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Efficient Space-Time Block CodesDesigned 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
100
101
102
103
104
105
106
0
50
100
150
200
250
300
generation
cost
(6,3,6)
(4,3,4)
Continuous alphabetDiscrete alphabet
(4, 3, 4) codes & QPSK
10
10-3
10
10-1
100
BER
10
-4
-5
-2
0 5 10 15 20 25 30 35 40
Es/No in dB
LD code with decoupled detection [8]
Evolved code with decoupled detection
Evolved code with ML detection
LD code with ML detection [8]
100,000 generations
100,000 generations1,000,000 generations
(6, 3, 6) codes & QPSK
LD code with decoupled detection [8]
Evolved code with decoupled detection
Evolved code with ML detection
LD code with ML detection [8]
10,000 generations
100,000 generations
1,000,000 generations10,000 generations100,000 generations
10-4
10-3
10-2
10-1
100
BER
10-5
0 5 10 15 20 25 30 35 40
Es/No in dB
SE = 3bits/s/Hz, 3 antennas
MDC-QO (4,3,4)
Evolved (4,3,4)
Evolved (6,3,6)
Orthogonal (3,3,4)
10-4
10-3
10-2
10-1
100
BER
10-5
10-6
0 5 10 15 20 25 30 35 40
Es/No in dB
SE = 3bits/s/Hz, 4 antennas
MDC-QO (4,4,4)
Evolved (4,4,4)
Evolved (8,4,8)
QO (4,4,4)
Orthogonal (3,4,4)
10-4
10-3
10-2
10-1
100
BER
10-5
10-6
0 5 10 15 20 25 30 35 40
Es/No in dB
Turbo-coded Performance
(3,4,4) Nakagami(2,2,2) Nakagami(4,4,4) Nakagami(3,4,4) Rayleigh(2,2,2) Rayleigh(4,4,4) Rayleigh
4 4.5 5 5.5 6 6.5 7 7.5 8Es/No in dB
10-4
10-3
10-2
10-1
100
BER
10-5
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.