Efficient Space-Time Block Codes
Designed by a Genetic Algorithm
Don Torrieri
U.S. Army Research Laboratory
Matthew C. Valenti
West Virginia University
Space-Time Block Codes
• Orthogonal STBC provides full diversity
at full rate and linear ML decoding but
exists only for 2 antennas.
• Some STBCs preserve full diversity and
full rate but have more complex
decoding.
• STBC may be evolved to have full rate
decoupled decoding at cost of diversity.
STBC
Generator Matrix
MDC-QO (4, 4, 4) STBC
Dispersion Matrices
Orthogonality Condition
Orthogonality Requirements
Cost function
Genetic Algorithm
• String of genes specifies the entries of
dispersion matrices of particular STBC
• Parents breed children
• Genes of child are identical to a parent
except at randomly chosen crossover
positions, and mutations are generated
• Selection entails replacement of parent or
culling of least fit
• Cloning and immigration moves genes from
one pool to another
Parent Selection
•
•
•
•
Random selection
Preferred parenting
Eugenic selection
Alpha-male parenting
Cost vs. generation
300
Continuous alphabet
Discrete alphabet
(6,3,6)
250
cost
200
150
(4,3,4)
100
50
0
0
10
1
10
2
10
3
10
generation
4
10
5
10
6
10
(4, 3, 4) codes & QPSK
0
10
LD code with decoupled detection [8]
Evolved code with decoupled detection
Evolved code with ML detection
-1
10
LD code with ML detection [8]
10-2
BER
100,000 generations
10-3
100,000 generations
10-4
1,000,000 generations
-5
10
0
5
10
15
20
25
Es/No in dB
30
35
40
(6, 3, 6) codes & QPSK
0
10
LD code with decoupled detection [8]
Evolved code with decoupled detection
Evolved code with ML detection
-1
10
LD code with ML detection [8]
10,000 generations
BER
10-2
10-3
100,000 generations
10-4
1,000,000 generations
10,000 generations
100,000 generations
-5
10
0
5
10
15
20
25
Es/No in dB
30
35
40
SE = 3bits/s/Hz, 3 antennas
0
10
MDC-QO (4,3,4)
Evolved (4,3,4)
Evolved (6,3,6)
Orthogonal (3,3,4)
-1
10
BER
10-2
10-3
10-4
-5
10
-6
10
0
5
10
15
20
25
Es/No in dB
30
35
40
SE = 3bits/s/Hz, 4 antennas
0
10
MDC-QO (4,4,4)
Evolved (4,4,4)
-1
Evolved (8,4,8)
QO (4,4,4)
10
Orthogonal (3,4,4)
BER
10-2
10-3
10-4
-5
10
-6
10
0
5
10
15
20
25
Es/No in dB
30
35
40
Turbo-coded Performance
0
10
-1
10
-2
BER
10
10-3
(3,4,4) Nakagami
(2,2,2) Nakagami
(4,4,4) Nakagami
(3,4,4) Rayleigh
(2,2,2) Rayleigh
(4,4,4) Rayleigh
10-4
-5
10
4
4.5
5
5.5
6
6.5
Es/No in dB
7
7.5
8
Conclusions
• Genetic algorithm produces STBCs
optimized for decoupled decoding.
• When spectral efficiency is specified,
outer code is used, and fading is
severe, evolved codes outperform
orthogonal STBCs.
• Alpha-male parenting and parallel
execution using cloning and immigration
expedite evolution.