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Incoherent Detection

Incoherent Detection. ECE 7251: Spring 2004 Lecture 38 4/21/04. Prof. Aaron D. Lanterman School of Electrical & Computer Engineering Georgia Institute of Technology AL: 404-385-2548 <lanterma@ece.gatech.edu>. A Problem with a Nuisance Parameter.

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Incoherent Detection

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  1. Incoherent Detection ECE 7251: Spring 2004 Lecture 38 4/21/04 Prof. Aaron D. Lanterman School of Electrical & Computer Engineering Georgia Institute of Technology AL: 404-385-2548 <lanterma@ece.gatech.edu>

  2. A Problem with a Nuisance Parameter • Discussion based on Van Trees, Sec. 4.4.1 • W(t) is WGN with power • Signal is an amplitude-modulated sinusoid with a slowly-varying normalized envelope f(t) and an unknown, random phase angle

  3. pull into threshold The Integrated Likelihood Ratio

  4. where Some Trignometry

  5. Rephrased Test Statistic • In a communication system, we may have some training data with which we can estimate the phase; try a Von Mises density • In a radar system, don’t have anything; pick to be uniform

  6. For a Uniform Density on  • Since I0 is monotone, it (and a bunch of other stuff) can be shoved over into the threshold

  7. Quadrature Demodulator Interpretation

  8. Under H1: Statistics of Lcand Ls (1)

  9. Statistics of Lcand Ls (2) • EFTR:Convince yourself that under H1, and under H0, and under either hypothesis,

  10. Probability of False Alarm

  11. Probability of Detection

  12. Assorted Algebra and Trignometry

  13. Probability of Detection

  14. Marcum’s Q function (not to be confused with our previous univariate Gaussian Q-function)! Marcum’s Q Function and • Let

  15. Comparing with the Coherent Case • Suppose we are comparing a coherent detection system with to an incoherent detection system with • According to Poor, p. 71 (citing Helstrom, 1968), the ROC curves of the two systems are approximately equal if

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