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ENE 623 Optical Networks

Explore photon statistics in optical receivers using Poisson distribution and Gaussian probability theory. Understand the relationship between error probability and digital communication in optical networks.

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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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