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.