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Efficient Space-Time Block Codes: Genetic Algorithm Design

Explore the optimization of Space-Time Block Codes (STBC) using a Genetic Algorithm, balancing diversity, rate, and complexity for improved performance in communication systems. Discover how evolved codes outmatch orthogonal STBCs, with focus on decoupled decoding and spectral efficiency under fading. Learn about the process of breeding and evolving STBCs through genetic algorithms, including gene selection, crossover, and mutation.

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Efficient Space-Time Block Codes: Genetic Algorithm Design

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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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