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DATA COMMUNICATION 2-dimensional transmission

DATA COMMUNICATION 2-dimensional transmission. A.J. Han Vinck May 1, 2003. we describe orthogonal signaling 2-dimensional transmission model. Content. „orthogonal“ binary signaling. 2 signals S 1 (t) S 2 (t) in time T Example: Property : orthogonal energy E. T. T.

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DATA COMMUNICATION 2-dimensional transmission

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  1. DATA COMMUNICATION2-dimensional transmission A.J. Han Vinck May 1, 2003

  2. we describe orthogonal signaling 2-dimensional transmission model Content

  3. „orthogonal“ binary signaling 2 signals S1 (t) S2 (t) in time T Example: Property: orthogonal energy E T T

  4. Quadrature Amplitude Modulation: QAM 1 0 0 S(t) 1 1 0

  5. QAM receiver 1/0 +/- r(t) 1/0 +/- r(t) = S(t) + n(t) Note: sin(x)sin(x) = ½ (1 – cos (2x) ) sin(x)cos(x) = ½ sin (2x)

  6. about the noise

  7. about the noise Conclusion: n1 and n2 are Gaussian Random Variables zero mean uncorrelated (and thus statistically independent (f(x,y) =f(x)f(y) ) with variance 2.

  8. Geometric presentation (1)

  9. Geometric presentation (2) 11 10 00 01 ML receiver:find maximum p(r|s) min p(n) decision regions

  10. performance From Chapter 1: P(error) =

  11. extension 4-QAM  2 bits 16-QAM  4 bits/s Channel 2 Channel 1

  12. Geometric presentation (2) 1 equal density transmitted 2 noise vector n received The noise vector n has length |n| = ( 12+22) ½ n has a spherically symmetric distribution!

  13. Geometric presentation (1) Prob (error) = Prob(length noise vector > d/2) d/2 r r‘

  14. Error probability for coded transmission The error probabiltiy is similar to the 1-dimensional situation: We have to determine the minimum d2Euclidean between any two codewords Example: C d2Euclidean = C‘

  15. Error probability The two-code word error probability is then given by:

  16. modulation schemes On-off FSK 8-PSK  3 bits/s 1 bit/symbol 1 bit/symbol 4-QAM  2 bits 16-QAM  4 bits/s

  17. transmitted symbol energy energy: per information bit must be the same FSK

  18. performance d/2 From Chapter 1: P(error) = FSK

  19. Coding with same symbol speed In k symbol transmissions, we transmit k information bits. We use a rate ½ code In k symbol transmissions, we transmit k bits ML receiver:

  20. Famous Ungerböck coding In k symbol transmissions transmit We can transmit 2k information bits and k redundant digits In k symbol transmissions transmit 2k digits Hence, we can use a code with rate 2/3 with the same energy per info bit!

  21. modulator info ci 23 encoder Signal mapper ci{000,001,010,...111}

  22. example transmit 00 00 00 10 10 01 Parity even Parity odd 11 11 11 or 00 01 00 01 10 11 10 11 Decoder: 1) first detect whether the parity is odd or even 2) do ML decoding given the parity from 1) Homework: estimate the coding gain

  23. Example: Frequency Shift Keying-FSK Transmit: s(1):= s(0):= Note: FSK

  24. Modulator/demodulator m modulator S(t) m r(t) Select largest demodulator m

  25. Ex: Binary Phase Shift Keying-BPSK Transmit: s(1):= s(0):= m m‘ > or < 0?  

  26. On-off BFSK BPSK Modulation formats

  27. PERFORMANCE 10-1 10-2 10-3 10-4 10-5 10-6 10-7 Error rate On-off BPSKQPSK 5 10 15 Eb/N0 dB

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