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Efficient Space-Time Block Codes Designed by a Genetic Algorithm

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.

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Efficient Space-Time Block Codes Designed by a Genetic Algorithm

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  1. Efficient Space-Time Block CodesDesigned by a Genetic Algorithm Don Torrieri U.S. Army Research Laboratory Matthew C. Valenti West Virginia University

  2. 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.

  3. STBC

  4. Generator Matrix

  5. MDC-QO (4, 4, 4) STBC

  6. Dispersion Matrices

  7. Orthogonality Condition

  8. Orthogonality Requirements

  9. Cost function

  10. 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

  11. Parent Selection • Random selection • Preferred parenting • Eugenic selection • Alpha-male parenting

  12. Cost vs. generation 300 Continuous alphabet Discrete alphabet (6,3,6) 250 200 cost (4,3,4) 150 100 50 0 0 1 2 3 4 5 6 10 10 10 10 10 10 10 generation

  13. (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] -2 10 100,000 generations BER -3 10 100,000 generations -4 10 1,000,000 generations -5 10 0 5 10 15 20 25 30 35 40 Es/No in dB

  14. (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 -2 10 BER -3 100,000 generations 10 -4 10 1,000,000 generations 10,000 generations 100,000 generations -5 10 0 5 10 15 20 25 30 35 40 Es/No in dB

  15. 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 -2 10 BER -3 10 -4 10 -5 10 -6 10 0 5 10 15 20 25 30 35 40 Es/No in dB

  16. SE = 3bits/s/Hz, 4 antennas 0 10 MDC-QO (4,4,4) Evolved (4,4,4) -1 Evolved (8,4,8) 10 QO (4,4,4) Orthogonal (3,4,4) -2 10 BER -3 10 -4 10 -5 10 -6 10 0 5 10 15 20 25 30 35 40 Es/No in dB

  17. Turbo-coded Performance 0 10 -1 10 -2 10 BER -3 10 (3,4,4) Nakagami (2,2,2) Nakagami -4 (4,4,4) Nakagami 10 (3,4,4) Rayleigh (2,2,2) Rayleigh (4,4,4) Rayleigh -5 10 4 4.5 5 5.5 6 6.5 7 7.5 8 Es/No in dB

  18. 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.

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