  c2 k  e2 k

k ;( c2 k 1 ,c2 k )  ( e2 k 1 ,e2 k ) 
coding gain
component
2

 Es  


 4 N 0 
2
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
c2k-1
c2k
(2D coordinate 2)
c2k-1
 In size
Ck=(c2k-1, c2k)
Ck=(c2k-1, c2k)
(4D point)
(2D coordinate 1)
c2k
Original M-ary
constellation
Expanded M2-ary
constellation
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 [D. Divsalar]
Expanded
constellation
Ck
 c*2k c2k 1
c2k c2k-1
OTD
Transmitter
c*2k 1 c2k
Simulation Results (1)
Comparison with AT&T smart-greedy code
R = 1 b/s/Hz
10
10
10
0
10
Frame Error Probability
Symbol Error Probability
10
-1
-2
Diversity 3
-3
Diversity 4
10
10
-4
AT&T smart-greedy space-time trellis code
Concatenated orthogonal space-time code
-5
-2
10
10
2
4
6
8
10
12
SNR per Bit (dB)
Fast fading channel
14
16
-1
-2
AT&T smart-greedy space-time trellis code
Concatenated orthogonal space-time code
10
0
0
-3
0
2
4
6
8
10
12
14
16
18
SNR per Bit (dB)
Slowly fading channel
Better performance with same complexity
20
Simulation Results (2)
Comparison of simple OTD with concatenated ST code
(Outer code: 4-dimensional MLC)
-1
10
Uncoded Orthogonal Transmission (R = 3 bits/s/Hz)
MLC for Orthogonal Transmission (R = 3 bits/s/Hz)
-2
Symbol Error Probability
10
Diversity 2
-3
10
Diversity 4
-4
10
-5
10
8
10
12
14
SNR per Bit
16
18
20
Generalized OTD
 OTD systems with nT>2 and nR1
 Achieve maximum diversity order (nTnR)
 Not full rate (R < 1)
Full rate, full diversity, complex orthogonal
designs exist only if nT=2
Slowly Fading Channels
 Upper bound for pairwise error probability

2   Es  

P(c  e)    cl  el  
  4 N 0 
 l 1
RL
 nT nR
spatial
diversity
coding gain
 Design criteria
 Maximization of free Euclidean distance
Fast Fading Channels
 Upper bound for pairwise error probability
temporal diversity

P(c  e) 
  c( k 1) RQ q  e( k 1) RQ q

k ;( c( k 1) RQ 1 ,...,ckRQ )  ( e( k 1) RQ 1 ,...,ekRQ ) 
 q 1
RQ
 Design criteria
2
  Es  


  4 N 
  0 
coding gain
component
 Maximizing Hamming and product distances
in expanded constellation
Point in expanded
constellation
Concatenation of RQ points
in original signal set
Ck = (c(k-1)RQ+1, …, ckRQ)
 nT nR
Simulation Results
R = 1.5 b/s/Hz
10
0
3 & 4 transmit,
1 receive
-1
10
-2
10
-3
10
3 & 4 transmit,
2 receives
-4
10
2
4
6
8
10
12
14
SNR per Bit (dB)
16
Symbol Error Probability
Frame Error Probability
10
10
10
10
10
10
R = 1 b/s/Hz
-1
-2
-3
3 transmit,
Diversity 6
-4
4 transmit,
Diversity 8
-5
-6
6
7
8
9
10
11
12
SNR per Bit (dB)
Slowly fading channel
Fast fading channel
8-state TCM outer code
optimum for AWGN
MTCM outer code
13
14
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
Contact Information
[email protected]
[email protected]
[email protected]
http://www.ece.rice.edu/~mohammad