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Performance of Coherent M-ary Signaling

Performance of Coherent M-ary Signaling. ENSC 428 – Spring 200 7. Digital Communication System. 1. M-ary PSK. T. sin. cont …. cont …. Integration over IQ plane. cont …. cont …. 2. M-ary Orthogonal Signaling. cont …. 3- ary orthogonal signal space.

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Performance of Coherent M-ary Signaling

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  1. Performance of Coherent M-ary Signaling ENSC 428 – Spring 2007

  2. Digital Communication System

  3. 1. M-ary PSK T sin

  4. cont …

  5. cont …

  6. Integration over IQ plane

  7. cont …

  8. cont …

  9. 2. M-ary Orthogonal Signaling

  10. cont … 3-ary orthogonal signal space

  11. cont … assume equally likely M-ary symbols a priori

  12. cont … assume equally likely symbols a priori

  13. cont … union bound

  14. cont …

  15. cont … • Performance improves as M increases (??) • In the limit (M∞), error probability can be made arbitrarily small as long as Eb/N0 > ln2 (-1.59 dB). • Proof in Gallager Lecture 19 section 4.3 • In fact, Information Theory also proves that we cannot achieve error probability arbitrarily small if Eb/N0 < ln2. • Most practical systems use non-coherent FSK rather than coherent FSK. We will discuss non-coherent FSK soon.

  16. Biorthogonal Signaling

  17. cont … 6-ary biorthogonal signal constellation

  18. Simplex Signaling

  19. cont … 3-ary simplex signal constellation

  20. cont …

  21. 3. M-ary QAM 16-ary QAM

  22. cont …

  23. cont …

  24. Symbol Error Rate (SER) or SEP

  25. Bit Error Rate (BER) or BEP(cf SEP, symbol error probability)

  26. Orthogonal signaling BEP e e e k bits, M=2k, each bit error pattern corresponds to a unique symbol, which is not the transmitted.

  27. Example: 8-ary PSK

  28. Gray Coding

  29. Gray-coded MPSK

  30. cont …

  31. cont …

  32. Gray code (Reflected binary code by Frank Gray) generation • Can be generated recursively by reflecting the bits (i.e. listing them in reverse order and concatenating the reverse list onto the original list), prefixing the original bits with a binary 0 and then prefixing the reflected bits with a binary 1.

  33. Gray code generation: another view

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