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ENE 623 Optical Networks

ENE 623 Optical Networks. Lecture 8. Comparison of modulaters. Optical Receiver. Converts optical signals to electrical signals. Photons to electrons. Consider the noise at the receiving side using SNR or BER. Optical Receiver. Photon Statistics. Poisson Distribution

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ENE 623 Optical Networks

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  1. ENE 623 Optical Networks Lecture 8

  2. Comparison of modulaters

  3. Optical Receiver • Converts optical signals to electrical signals. • Photons to electrons. • Consider the noise at the receiving side using SNR or BER.

  4. Optical Receiver

  5. Photon Statistics • Poisson Distribution • P( ) = Probability that N photons will arrive during time interval T. • N = number of photoelectrons produced in time interval T. • = rT = the average number of photoelectrons in time T. • r = average rate at which photoelectrons are produced.

  6. Photon Statistics

  7. Photon Statistics

  8. Photon Statistics

  9. Photon Statistics

  10. Photon Statistics • The Poisson distribution has the interesting property that the variance and the mean are equal. • Mean square deviation in N = average value of N.

  11. Gaussian probability • Gaussian probability distribution function is a good approximation to Poisson distribution function for sufficiently large, say .

  12. Gaussian probability

  13. Gaussian probability • Assume that the variance and the meal are equal as in Poisson distribution, we have

  14. Probability of error in digital communication

  15. Probability of error in digital communication • Average number of electrons in time T for “0” transmitted = • Average number of electrons in time T for “1” transmitted = • Probability of error is the area of tail of Gaussian distribution.

  16. Probability of error in digital communication • If equal number of “1’s” and “0’s” transmitted, then the probability of error is equal to ‘bit error rate’ or BER.

  17. Probability of error in digital communication • The area under a curve to one side of a point = is given by a Q-function.

  18. Probability of error in digital communication

  19. Probability of error in digital communication

  20. Probability of error in digital communication • Assume

  21. Probability of error in digital communication

  22. Probability of error in digital communication • Relate BER to electrical signal-to-noise ratio (SNR) in receiver. • ns = number of photoelectrons per time interval produced by turning light on. •  = root mean square deviation in number of photoelect.rons per time interval

  23. Probability of error in digital communication • Assume

  24. Probability of error in digital communication

  25. Example • In an optical communications experiment, an average of m1, photons is detected when a “1” is transmitted and m0 when a “0” is transmitted. What is m1 for error rates of 10-3 and 10-10, if (a) m0 = 0 and (b) m0 = 1. Assume Poisson statistics.

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